Stiffness Ratio Research Articles

Ultimate tensile properties of bolted stiffened angle connections

In this paper, monotonic tensile tests were carried out on 20 bolted stiffened angle connections. The failure mode and ultimate tensile performance of the connections were studied in the terms of stiffened angle thickness, bolt pitch distribution, bolt diameter and preload. The test results show that the failure mode of the connection is closely related to the stiffness ratio between the bolt and stiffened angle. When this ratio was less than 1, the bolt fractured first, otherwise the stiffened angle fractured before the bolt. The fracture position of the stiffened angle was also different according to the different design parameters. The stiffened angle thickness has the most significant effect on the ultimate bearing capacity of the connection which increases with the increase in the thickness. The deformation capacity of the stiffened connection is closely related to the failure mode. Among the design parameters, horizontal bolt pitch has the most significant effect on the deformability of stiffened connection. The initial stiffness of the connection is positively correlated with stiffened angle thickness and bolt preload, but negatively correlated with bolt pitch distribution. Based on the test results and corresponding theoretical analysis, a mechanical model of the load-displacement curve for bolted stiffened angle connections is proposed and verified by the test results. The results show that the proposed model could well present the ultimate tensile properties of bolted stiffened angle connections.

Enhancing seismic performance of brace frame using self-centering friction damper with variable slip stiffness

A novel self-centering friction damper with variable slip stiffness (VSFD) is proposed to achieve ideal self-centering capability and limit the responses of the brace frame structure under the extremely rarely occurring earthquake (EROE), and its critical difference from the self-centering friction damper with constant slip stiffness (CSFD) is the hardening post-yielding stiffness. Through mechanical analysis, the VSFD exhibits ideal flag-shaped hysteretic behavior with the desired self-centering and energy dissipation capacity. The experimental study confirms that the hysteretic behavior of the VSFD is affected by friction coefficient, slope angle and transverse compressive force. The combination of disc spring stacks with various stiffness can provide variable compressive stiffness for the VSFD. The ratio of the residual sliding load to the initial sliding load increases with pre-compressive force, and so does the self-centering capacity. The hardening post-yielding stiffness ratio is proportional to the ratio of strong to weak stacks of the disc springs. The displacement corresponding to the hardening point decreases as the preloading weak stacks’ deformation capacity decreases. The VSFD can dissipate energy even if the deformation is small, and the damping ratio drops with increasing deformation, pre-compressive force and compressive stiffness. The updated displacement-based design procedure is proposed and the comparative dynamic time history analysis is conducted for the brace frames with different kinds of braces. The results show that the seismic responses of brace frames with the CSFDs and VSFDs are comparable under the rarely occurring earthquake (ROE), which meet the performance objectives, while the latter has smaller displacement response and larger floor acceleration than the former owing to its hardening post-yielding stiffness. Due to the considerable residual deformation under the ROE and EROE, the response of brace frame with the conventional friction dampers (CFDs) differs dramatically.

H∞ Optimization of Three-Element-Type Dynamic Vibration Absorber with Inerter and Negative Stiffness Based on the Particle Swarm Algorithm.

Dynamic vibration absorbers (DVAs) are extensively used in the prevention of building and bridge vibrations, as well as in vehicle suspension and other fields, due to their excellent damping performance. The reliable optimization of DVA parameters is key to improve their performance. In this paper, an H∞ optimization problem of a novel three-element-type DVA model including an inerter device and a grounded negative stiffness spring is studied by combining a traditional theory and an intelligent algorithm. Firstly, to ensure the system's stability, the specific analytical expressions of the optimal tuning frequency ratio, stiffness ratio, and approximate damping ratio with regard to the mass ratio and inerter-mass ratio are determined through fixed-point theory, which provides an iterative range for algorithm optimization. Secondly, the particle swarm optimization (PSO) algorithm is used to further optimize the four parameters of DVA simultaneously. The effects of the traditional fixed-point theory and the intelligent PSO algorithm are comprehensively compared and analyzed. The results verify that the effect of the coupling of the traditional theory and the intelligent algorithm is better than that of fixed-point theory alone and can make the two resonance peaks on the amplitude-frequency response curves almost equal, which is difficult to achieve using fixed-point theory alone. Finally, we compare the proposed model with other DVA models under harmonic and random excitation. By comparing the amplitude-frequency curves, stroke lengths, mean square responses, time history diagrams, variances and decrease ratios, it is clear that the established DVA has a good vibration absorption effect. The research results provide theoretical and algorithm support for designing more effective DVA models of the same type in engineering applications.

