1.1 Material overview and introduction to different alloys

Shape memory alloys (SMAs) represent a group of materials with distinctive properties. These properties are reflected in the unique relationship between their Young’s modulus and temperature, their shape memory behaviour, and their high damping capacity [2].

Among these are the following: Au-Cd, Ag-Cd, Cu-Al-Ni, Cu-Sn, Cu-Zn-Al, In-Ti, Ni-Al, Ni-Ti, Fe-Pt, Mn-Cu, and Fe-Mn-Si. However, only three of them are commercially available: Ni-Ti, Cu-Zn-Al, and Cu-Al-Ni [3].

These materials exhibit four key properties [4]:

• – Pseudoplasticity, or one-way shape memory effect, where the material, after being deformed at a low temperature, returns to its original shape upon heating

• – Pseudoelasticity, or superelasticity, where no thermal stimulus is required, and the material recovers its original shape upon the removal of an applied force, even after significant deformation

• – Exceptional damping capacity, allowing the material to dissipate substantial amounts of energy

• – Two-way shape memory effect, where, due to specialized thermomechanical training, the material can “remember” two distinct shapes depending on the prevailing temperature

These properties stem from the phase transformations occurring within the material’s crystalline structure.

1.2 Crystalline structure

Metals, in general, exhibit allotropy, meaning they can exist in multiple crystalline structures within the same physical state [5]. In the case of steel, for example, its crystalline structure varies depending on carbon content and temperature [6]. Under equilibrium conditions, five phases can be distinguished (ferrite = α-iron, austenite = γ-iron, cementite = Fe₃C, ledeburite, and pearlite), while under non-equilibrium conditions, two additional phases may occur (martensite and bainite).

These crystalline states significantly influence the mechanical properties of steel. For instance, in the hardening process, the goal is to transform the steel into its martensitic phase, thereby increasing its hardness.

In shape memory alloys, phase transformations follow a unique pattern, endowing these materials with distinct properties compared to conventional metals. SMAs exhibit two crystalline phases: martensite and austenite, with the latter often referred to as the “parent phase”. The phenomena described in Section 1.1 also arise as a consequence of phase transformation, i.e., crystalline rearrangement [4]. This structural transition can be induced by temperature changes or mechanical loading. At low temperatures, the martensitic phase is predominant, while at higher temperatures, the austenitic phase dominates [7].

In addition to the two phases, three distinct microstructural arrangements can be observed. To illustrate this concept, a simplified two-dimensional example is used, although in real materials, the crystal lattice is naturally three-dimensional. As shown in Figure 1, the austenite phase is characterized by a right-angled system, where the unit cells are arranged perpendicularly. This indicates that the crystal lattice associated with the austenite phase possesses higher symmetry compared to the martensitic phases.

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Crystalline rearrangement in SMAs and the resulting phases (austenite, martensite I – “twinned”, martensite II – “detwinned”). The transformation from the austenite phase to the martensite I phase occurs upon cooling, while the transition from martensite I to martensite II is induced by deformation. Phase transformation from both martensite I and martensite II back to the austenite phase occurs upon heating [8, 9]

Citation: Építés – Építészettudomány 53, 1-2; 10.1556/096.2025.00139

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Upon transformation, the rows begin to deviate from the strictly orthogonal arrangement, leading to a reduction in the number of symmetries in the crystal lattice. In the martensitic phase, two possible configurations can be distinguished. In the first arrangement, adjacent rows – forming twin crystal layers – shift in opposite directions relative to one another (Martensite I – twinned). In the second case, the rows shift in the same direction (Martensite II – detwinned). The latter configuration (detwinned) can be induced either by external loading of the austenite phase or by applying stress to the first martensitic variant (twinned) [8].

The shape memory effect is closely related to the high symmetry of the austenitic lattice: during the transformation from martensite to austenite, the crystal lattice must restore its original geometry to fill space seamlessly. Due to the two types of martensitic transformations, numerous crystal arrangements are possible in the martensitic phase, as each row can shift in two possible directions relative to the row beneath it. Consequently, for a system with n rows, 2^(n–1) different configurations are possible.

Empirical data suggest that after multiple cooling-heating-loading cycles, the martensitic crystal structure can become stabilized, which enables the development of the two-way shape memory effect [3].

The unit cells differ depending on the alloy composition. Figure 2 illustrates examples of crystal structures:

1. Austenite – Body-centered cubic (BCC)

2. Martensite / Austenite – Face-centered cubic (FCC)

3. Martensite – Hexagonal close packed (HCP)

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Examples of unit cells – (1) body-centered cubic (BCC) (2), face-centered cubic (FCC), (3) hexagonal close packed (HCP) [4]

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In the case of the Ni-Ti alloy (also known as Nitinol), which is the most widely used and well-known shape memory alloy, the austenitic phase exhibits a body-centered cubic (BCC) lattice, while in the martensitic phase, it transforms into a face-centered cubic (FCC) structure. In contrast, the Fe-Mn-Si alloy has a body-centered cubic (BCC) austenitic phase, which transitions into a hexagonal close packed (HCP) structure in the martensitic phase. This clearly demonstrates that despite exhibiting similar properties, different shape memory alloys behave differently [4].

Comparing the previously discussed phase transformation in steel with that of shape memory alloys, it becomes evident that SMA transformation is much more straightforward, involving fewer phases. In steel, shape memory behaviour is not possible because while the austenite-to-martensite transformation can be induced through rapid cooling, this process is irreversible – reheating does not restore the original austenitic arrangement. It is crucial to emphasize that shape memory alloys can only be composed of materials in which phase transformations between different crystal structures occur in a reversible manner without energy loss.

In shape memory alloys, the austenitic phase is so stable that the material must adopt a specific shape to ensure that unit cells can properly arrange themselves within the corresponding lattice structure.

1.3 Behaviour under thermal influence

During heating, the transformation of martensite into austenite begins at the A_s (austenite start) temperature and completes at the A_f (austenite finish) temperature. Conversely, during cooling, the transformation from austenite to martensite initiates at the M_s (martensite start) temperature and completes at the M_f (martensite finish) temperature [7]. The stress (σ) – strain (ε) diagram (Fig. 3a) clearly demonstrates the material’s behaviour. In the martensitic state, the material deforms under applied stress, exhibiting initially small, then increasingly significant strain with rising stress. Upon unloading, the material can recover nearly, or even entirely, to its original shape through heating, though minor residual deformation may remain. Once the A_f temperature is reached, the crystal structure reverts to its austenitic state, adopting the shape associated with this phase. As shown in Figure 3b, this heat-induced behavior can be observed when the element is in the martensitic phase in its deformed state and transitions to the austenitic phase upon heating, meaning it only attempts to regain its original shape at high temperatures as a result of the crystal structure transformation.

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Theoretical stress-strain diagram of SMAs (a) and the corresponding temperature values in relation to martensitic phase transformation (b) (z – phase fraction, 100% – martensite, 0% – austenite), illustrating shape memory behaviour [4]

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As previously mentioned, a two-way shape memory effect is also possible, meaning that the martensitic phase can also possess a distinct, memorized shape. This shape can be achieved upon cooling, just as the austenitic shape is attained through heating.

The transformation temperatures (A_s, A_f, M_s, M_f) can vary significantly depending on the material, and they require careful consideration in construction applications, particularly for structural elements exposed to outdoor conditions or direct sunlight. These transformation temperatures depend on the material composition, the thermomechanical processing applied during manufacturing, and the mechanical stress and loading conditions the material is exposed to [4].

1.4 Superelasticity

In the stress-strain diagram (Fig. 4a), it is clearly shown that in the austenitic phase, when the material is subjected to stress, deformation occurs. When the martensitic phase material is relieved of stress, it spontaneously returns to the austenitic phase, regaining its original shape without any external influence, solely due to the removal of the applied stress, thereby returning to its undeformed state. This entire process occurs independently of temperature. This phenomenon is known as pseudoelasticity, or superelasticity. The curve illustrates that diagram plateaus and hysteresis can be observed. This means that the extent of deformation varies depending on whether the stress is increasing or decreasing, i.e., the direction of loading [4].

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Theoretical stress-strain diagram of SMAs (a) and the corresponding temperature values in relation to martensitic phase transformation (b) (z – phase fraction, 100% – martensite, 0% – austenite), illustrating superelastic behaviour [4]

Citation: Építés – Építészettudomány 53, 1-2; 10.1556/096.2025.00139

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As shown in Figure 4b, the superelastic properties are observed if in the temperature where the deformation occurs the material is in the austenitic phase, meaning its crystal structure is stable. Therefore, without the effect of heat, the material tends to return to its original shape simply upon removal of the load.

The industrial and construction applications of shape memory alloys primarily rely on the property of superelasticity, which is why this study places particular emphasis on it.

1.5 Damping properties

A key characteristic of shape memory alloys is their motion damping properties. The magnitude of this damping, or the amount of dissipated kinetic energy, is determined by the area enclosed by the stress-strain diagram. The material is capable of converting the kinetic energy it absorbs – such as that generated by an earthquake – into heat energy [10]. This allows it to reduce the level of motion and vibration experienced by structures. This phenomenon is due to the formation of internal friction, that can occur through three different mechanisms [11]:

• – In the austenitic phase, reversible dislocation movement creates internal friction.

• – In the martensitic phase, internal friction develops between martensite-martensite elements.

• – During phase transformation, movement typically occurs at the boundaries between the austenite and martensite phases.

Among these, the highest level of internal friction arises from the movement at the austenite-martensite phase boundaries.

Since the material’s crystal structure changes under thermal influence, it is important to consider its self-heating at higher stress levels.

1.6 Comparison with steel

To gain a more comprehensive understanding of the material’s properties, it is useful to compare SMA with steel (Table 1), which was previously analyzed in terms of its crystal structure. In structural applications, the most commonly used shape memory alloy is the Ni-Ti alloy, also known as Nitinol, as it is considered the most suitable for this purpose due to its superelasticity, exceptional corrosion resistance, and excellent shape recovery capability [12]. Consequently, most research has been conducted on Nitinol. The other two commercially available shape memory alloys are Cu-Zn-Al and Cu-Al-Ni.