Synthesis of Compliant Parallel Mechanisms Using an Improved Beam-Based Method with the Optimization of Multiple Resonant Modes

This paper proposes an improved beam-based method to synthesize a compliant parallel mechanism (CPM) with multiple degrees of freedom (DoFs). The proposed method utilizes a structural optimization technique to synthesize a three-legged CPM with a single-beam structure constructed by two perpendicular segments in each leg to achieve the desired DoFs and fully decoupled motion. In addition, an objective function is proposed to optimize the primary resonant frequencies in actuating directions to targeted values to achieve the desired dynamic behaviors. A 4-DoF CPM, with one translation and three rotations, is synthesized using the improved beam-based method and all of the primary resonant frequencies are optimized to the targeted values. The 4-DoF CPM prototype is fabricated monolithically and evaluated experimentally in terms of its mechanical characteristics, workspace, and resonant modes. The obtained results show that the experimental stiffness and dynamic properties agree with the predictions. In particular, the prototype has good motion decoupling capability, as reflected by the high stiffness ratios of more than 500 between the non-actuating and actuating directions; the large workspaces of up to 4.0 mm and 7.2° for the translation and rotations, respectively; and the resonant frequencies being close to the targeted ones. In addition, the highest deviations between the predicted and experimental results are 9.49% and 9.13% for the stiffness and dynamic behaviors, respectively, demonstrating the correctness and effectiveness of the proposed method.

Comparative study on failure mechanism of multi-storey planar composite frames with RC beams to CFST columns subjected to compartment fire

This paper presents a theoretical study of the failure mechanism of planar composite frames composed of reinforced concrete (RC) beams to concrete-filled steel tubular (CFST) columns subjected to compartment fire. The numerical analyses on the planar composite frames with multiple stories and spans are meant to reproduce the conditions of framed members in multi-storey composite structures in real buildings. A refined finite element model is established and calibrated against the thermal and mechanical results from physical testing and shows good reliability in general. Using this model, this study proposes comparative analyses on the failure mechanisms of three typical composite frames, and discusses the effects of two significant parameters: the beam-to-column linear stiffness ratio and the fire protection thickness of the composite column. The responses of the heated composite frames, including the rotational deformation and stiffness degradation of framed joints, the internal force redistribution within framed members, and the failure mode of framed structures are investigated and discussed. The results indicate that there are two important parameters should be considered in the design of composite frames in fire.

Low melting point alloy modified polymer composite with sharp stiffness switch for soft actuator

Materials possessing switchable stiffness, particularly dynamically switchable stiffness, have generated a lot of attention in the soft actuator. Herein, we proposed a facial poly (vinyl alcohol) (PVA) coating method to fabricate the micron-sized Field's metal (FM) phase-changing particles with an average particle size of about 1.2 μm, and obtained a series of stiffness variable polymer composites via incorporating FM particles into the designed stiffness variable polymer matrix. Owing to the rapid solid-liquid change and ultra-high modulus of FM, the rigid/soft stiffness ratio of the composites improved to 1442-folds. Moreover, the shape fixity (Rf) and shape recovery ratio (Rr) values of the shape memory properties could reach up to ultra-high values of 99.4% and 99.6%, respectively. Subsequently, the prepared composites were selected and used a 3D printing soft actuator as the stiffness variable units. The soft actuator exhibits short heating-cooling time of 36s under 1.2A current and with 4 °C water as the coolant, and it is able to lift a 200 g weight at the rigid state. Furthermore, the stiffness of obtained actuator can achieve high value 779 mN/mm. The results indicate that the obtained soft actuator possesses excellent actuate behavior and stiffness switchable ability. This work might provide faster and more rigid variable stiffness materials for soft actuators application in the real world.