The stress-strain diagram of steel (Fig. 5) can be divided into the following stages:

1. linear elastic region

2. yield point

3. yield plateau

4. strain hardening

5. necking

6. ultimate tensile strength

7. fracture

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Stress (σ) – strain (ε) diagram of steel

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The stress-strain diagram of Nitinol (Fig. 6) can be divided into the following stages:

1. initial linear elastic region

2. plateau corresponding to deformation (phase transformation process)

3. region related to the transformed crystal structure, characterized by a higher modulus of elasticity than before

4. unloading phase, exhibiting a high modulus of elasticity

5. plateau linked to unloading, during which the crystal structure reverts (at a lower stress level than during loading, leading to hysteresis)

6. full reversion of the crystal structure to its initial state (austenite)

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Stress (σ) – strain (ε) diagram of Nitinol. T > Af

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The material exhibits the same behaviour under both tension and compression, resulting in a nearly centrally symmetric stress-strain diagram.

For steel, the amount of dissipated energy is determined by the area beneath the stress-strain curve, whereas for SMA, it corresponds to the area enclosed by the curve. This area represents the strain energy density, which is the volume-specific derivative of strain energy. In both cases (steel and Nitinol), identical test specimen geometries are assumed. Consequently, the ratio of dissipated energy for the two materials is equivalent to the ratio of their strain energy densities, which equals the area below/enclosed by the curve, allowing us to further discuss the relative magnitudes of dissipated energy.

In the case of steel, this area extends up to fracture. Within the linear elastic region, the material fully recovers upon unloading, allowing for multiple loading cycles as long as plastic deformation is not reached. Beyond yielding, the material cannot return to its original shape, resulting in permanent deformation. Therefore, when analyzing the maximum dissipation capacity of the material, the total area under the stress-strain curve is considered. However, this damping effect occurs only once, as the material does not revert to its original state.

For SMA, the dissipated energy can also be determined from the curve, but unlike steel, this dissipation can occur repeatedly due to the material’s cyclic behaviour. Hysteresis causes the material to follow different curves during loading and unloading, with the enclosed area between these curves representing the dissipated energy. According to various studies, the energy dissipation capacity of the material deteriorates after a certain number of cycles [4], as the height of the plateaus change, reducing the enclosed area. However, even after this, the material retains its ability to dissipate energy.

To perform an accurate comparison of the energy dissipated by the two materials, further laboratory experiments are necessary. Within the scope of this study, an approximate calculation can be made based on the previously presented stress-strain diagrams of steel and Nitinol (Figs 5–6) and the comparative data provided in Table 1.

According to Table 1, considering both the lower and upper bounds, the elongation at fracture for Nitinol is approximately 1.6 times that of steel. Regarding ultimate tensile strength, Nitinol exceeds steel by more than twice its value.

In the first scenario, when both materials are subjected to the same maximum load and identical elongation (Fig. 7), the area enclosed by the Nitinol curve is only about 30% of the area under the curve for steel. This indicates that Nitinol is capable of dissipating significantly less energy. However, at this level, Nitinol remains far from failure and can sustain additional loading cycles.

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Comparison of the stress (σ) – strain (ε) diagrams of steel and Nitinol under identical maximum stress and strain

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After four cycles, Nitinol dissipates energy equivalent to 120% of the total energy dissipated by steel, with further cycles increasing this value. As previously discussed, steel can exhibit cyclic behaviour within its linear elastic range, but the amount of energy dissipated in this range is minimal.

If the maximum stress for Nitinol is increased to twice the ultimate tensile strength of steel and the strain to 1.5 times, the previously mentioned ratios indicate that Nitinol’s ultimate tensile strength and fracture strain are still not reached. In this case (Fig. 8), the areas under the curves for steel and Nitinol become nearly equal. However, even at this point, the Ni-Ti still does not reach failure.

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Comparison of the stress (σ) – strain (ε) diagrams of steel and Nitinol, where the maximum stress for Nitinol is set at twice that of steel, and the maximum strain is 1.5 times greaters

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Such significant strain levels, however, may pose challenges in structural applications and are therefore typically acceptable only in specific scenarios, such as during seismic events.

These diagrams are approximate representations derived from scaling typical material-specific stress-strain diagrams. Accurate data would require experimental testing, particularly for Nitinol, as the placement of its plateau regions is influenced by multiple factors. Depending on the location of these plateaus, the energy dissipated by Nitinol may surpass that of steel. Conversely, it may also be significantly lower, especially after multiple cycles, as previously noted. Over successive cycles, the plateaus on Nitinol’s stress-strain curve tend to converge, reducing the dissipated energy.

In summary, understanding the crystal structure of shape memory alloys facilitates a deeper comprehension of the mechanisms behind their unique properties (pseudoplasticity, pseudoelasticity, damping capacity, and two-way shape memory effect). A comparison with steel – currently the most commonly used metallic construction material in modern building practices – highlights the potential advantages of shape memory alloys. This knowledge paves the way for their appropriate integration into design processes, promoting effective use of these materials in construction.

2 VARIOUS APPLICATIONS OF SMAS IN STRUCTURAL DESIGN

The previously discussed four unique properties of shape memory alloys enable their application in diverse scenarios and for different purposes. These uses extend beyond structural design and encompass other fields such as robotics and the automotive industry. Below, the potential applications are presented, categorized by each specific property.