The role of shear wave elastography in early prediction of response to neaodjuvant chemotherapy in cases of breast cancer

BackgroundBreast cancer is the most common malignant tumor and the commonest cause of death in female between 35 and 55 years of age. Neoadjuvant chemotherapy (NACT) is used in large scale nowadays in management of breast cancer. Recent studies propose that shear wave elastography (SWE) can early predict tumor therapy response during NACT for invasive breast cancer.Aim of workTo study the ability of SWE to predict pathological complete response (pCR) during NACT as early as first cycle.Subjects and methodsThe study analyzed data of 48 patients breast cancer who were scheduled for receiving NACT before surgery. During treatment, SWE examination was done at first four cycles.ResultsForty-eight breast cancer cases were included in the study with one hundred and ninety two examinations done. The cutoff point of stiffness ratio percent change post-first cycle in differentiating pCR and npCR groups was − 20% (AUC 0.755, sensitivity 81.8%, specificity 61.5%). The cutoff point of stiffness ratio percent change post-second cycle in differentiating pCR and npCR groups was − 49% (AUC 0.741, sensitivity 72.7%, specificity 76.9%). The stiffness ratio could predict pCR in early cycles of NACT.ConclusionsUS using shear wave elastography is an available, cheap, non-contrast, non-ionizing radiation method that predicts pCR in cases of breast cancer at neoadjuvant setting as early as first cycle.

A novel self-centering friction damper with elastic post-buckling plates to retrofit bridge bents

The self-centering energy dissipation dampers (SCEDs) have been demonstrated in mitigating the residual deformation of structures under strong ground motions. However, existing researches show that the damping force demand of SCEDs is higher than conventional dampers such as viscous dampers, BRBs or friction dampers for same design displacement of self-centering retrofitted structures, which could lead to higher base shear and acceleration responses of structures. In order to alleviate the problem, a novel self-centering damper composed of elastic post-buckling plates and adjustable friction devices (PBSCFD) was proposed. Compared with conventional SCEDs, the proposed PBSCFD has low secondary stiffness and adjustable energy dissipation capacity, which is beneficial to control the additional internal force of members adjacent to the damper in self-centering retrofitted structures. Based on the configuration and working principle of the PBSCFD, the theoretical force-displacement relationship of the damper was derived. Subsequently, a scaled PBSCFD was manufactured and tested under quasi-static loading to investigate its mechanical properties and to verify the theoretical constitutive model. In order to demonstrate the seismic performance of PBSCFDs, the double-column bridge bent retrofitted with PBSCFDs was designed by direct displacement-based seismic design method (DDBD), and its seismic performance was examined by elastic-plastic time-history analysis. Finally, effects of secondary stiffness ratio of self-centering dampers on seismic mitigation of self-centering retrofitted bridge bent were investigated. The results show that PBSCFDs have certain advantages in controlling the base shear and acceleration of the retrofitted bridge bent compared to conventional SCEDs with significant secondary stiffness.

A Study on the Stability of Reinforced Tunnel Face Using Horizontal Pre-Grouting

As tunnel excavation under poor geological conditions is liable to cause ground collapses, reinforcement measures are necessary to reduce construction risks. The stability of a tunnel face that was reinforced using horizontal pre-grouting was investigated through numerical simulation and theoretical analysis in this study. An analytical model was developed using the limit equilibrium method and taking into account the impact of horizontal grouting reinforcement (HGR) on the tunnel face. Subsequently, a comprehensive numerical simulation was conducted to confirm the validity of the model. By performing a parametric analysis, it was found that the limit support pressure exhibited a linear relationship with the cohesion and friction angle. In addition, the limit support pressure is more sensitive to changes in the cohesion and friction angle than changes in the stiffness ratio and thickness of HGR. The HGR more effectively decreases the limit support pressure in conditions of low cohesion (or friction angle) compared with conditions of high cohesion (or friction angle).

Vibrational energy transfer in coupled mechanical systems with nonlinear joints

This study investigates vibrational transfer and energy flow in nonlinearly coupled systems, each subjected to a harmonic force with different excitation frequency. A nonlinear joint having either smooth or non-smooth stiffness characteristics at the coupling interface is considered. The steady-state dynamic responses are obtained by a method of harmonic balance with alternating frequency and time and by a direct numerical integration. The time-averaged transmitted power is used to assess the direction of energy flow and the power transfer between the systems. It is shown that as the excitation frequency ratio increases, the point of zero net power transfer between subsystems moves to lower frequencies. The cubic stiffness nonlinearity mainly affects the power transfer in the vicinity of the second resonance frequencies. It is also shown that the second resonance frequencies of both subsystems and the point of zero net power transfer shift to higher frequencies when the bilinear stiffness ratio increases. For the power transfer curves, the bilinear stiffness ratio controls the location of the second resonance frequencies. Findings from this study can provide insights to aid design of interfacial joints with regards to vibration transfer in coupled systems under multi-frequency excitations. The study reveals energy flow mechanisms through joint structures, which should benefit their dynamic designs aiming at an enhanced vibration suppression performance.