2.1 Use of SMAs as passive vibration dampers

In passive vibration damping, the damping effect of SMAs – i.e., their energy dissipation capability – is utilized in structures made of shape memory alloys. This means vibrations that would otherwise affect and damage the load-bearing structures of buildings are dampened using SMA components. The SMA element dissipates the kinetic energy of the vibrations, thereby protecting the structural system from damage. Achieving this effect does not require external heating, as the material’s superelastic property allows it to return to its original state once the external load is removed.

Although several studies have explored this phenomenon and its applications, it remains less widely recognized and implemented. This is likely due to the current lack of comprehensive information about the materials and their behaviour. Notable projects in this field include:

• – ISTECH [14] – Development of Innovative Techniques for the Improvement of Stability of Cultural Heritage, in Particular Seismic Protection

• – MANSIDE [15] – Memory Alloys for New Seismic Isolation and Energy Dissipation Devices

When using SMAs, it is essential to ensure a compact and stable design if the structure is subjected to both tensile and compressive forces. This is necessary to prevent stability loss, which could compromise the shape memory capability. For structures subjected to bidirectional bending and torsion, it is also important to consider that the behaviour of the material may vary across different sections of the cross-section and under different types of loading [4].

Examples of passive vibration damping applications include the restoration of the San Francesco Basilica in Assisi, Italy, and the San Giorgio Church bell tower in Trignano, Italy, which are discussed in detail later.

2.2 Use of SMAs as active vibration control elements

In active vibration control, the adaptability of SMAs is utilized to modify the motion frequency and/or the natural frequency of a structure, which depends on its mass, stiffness, and support conditions. Therefore, a structure’s natural frequency can change if its mass is altered or if its static model is modified. The stiffness of SMAs varies under different load levels, and when integrated into a structure, they influence the structure’s stiffness, thereby altering its natural frequency. Active vibration control is a well-researched and continuously studied area.

One approach combines the damping capability of the alloys with frequency modification. For example, Nae and colleagues [16] achieved frequency modulation by controlling the material’s temperature.

Another method involves using SMAs alongside traditional damping systems. In such cases, SMA components participate in load transfer by utilizing their adaptive stiffness or force transmission capability [4].

2.3 Use of SMAs as actuators

Actuation refers to the function of a control system within a structure, which modifies the fundamental behaviour of the structure. For SMAs, this capability arises from their shape memory properties, enabling both force generation and structural deformation.

In other industries, such as automotive and robotics, the use of SMAs as actuators has been observed, particularly for generating cyclic motion dependent on thermal effects. Such applications include dynamic systems like pistons, where the movement of the piston is controlled by SMAs, or joints, where the tensioning of an SMA wire regulates the joint’s position. In these cases, the temperature of the SMA wire is altered by passing an electric current through it [3].

In the construction industry, the primary challenges associated with using SMAs as actuators lie in their high material costs and the inertia caused by heating and cooling processes [4].

2.4 Use of SMAs as tensioning elements

In the absence of restoration efforts for older structures, various damages and deformations can lead to further deterioration. In extreme cases, even the structural model may change, complicating the restoration process. In such scenarios, the installation of tensioned steel elements is a standard procedure. Using fiber-reinforced polymers (FRP) also becomes increasingly popular.

Shape memory alloys offer an alternative solution in these cases. Unlike traditional methods requiring additional post-tensioning – often involving extra labour –, SMAs can generate the required tension through thermal effects, such as the application of electrical current. This induces a shape change in the SMA element, thereby introducing stress into the structure. Another advantage is the minimization of friction losses, as the shape memory effect occurs uniformly along the entire length of the SMA element [4].

A potential application of this method could be in the retrofitting of walls supporting vaulted structures. By applying tension to the upper parts of the walls using tie rods, the lateral forces acting on the walls can be counteracted. While such tie rods are traditionally made from steel, the use of SMAs eliminates the need for conventional post-tensioning of the steel rods.

Additionally, SMAs provide the possibility of applying stress not during the construction of the structure but after its completion, using the shape memory effect. For example, this approach could be advantageous for thin reinforced concrete cross-sections, where traditional tensioning methods are inadequate [17].

3.1 Bell tower of San Giorgio Church – Trignano, Italy

The renovation of the bell tower of the San Giorgio Church in Trignano represents a well-documented application of shape memory alloys (SMAs) [18]. The church sustained significant damage during the earthquake on October 16, 1996, which had a magnitude of 4.8 on the Richter scale. The church is located approximately 12 km from the epicenter.

The church was built in 1302, while the adjoining structures were added around 1700. The building was transformed into its current state in the latter half of the 19^th century. The church tower stands 18.5 meters tall with a square floor plan measuring approximately 3×3 meters. It has four masonry piers at each corner, connected by walls that are 0.3 meters thick, increasing to 0.42 meters towards the corner piers. The adjacent structures provide bracing to the tower at three of its corners up to a height of 11 meters. The floors of the first three levels of the tower are made of wood, while the fourth level features a brick vault supported by a centrally placed steel I-beam.

The restoration began in 1999, with the first phase focusing on comprehensive structural rehabilitation. This included replacing damaged bricks, injecting specific areas with special mortar, and replacing the floors with lightweight materials such as wood and hollow elements.