Numerical study on the VIVs of two side-by-side elastically coupled cylinders under different Re and natural frequencies

Vortex-induced vibration (VIV) is very significant in influencing the structural safety of many practical engineering applications. However, the VIV mechanism of multiple elastically coupled cylinders is poorly understood. In this paper, the VIVs of two elastically coupled cylinders in a side-by-side arrangement is numerically studied under different effects, including the stiffness ratio of the two springs (K2/K1), the diameter ratio of the two cylinders (D2/D1), and the Reynolds number. The mass ratio of the two cylinders is 1.92. K2/K1 and D2/D1 have a significant impact on the maximum vibration amplitude and vibration frequency of the two-cylinder system. Furthermore, unlike the resonance of a single cylinder, no frequency-locking phenomenon occurs. When the Reynolds number is constant, it is found that the changes in K2/K1 and D2/D1 change the natural frequency of the system, and the lift force coefficient (CL) of the cylinders and the phase between the lift force and displacement (φ) change accordingly. The maximum vibration amplitude of a cylinder is proportional to the parameter CLsinφ. Under certain frequency conditions, the amplitude of one cylinder is significantly suppressed. In addition, when the natural frequency of the system is fixed, the Reynolds number also changes the CL and φ of the cylinders. Therefore, the method of suppressing the vibration of one cylinder by coupling the other cylinder in parallel is severely restricted by the Reynolds number. The conclusion of this study has certain guiding significance for the structural design of dual submerged floating tunnels with elastic connections.

Performance Evaluation of Inerter-Based Dampers for Bridge Flutter Control: A Comparative Study

As the number of long-span bridges continues to grow, wind-induced vibration issues have become increasingly intensified. Among them, flutter is a serious wind-induced vibration that can lead to bridge collapse. To address this problem, this paper proposes inerter-based dampers as a solution for flutter control and compares their performance to traditional tuned mass dampers (TMDs). Firstly, eight distinct inerter-based dampers were proposed, based on various combinations of mass-inerter-spring-damper (MISD) components. Secondly, the equations of motion of the bridge-MISD system were derived based on the two-mode coupled flutter theory and the mechanical impedance analysis method. Thirdly, the flutter control performance of the eight proposed MISDs is examined using a simply supported beam, with the six better-performing dampers further evaluated using the Jiangyin Bridge. The results show that inerter-based dampers can effectively improve the critical flutter wind speed of bridges, with performance sensitive to frequency. Additionally, incorporating an inerter decreases the static displacement of the mass block, while increasing the mass of MISD and the distance between the damper and the section center improves flutter control performance. The optimal spring stiffness ratios for the six MISDs are identified, largely dependent on the damper’s inertance and mass. In conclusion, this paper offers a promising solution to addressing flutter in long-span bridges and provides insights into the design and optimization of inerter-based dampers.

Accurate Estimation of Inter-Story Drift Ratio in Multistory Framed Buildings Using a Novel Continuous Beam Model

This study presents a novel method for accurately predicting the dynamic behavior of multistory frame buildings under earthquake ground motion. The proposed method allows approximately estimating the inter-story drift ratio, a crucial parameter strongly associated with building damage, its distribution along the building height, and its maximum value location. An equivalent continuous beam model with a rotation at the base, consisting of a combination of a shear beam and a flexural beam, is proposed to achieve this. This model derives closed-form solutions for the building’s dynamic characteristics. The lateral deformations along the height of frame buildings subjected to a given earthquake load, particularly the inter-story drift ratio profiles, and the maximum inter-story drift ratio parameter, are investigated. The proposed continuous model requires two dimensionless parameters: the lateral stiffness ratio (α) and the rotation at the base (θ), representing the drift ratio of the first story. For the expression of the lateral stiffness ratio (α) coefficient, a simple equation is also proposed using the beam-to-column stiffness ratio (ρ, or Blume coefficient) associated with the framed (discrete) system. Various building models are employed to validate the proposed method, demonstrating its applicability to both high-rise and low-rise building configurations. With the results obtained, it is shown that the proposed continuous model can be used not only for high-rise or multistory building models but also for low-rise building models.