Following the general restoration, SMAs were implemented in the second phase. Four steel rods were installed within the tower’s interior at its corners, avoiding direct contact with the walls (Fig. 9). These rods were intended to increase the tower’s bending stiffness and resistance. Each rod was composed of six bolted segments for easier installation, with a Shape Memory Alloy Device (SMAD) integrated at the height of the third floor. Each SMAD consisted of 60 Ni-Ti wires, each 300 mm in length and 1 mm in diameter. The steel rods extended the full height of the tower and were anchored only at the base and roof structure.

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Schematic drawing of the placement of steel elements in the San Giorgio Church (Trignano, Italy) tower [18]

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The SMA elements were post-tensioned to apply a constant compressive force of less than 20 kN on the masonry walls. The target was to reach the plateau of the SMA stress-strain curve, ensuring that even in the case of significant displacements, the system would avoid over- tensioning and maintain forces within the desired operational range. Additionally, the SMADs were designed not only to limit loads but also to enhance damping performance, leveraging the material’s passive vibration damping properties, as discussed in Section 2.1.

A finite element model (FEM) of the structure was also developed. The analysis confirmed that during seismic events, the integrated SMA-based system effectively reduced tensile stress on the walls, mitigating potential damage.

Additionally, in situ investigations were conducted in three distinct phases. In the first phase, dynamic effects on the damaged structure were examined using a seismometer. This method involved measuring both ambient vibrations and forced vibrations, with the latter generated by dropping heavy weights. In the second phase, the impact of aftershocks was measured by installing an accelerometer network on the structure. In the third phase, the dynamic tests conducted in the first phase were repeated using a seismometer, but this time on the restored and reinforced structure.

The comparison between the first and third tests led to several conclusions, including the following: the frequency of vibrations was noticeably higher in the restored structure, increasing from 2.7 / 2.9 Hz to 3.2 / 3.5 Hz. This indicates that the structure became stiffer. However, due to the low intensity of both ambient and induced vibrations, the effect of the installed SMA elements was less perceptible.

On June 18, 2000, another earthquake with a magnitude of 4.5 and the same epicenter struck the area. A post-earthquake inspection of the building revealed no damage, affirming the successful implementation of the SMA devices.

Summarizing the advantages of using SMAD compared to traditional steel structures, it offers technological simplicity as SMAD itself serves as both the tensioning element and the device, eliminating the need for separate equipment for tensioning. Another advantage is the avoidance of over-tensioning. In the case of larger deformations, the tension remains constant, unlike steel, where the tension value changes with displacement. Consequently, the shape memory alloy ensures the required stress under all circumstances, but in the event of significant deformations caused by movements, the stress on the structure will not reach a level that could lead to its failure.

3.2 San Francesco Basilica – Assisi, Italy

The San Francesco Basilica in Assisi, Italy [19], built in the 13^th century, had suffered damage from numerous earthquakes in the past. However, the most severe destruction occurred during the earthquake of September 1997. Most of the vaults in the upper basilica collapsed, while cracks and deformations appeared in the remaining vaults. Additionally, the tympanum of the right transept was damaged, and the tympanum of the left transept collapsed entirely.

The damage to the tympanums occurred for two main reasons: first, due to the deterioration of mortar quality caused by aging, and second, due to the lack of proper connection between the roof and the façade walls, which allowed collisions between the roof and the tympanum during dynamic impacts.

The primary goal during the reconstruction of the tympanums was to establish a proper connection between the roof and the façade walls. This was achieved by installing a total of 47 SMADs: 24 in the left transept and 23 in the right transept. These devices were produced in three sizes to match the calculated forces at the installation points, ranging from 7 kN to 52 kN, and allowing displacements between ±8 mm and ±25 mm.

The design of the SMADs is shown in Figure 10. During the reconstruction, metal plates were embedded in the façade wall as anchors, and threaded rods were extended from these plates toward the roof. A reinforced concrete top beam was constructed along the edge of the existing roof. The SMADs were connected on one side to the threaded rods and on the other side to the new concrete beam using an embedded and bolted counterplate. This configuration ensured the connection and load transfer between the sidewalls and the roof while allowing horizontal displacements under dynamic forces with the help of the SMADs.

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Schematic installation and detail drawing of the SMA devices used in the San Francesco Basilica (Assisi, Italy) to ensure the proper connection between the tympanum and the roof structure [19]

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In addition to the SMA devices, high-strength stainless steel STUs (Shock Transmission Units) were installed in the building. These devices become active under high loading speeds, connecting two structures, but remain inactive under low-speed loading, allowing relative movement between the structures. At the mid-height of the sidewalls, a steel truss was installed and connected to the walls using STUs. The purpose of this was to enable the walls and the structure to move independently under general usage and environmental loads, while during short-term dynamic movements caused by earthquakes, the forces would transfer to the high-strength steel structure. In such cases, the STUs provide a continuous and rigid connection. This setup ensures greater stiffness of the walls due to the added support, and it maintains the condition of previously formed cracks, preventing their further expansion.

Despite the high cost of shape memory alloys, their implementation is justified by the fact that the SMADs and STUs installed in the building accounted for only 1% of the total restoration cost.

3.3 San Feliciano Cathedral – Foligno, Italy

The San Feliciano Cathedral in Foligno, Italy [19], was originally built in 1133. It underwent expansions in the 15^th century and further modifications in subsequent centuries. The roof structure was replaced in the 1950s with a new steel-framed roof.

During the 1997 earthquake, the building sustained significant damage. The façade wall detached and shifted horizontally by 8 cm from the adjoining vaults. This was caused by the initial overturning failure of the façade wall, which had not been properly connected to either the perpendicular sidewalls or the roof. The primary goal of the restoration was to establish adequate connections to prevent the wall from overturning and detaching from other structural elements (Fig. 11).

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Position and schematic details of the SMA devices installed during the restoration of the San Feliciano Cathedral (Foligno, Italy) [19]

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The connections between the walls were reinforced using traditional steel structures. The main façade was anchored to the roof with nine SMA devices operating on the same principle as those used in the San Francesco Basilica in Assisi (see Section 3.2). Each device was designed to handle a force of 27 kN and accommodate a maximum displacement of ±20 mm.

The SMA devices were connected on one side to plates anchored to the wall and on the other side to a V-shaped beam attached to the existing steel roof structure installed in the 1950s. The ends of the roof beams resting on the wall were designed with sliding connections, allowing dynamic displacements to be managed by the shape memory alloy devices.

This configuration ensures that horizontal forces are transmitted to the wall exclusively through the SMADs. Due to the stress-strain characteristics of the SMA material, the stress remains constant within a specific displacement range, limiting the forces exerted on the wall. The system permits horizontal movement of the wall, while, after the force subsides, the SMADs restore the wall to its original position. This behaviour contrasts with that of steel, which cannot return to its original shape after plastic deformation, leaving the wall in a displaced state.

By allowing controlled movement under significant forces, the wall can participate in dissipating seismic energy. Allowing this movement is optimal because overly rigid structures are more prone to breaking under high forces during an earthquake. In this case, the SMA ensures a constant pulling force to prevent the wall from overturning while accommodating dynamic displacements.

3.4 San Serafino Church – Montegranaro, Italy

The San Serafino Church in Montegranaro, Italy [19], was built in 1603 alongside the adjacent monastery, on the ruins of a church that had collapsed in 1431. During the 1997 earthquake a part of the roof structure collapsed. Similar to the case of the San Feliciano Cathedral (Foligno, Italy – Section 3.3), the damage was caused by the lack of proper connections between the side-walls and the roof structure.

In this case two SMA devices with a different design from the previously discussed examples were installed to reinforce the connection between the main façade and the sidewalls (Fig. 12). A HEA180 steel beam was fixed to the top of each sidewall, while a U-shaped steel beam was mounted on the main facade’s inner side, following the slanted upper edge of the wall. The HEA beams on the sidewalls were connected to the U-shaped beam on both sides, just next to the ridge beam’s connection point. The SMA devices were incorporated into these connections, ensuring proper linkage. This solution limited excessive movements while avoiding excessive stiffness, which could lead to structural failure.

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Illustration of the SMA devices installed during the restoration of San Serafino Church (Montegranaro, Italy), which secured the connection between the sidewalls and the main façade.The figure also depicts the anticipated movements that can be caused by dynamic forces due to the lack of proper connections between the walls and the roof [19]

Citation: Építés – Építészettudomány 53, 1-2; 10.1556/096.2025.00139

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4.1 History of the church

The existing medieval Saint Michael Church, located on a sloped site, was built on the ruins of a previous church destroyed during the Turkish era [23]. Evidence suggests that rubble from the demolished church was used to fill the site before construction, meaning the new church was partially built on the old ruins and partially on new foundations laid over low-quality fill material. Its layout (Fig. 13) is simple, with a nave covered by barrel vaults and two transverse vaults without ribs, which forms groin vault. On its western side, a bell tower connects to the nave, with the main entrance located on the west side of the tower, allowing access to the church through the ground floor of the tower.

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Schematic floor plan of the Saint Michael Church in Érd, Hungary [23]

Citation: Építés – Építészettudomány 53, 1-2; 10.1556/096.2025.00139

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The tower, constructed later in the late 18^th century, rises above the main entrance. An earlier northern entrance was sealed off in 1955. The organ loft, built at a later date, is accessible from the first floor of the tower. The sanctuary leads to a sacristy to the north and an oratory to the south, both added after the initial construction.

The structure of the building is primarily stone masonry, supplemented with brickwork in certain areas. Wall thickness varies between 80 and 130 cm. On the exterior of the nave and apse, buttresses reinforce the structure. The bell tower is also constructed from stone and brick.

The nave of the church is constructed with a groin vault formed by the intersection of one longitudinal barrel vault and two transverse barrel vaults. Between the two transverse vaults, a horizontal strap is located on the upper plane, supporting a wooden beam that functions as a tie rod. This wooden beam is anchored into the masonry with an iron rod. The apse is also covered with a groin vault.

The roof has a baroque-style roof structure. Above the nave, there are four principal trusses, and above the apse, there are three smaller ones, differing in size from those over the nave.