Investigation of Pounding between Two Adjacent Building Models with Experimental Methods

This study investigates the pounding phenomenon by shaking table experiments on two scaled building models. Representing the situation where the seismic gap is insufficient, two building models are adjacently positioned on the shaking table, and pounding was investigated for harmonic and strong ground motion excitations. Displacement and acceleration responses were obtained to observe the pounding effect experimentally from video and accelerometer recordings, respectively. The Kelvin-Voigt Model consisting of spring and damper was used for numerical pounding analysis. The most critical parameters of the Kelvin–Voigt model, which are the spring stiffness (ks) and the damping, are calculated according to the coefficient of restitution (r) and were investigated and compared with harmonic experimental results. The obtained parameters, compatible with the harmonic experiments, were used to examine structural behavior under earthquake effect for the case where the building models are positioned for an insufficient seismic gap. For comparison, numerous numerical simulations were realized using different spring stiffnesses and coefficients of restitution. The study shows that when the coefficient of restitution is taken as 0.2 or 0.4, and the ratio of spring stiffness to shear stiffness (ks/k) is 1 or 5, reasonable results in numerical earthquake simulations can be obtained.

Prediction of single pile response to lateral soil movement in model test

An analytical approach is presented for predicting the response of the pile by lateral soil movement in a model test in terms of the two-stage procedure. The prescribed lateral soil movements with inverse triangular, uniform, and arched profiles are examined in the analysis. The free-field displacement is obtained explicitly by the elasticity and Fourier expansion technique. The soil–pile interaction is considered for the response of the pile under soil movement in light of the theory of a beam on the Winkler foundation. Parametric studies are performed to investigate the effects of the soil–pile system and the loading conditions on the response of the pile. The free-field displacement attenuates quickly with its distance to the loading block. The pile response under lateral soil movement in the model test is greatly dependent on the pile location and the loading conditions. For the pile with a free tip, the deflection and bending moment of the shaft are relative to the restraint condition at the top. The effect of the pile-soil stiffness ratio is not great on the deflection of the pile but significant on the bending moment of the shaft.

Experimental and numerical study on the seismic behavior of an external prestressed self-centering frame structure

A kind of external prestressed self-centering frame (EPSCF) structure is proposed, and the numerical analytical modeling is given. In such a structure, the pure hinged beam-column joints and column base joints are adopted, the externally prestressed steel strands are utilized to provide lateral stiffness and restoring forces, and the inter-story metal dampers are installed to control displacement response. Based on the quasi-static cyclic tests of the EPSCF test frame, the prestressing forces and the hysteretic behavior of the EPSCF structure are investigated. The test results show that the load-displacement hysteretic curves of the EPSCF without damper exhibit a linear elastic characteristic with small residual displacement, and the load-displacement hysteretic curves of the EPSCF with damper show a full S-shape and significant two-stage characteristics. Installation of the X-type metal damper provides additional stiffness and improves the energy dissipation capacity for the EPSCF. FE model of EPSCF is established, and the hysteretic curves obtained by tests are in good agreement with the numerical simulation results. Parametric analysis indicates that with the increase of the relative stiffness ratio of the lateral stiffness, the seismic response of EPSCF shows a trend of decreasing structural displacement, increasing structural acceleration and base shear. Moreover, the simulation results suggest that the optimum range for the relative stiffness ratio is roughly 0.02–0.10.

Assessment of Soil-Structure Interaction in Reinforced Concrete Buildings Based on Structure to Soil Stiffness Ratio

Zemin-yapı etkileşimi (ZYE) binanın periyodunu uzatırken yapısal sönüm oranını artırır. Binanın dinamik özelliklerindeki söz konusu değişim genellikle dinamik davranış açısından elverişli kabul edildiğinden ZYE tasarım yönetmeliklerinin birçoğunda ihmal edilmektedir. Fakat çok sayıda araştırma ZYE’nin ihmal edilmesinin binanın dönme sünekliği talebinin ve tepe deplasmanının olduğundan az hesaplanması yoluyla güvensiz tasarıma neden olduğunu işaret etmektedir. Bu sebeple ZYE’nin öneminin belirlenmesi güvenli tasarım için gereklidir. Bu çalışmada ZYE’nin tasarımdaki önemi periyot uzamasını kontrol eden en önemli parametre olan yapının zemine rijitlik oranı yardımıyla değerlendirilmiştir. Rijitlik oranı, faklı kat adedine sahip çerçeve taşıyıcı sisteme sahip binalarda farklı zeminler için hesaplanmış ve %5 periyot uzamasına sebep olan 0.1 değeri eşik kabul edilmiştir. ZYE'nin ZE, ZD ve ZC zeminlerde göz önüne alınması gerektiği, ZB ve ZA zeminlerde ihmal edilebileceği gösterilmiştir.