4.2 Condition of the church before renovation

Due to the sloping terrain, the external ground level is up to two meters higher than the interior floor level in certain areas. The church was built on earlier ruins, meaning that in some sections, the foundations rest on these ruins, while in others, they were constructed from stone on low-quality, debris-filled soil. Additionally, the foundation depth varies. Since construction took place at different times, on varying soil conditions, and with differing foundation levels, combined with inadequate drainage, differential settlements occurred.

Significant cracks were visible inside the building, particularly at the keystones of the vaults, originating from and above the corners of the windows, as well as running longitudinally in the apse and the nave. The crack in the apse extended across the entire height of the wall, indicating a complete fracture. Cracks around the windows were present at every window but were larger on the southern side and along the later-added gallery. After cleaning, some cracks were found to be several centimetres wide.

These cracks were caused by poor-quality foundations, damage to the roof structure, and the loads exerted by the vaults. The compressive force acting on the wall is minimal, so the wall material is not near failure. Instead, the cracks resulted from shear and bending stresses caused by uneven settling.

Cracks were also observed between the cross vault covering the nave and the western wall, as they had not been bonded together during construction, allowing independent movement. At the junction of the apse and the nave, cracks were present at the arch closure due to wall movement. The apse vault has a segmented design, and a crack was visible in the central segment behind the altar due to the fracture in the wall. Damage to the roof structure was evident at the connection between the nave and the apse, where slight variations in the dimensions of the roof ’s main structural elements led to an improper joint, resulting in inadequate roof covering. Consequently, water infiltration and structure decay occurred. Over the centuries, the roof structure suffered continuous damage and underwent multiple repairs, some of which were of questionable quality.

The Komárom earthquake of 1763 (magnitude 6.3, with a direct distance of 72.6 km from Komárom to Érd) affected the region, likely causing structural damage to the church. In January 1956, another earthquake struck the area. This event, with a magnitude of 5.6 and an epicenter in Dunaharaszti (12.5 km from Érd), did not result in any newly documented cracks beyond those already existing.

4.3 Restoration works of the church

The full-scale renovation began in 2009 and was completed in 2013, carried out in multiple phases. One of the most crucial steps of the restoration was ensuring proper drainage to prevent further damage caused by moisture and water infiltration.

During the works, gypsum seals were placed on the walls to monitor whether foundation movement was still ongoing. Cracks appeared in the seals, indicating that the movement persisted during the renovation. This was caused by the poor-quality subsoil, drainage issues, and other environmental factors. Due to these issues, strengthening the foundation became necessary by constructing a monolithic reinforced concrete ring beam enclosing the entire foundation and supplementing it with tie rods at the foundation level, connecting the longitudinal walls. The connection was established by drilling through the foundation and subsoil beneath the church and using prestressed tendons. This method was chosen to avoid disrupting the use of the interior space, which was renovated in a later phase. From a heritage conservation perspective, the creation of the monolithic reinforced concrete ring beam raised concerns, as existing wall sections and foundation elements had to be cut in several places. However, the deteriorated structural condition made this intervention unavoidable.

There was no need to reinforce the walls, as their compressive strength was adequate. However, the existing cracks required treatment. A specialized technique called “Brutt Saver” was applied, where stainless steel helical rods were embedded perpendicularly into the cracks, and the carved grooves were injected with binding material. At the corners of the walls, additional steel spiral connectors were installed to ensure proper structural integration. Following these repairs, new cracks appeared in different areas of the walls, suggesting that while the crack repairs were effective, the building continued to experience uneven settlement.

To provide the necessary horizontal support for the vaults, a tensioned tie rod system with a counter-threaded connecting element was installed. The tie rods run longitudinally beneath the wall plate and transversely above the vaults along the lines of the buttresses. To ensure proper load transfer, the tie rods were extended to the exterior façade.

Regarding the roof structure, some elements or sections were replaced. At the junction between the apse and the nave, the ends of the decayed elements were supported with steel reinforcements. The main roof structure elements of the apse had previously slipped out of alignment, so they were rebuilt, and the roof components were treated to ensure durability.

4.4 Potential applications of shape memory alloys

The Saint Michael Church in Érd has previously been exposed to the effects of earthquakes. Due to this, and the thorough documentation of both the building and its restoration, the potential applications of shape memory alloys are analyzed, assuming the possibility of future earthquakes and the need for protection against them.

Summarizing the main structural issues before the reconstruction, the following problems were identified:

• – Moisture infiltration in the walls due to inadequate drainage

• – Poor-quality foundation

• – Cracking and fracturing of masonry walls due to foundation movement

• – Damage to vaults caused by wall movement

• – Structural deterioration resulting from inadequate connections between vaults and walls

• – Roof leakage, leading to wood decay and damage to connections

Among these issues, the application of SMA is primarily relevant for addressing wall and vault cracks caused by uneven foundation settlement, as well as problems at vault-wall connections. Additionally, considering seismic effects, SMAs may provide solutions for other movement-related structural concerns.

4.4.2. Partial replacement of the foundation ring beam’s steel reinforcement with SMA

In the case of the reinforced concrete ring beam at the foundation level, it is worth considering whether structural advantages could be achieved by incorporating SMA reinforcement. The superelastic properties of SMA are particularly beneficial under dynamic loading conditions. However, in this case, the foundation is primarily subjected to slow and prolonged movements.