Improving energy harvesting from low-frequency excitations by a hybrid tri-stable piezoelectric energy harvester

This paper presents the design of a novel hybrid tri-stable piezoelectric energy harvester (HTPEH) that improves the energy harvesting efficiency of piezoelectric energy harvesters operating at low frequencies. The proposed HTPEH is an extension of a conventional tri-stable cantilever piezoelectric energy harvester with an elastic base (TPEH + EB), and it incorporates vertical and rotational elastic amplifiers that are installed between the mass block at the left end of a cantilever beam and the left side of a U-shaped frame to enhance the system's nonlinear characteristics. By utilizing Hamilton's principle, a HTPEH's nonlinear electromechanical equation is formulated, and the harmonic balance method is used to obtain analytical solutions for the displacement amplitude, voltage amplitude, and power amplitude. The study investigates the effects of various parameters, including the elastic amplifier-to-base stiffness ratio and elastic amplifier-to-piezoelectric cantilever beam mass ratio on the energy harvesting performance of the HTPEH. The results indicate that the displacement and voltage amplitude of the HTPEH exhibit two peaks as the external excitation frequency increases, and adjusting the relative mass and stiffness between the elastic amplifier and the piezoelectric cantilever beam can alter the frequency band interval where the two response peaks of the system are located. This allows the HTPEH to enter inter-well motion at low-level external excitation, resulting in high output power. The HTPEH outperforms the TPEH + EB in terms of energy harvesting efficiency under low-frequency environmental excitation.

Numerical and analytical investigation of U-shape dampers and its effect on steel frames

Yielding dampers are one of the structural systems which dissipate a portion of the seismic force via premature yielding. The numerical and analytical methods were used in this study to investigate the behavior of the U-Shape Damper (USD) and its effect on steel frames. For this purpose at first, extensive parametric studies were performed using calibrated USD model. The parametric studies involved investigating the effect of USD dimensions on its elastic stiffness, strength, effective stiffness, and equivalent viscous damping ratio. Finite element models were analyzed under cyclic loading using nonlinear static analysis. An analytical equation was then presented to estimate seismic parameters of the USD. In the second part, the effect of this damper on the steel frame was investigated using push over analysis. The seismic parameters of the frame, including elastic stiffness, strength, ductility, and energy dissipation, were investigated through 56 numerical models to determine the effects of the number of USDs and the axial force of the column. The results indicated that reducing the radius and increasing the thickness of the damper led to an increase in effective stiffness, energy dissipation, and strength, while reducing the equivalent viscous damping ratio. Furthermore, the results obtained from the steel frame equipped with a USDs revealed that the addition of the damper mitigates the adverse effects of axial force on the frame.

Reinforcement of cracked aluminum plates using polymeric composite patches embedded with prestressed SMA wires

Many studies have been performed on composite patches as reinforcement of cracked metal sheets. However, in most previous research, composite patches without prestressing have been used to repair cracks. In the present study, a novel method for repairing cracked aluminum sheets is proposed by using polymer composite patches with embedded prestressed Nitinol shape memory alloy (Ni-Ti SMA) wires. Elastic-plastic finite element analysis of an aluminum plate, with a central crack in the pure mode I and the mixed-mode I/II fracture, repaired with SMA wires reinforced composite patch (SMA-CP) was performed. The peel stress on the adhesive layer between the composite patch and the aluminum plate was calculated to evaluate the performance and efficiency of the repair. The effect of the prestress of the embedded Ni-Ti SMA wires on the efficiency of the composite patch was examined. The results show that embedding prestressed SMA wires in the composite patch reduces the stiffness ratio of the patch. Also, the value of the J-integral and the size of the plastic area compared to the patch without SMA wires were decreased.