Taking long-term deformations into account, the shape memory effect could be utilized when integrating SMA along the longitudinal reinforcement of the foundation ring beam. Post-construction observations revealed that due to the discontinuous support of the ring beam, vertical displacements developed along the structure, generating shear stress within it. By leveraging the shape memory effect, a continuous longitudinal SMA element embedded throughout the ring (Fig. 14) could counteract this shear force when activated by applying electrical current to induce heating.

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Possible application of SMA in the foundation ring beam of the Saint Michael Church in Érd. The shape memory effect, activated by electrical heating, could counteract vertical displacements caused by uneven settlement of the underlying soil

Citation: Építés – Építészettudomány 53, 1-2; 10.1556/096.2025.00139

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This mechanism functions by ensuring that the SMA’s austenitic phase corresponds to a fully horizontal reinforcement. When subjected to shear stress, the SMA transitions to its martensitic phase and deforms. By reapplying heat, it would revert to its original austenitic phase, thereby restoring the initial geometry. However, this solution would require continuous monitoring. A key challenge is that once the ring fully returns to a horizontal position, it may detach from the foundation, forcing it to bear the entire weight of the superstructure. This approach would be viable if continuous monitoring allowed for the gradual filling of gaps between the foundation and the ring beam until the subsoil stabilizes permanently, preventing further settlements.

4.4.3. Application of active confinement

Shape memory alloys can be effectively used as post-tensioning elements in both curved and angular structural forms. Their key advantage lies in the uniform force distribution along their entire length during deformation recovery. This results in the phenomenon of active confinement, where an SMA element wrapped around a column transmits uniform compressive stress along the entire perimeter [4]. This is beneficial because putting concrete in a triaxial stress state significantly enhances its strength, making its load-bearing capacity more predictable. Experimental studies on this phenomenon have been conducted by Krstulovic-Opara et al. [29, 30].

Active confinement can be considered not only for the foundation ring but also along the upper perimeter of the building to support the vaults.

In the foundation system, the tie rod network is located beneath the internal flooring, while in the upper section, it runs above the vaults. In this configuration, the system does not compromise the interior aesthetics. However, in cases where hidden placement is not feasible any other way, an active confinement system encircling the entire structure – including integration into the ring beam – could be explored. This would provide a uniform compressive force along the entire perimeter of the building.

A potential implementation would involve a pre-shaped SMA element following the tracing of the ring beam, initially set in its austenitic form. If lateral deformations occur, transitioning to the martensitic phase, heat application would restore the element to its original austenitic configuration (Fig. 15). This would replace conventional tie rods and tensioning mechanisms, preventing vault displacement while ensuring controlled post-tensioning. Additionally, the plateau stress-strain behaviour of SMA would prevent excessive over-tensioning under large deformations.

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Potential application of SMA in the upper perimeter of the Saint Michael Church in Érd, encircling the entire structure. This system would counteract lateral displacements of the walls, providing stable lateral support for the vaults

Citation: Építés – Építészettudomány 53, 1-2; 10.1556/096.2025.00139

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An alternative approach would involve a hybrid system where a partially SMA-based reinforcement is integrated into a conventional steel reinforcing structure. This would allow for controlled stressing at a lower cost, though the resulting stress distribution would be less uniform.

If this technique were also applied within the foundation ring beam at the substructure level, it could be integrated with the previously discussed vertical deformation compensation system.

This method is worth considering when hidden tie rods are unfeasible due to space constraints, and visible structural elements are aesthetically unacceptable. However, due to the large material quantities required, this approach remains a costly solution.

4.4.6. Crack Mitigation

The Brutt Saver method used for crack mitigation has proven effective. However, additional cracks have formed due to continued differential settlements.

SMA elements have already been used for crack closure applications in past studies. For example, Soroushian et al. [31] utilized Fe-Mn-Si-Cr shape memory alloy rods to close cracks in highway bridges (Fig. 16). These elements were activated by electrical heating. However, such visible reinforcements would be aesthetically unacceptable in a historical building.

Another option is the application of the Brutt Saver method, using elements made of SMA instead of stainless steel. When stainless steel elements are installed, there is a risk of overstrain if significant movements occur within the structure, potentially leading to even greater damage. By consolidating existing cracks, higher stresses could cause new large cracks, or additional weak points could emerge elsewhere in the structure.

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Crack closure using Fe-Mn-Si-Cr SMA rods in an outdoor highway bridge with post-tensioning [4, 29]

Citation: Építés – Építészettudomány 53, 1-2; 10.1556/096.2025.00139

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With the installation of SMA components, this can be controlled by allowing stress to develop during the initial phase due to displacement, meaning that multiple smaller cracks can form elsewhere. Under higher stress, when the stress on the SMA reaches the plateau on the stress-strain diagram, rather than forming another large crack, further displacement is allowed in the existing crack. This ensures no new weak points are created in the structure, aside from the existing one. Further deformations will occur within the consolidated crack.

This approach minimizes interference with the overall force distribution of the structure, while optimizing the damage based on the stress level, avoiding the creation of additional heavily damaged areas.