Shape memory alloys (SMAs) often exhibit functional fatigue, characterized by the accumulation of reorientation-induced plasticity and a decrease in the hysteresis loops presented in the stress–strain curves during thermomechanical cycling. While existing cyclic models capture these mechanisms, they require expensive cycle-by-cycle simulation. In this study, thermomechanical cyclic experiments are conducted to characterize the evolution and saturation of reorientation-induced plastic strain during training. An engineering numerical model is developed to efficiently predict the stabilized trained configuration and actuation performance without simulating the full cyclic degradation process. For finite element implementation of the developed model, a return mapping integration algorithm is proposed and programmed into an ABAQUS UMAT subroutine. Comparisons between simulations and experiments show that the proposed model can capture the stabilized thermomechanical response and provide predictions of trained shape and actuation capacity.

Flexible piezoelectric composites are increasingly used in wearable and adaptive structures. However, their geometric nonlinearity and pronounced anisotropy pose significant challenges for reliable prediction of fracture and fatigue under electromechanical loading. This work develops an anisotropic phase-field fracture model for flexible piezoelectric composites at finite strains, in which distinct softening laws are assigned to the isotropic matrix and anisotropic fibers. To eliminate unphysical fracture modes, the energy density is decomposed using the volumetric-stretch tension-compression scheme. This model is further extended to fatigue by introducing a cumulative history variable that captures the progressive degradation of fracture toughness under cyclic loading. Numerical results demonstrate that, with a large penalty parameter in anisotropic crack surface density function, the predicted crack path aligns with the fiber orientation, and the global responses are consistent with available experimental observations. For flexible piezoelectric composites, the fracture behavior is influenced by fiber orientation and applied electric fields. For composites with symmetric fiber families, enhanced mechanical performance and stabilized crack trajectories are observed. The proposed framework provides theoretical flexibility and computational robustness for predicting fracture and fatigue failure in flexible piezoelectric composites, enabling reliability-driven design of next-generation flexible piezoelectric devices.

A phase field framework is developed to simulate fracture behavior in flexible piezoelectric composites under electromechanical loading. Existing piezoelectric phase field fracture models may encounter numerical challenges for highly stretchable systems, such as spurious damage evolution near electrode edges. To mitigate this issue, we introduce a higher-order exponent degradation function to locally reduce the piezoelectric and dielectric parameters near the electrodes. This localized treatment regularizes the electromechanical contribution to the stress response while retaining the original crack-driving energetic formulation, thereby suppressing non-physical crack growth near electrodes. Notably, the original material properties are preserved in the remaining regions. The formulation is implemented in ABAQUS via a user element subroutine (UEL). Numerical results show that the unmodified formulation may develop spurious electrode-edge damage, which can trigger premature failure; the proposed modification effectively suppresses this numerical artifact. When spurious damage does not occur, the modified and unmodified predictions are nearly identical, indicating a negligible impact on the global response. In addition, systematic simulations are performed to quantify the effects of inclusion type, size, and spatial arrangement on the fracture behavior of flexible piezoelectric composites.

Within the finite-deformation framework, a unified modeling approach is developed for flexible piezoelectric composites based on the phase-field cohesive zone model (PF-CZM), accounting for both bulk fracture and interfacial failure. Unlike previous studies that primarily address brittle composites under small deformations, this work focuses on stretchable flexible piezoelectric materials exhibiting pronounced geometric and material nonlinearities, which lead to strongly coupled governing equations and increased computational complexity. An interface phase-field parameter is introduced to describe diffuse interfaces, while a crack phase-field parameter governs crack propagation. The model accommodates various cohesive softening laws to simulate interfacial failure and captures the influence of interface strength on overall fracture performance. The numerical framework is implemented in ABAQUS, with a HETVAL subroutine used for the diffuse interface modeling and UEL for fracture simulations. When damage is primarily localized within the matrix, neglecting the interface effects significantly reduces computational cost without compromising accuracy. In cases involving interfacial failure, the model effectively investigates the role of interface strength in crack propagation and fracture characteristics. Numerical results demonstrate the effects of interface strength, applied electric fields, and inclusion size on fracture behavior. Higher interface strength enhances peak load capacity and resistance to failure, with weaker interfaces favoring interfacial cracking and stronger interfaces promoting matrix cracking. Furthermore, in flexible piezoelectric materials bonded to soft substrates, interfacial debonding may be triggered by applied electric fields, a phenomenon supported by both numerical simulation and experimental observation.

Based on the Hilbert–Riemann theory, this paper develops a simplified model to address interfacial fracture in bi-layer laminated solar cells with significantly dissimilar thermal properties. The model is used to analyze interfacial normal stress distributions and identify critical stress points, taking into account the substantial mismatch in the coefficients of thermal expansion between the semiconductor and encapsulation layers. The predicted temperature and stress fields are validated through finite element simulations. Furthermore, by investigating commonly used encapsulation films and solar cell modules, the coupled effects of the thermal expansion coefficient and elastic modulus are elucidated. The results demonstrate that, under a constant layer thickness, the position of the stress critical point is governed by two dimensionless parameters: the ratio of thermal expansion coefficients and the ratio of elastic moduli. This work offers an efficient and practical approach for predicting thermal stress concentration trends in laminated solar cell structures, thereby providing useful insights for the design and fabrication of solar modules.

Strain solitons have been widely observed in van der Waals materials and their heterostructures. They can manifest as one-dimensional (1D) wires and quasi-two-dimensional (2D) networks. However, their coexistence within the same region has rarely been observed, and their interplay remains unexplored. Here, employing lateral piezoresponse force microscopy, we show that 1D linear solitons and 2D moiré solitons appear simultaneously and interact in twisted multilayer graphene. In twisted monolayer-bilayer graphene, when a linear soliton intersects with moiré solitons, the polarization reverses across the intersections, splitting a polar vortex into two vortices. Interestingly, when a linear soliton is parallel to a moiré soliton, they can annihilate each other in certain case, resulting in the unification of polar vortices. In twisted monolayer-trilayer graphene, linear solitons from different interfaces can be resolved. Our results provide new insights for the interplay between different solitons and pave a new way for engineering moiré physics.

Light-based 3D printing techniques have recently been used to construct soft materials like hydrogels into complex architectures. However, when these extremely soft materials are printed into fine structures with feature sizes as small as microscale or even nanoscale, the resulting structures may be distorted by surface tension, which comes into play when the surface energy exceeds the material’s bulk elastic energy. In order to elucidate the basic effects of surface tension on shape distortion, we here develop a finite-element modeling method to study the difference between the resulting shape and designed shape of a photo-cured micro-strut. This method relies on a continuum framework that efficiently considers the evolution of material properties and the action of surface tension during the photo-curing process. The modeling results show that the resulting shape of the micro-strut is highly correlated with the strength of the surface tension, which can sometimes hinder the undesired deformation caused by the volume shrinkage associated with photo-polymerization. This study can provide some basic understanding for the reduction of shape distortion in printing soft materials with microscale and nanoscale features, and facilitate the design of devices with better performance.

Topological polar textures in ferroelectrics have attracted significant interest for their potential applications in energy-efficient and high-density data storage and processing. Among these, polar merons and antimerons are predicted in strained and twisted bilayers of inversion symmetry broken systems. However, experimental observation of these polar textures within twisted two-dimensional van der Waals materials remains elusive. Here, we utilize vector piezoresponse force microscopy to reconstruct the polarization fields in R-type marginally twisted hexagonal boron nitride. We observe alternating out-of-plane polarizations at domain regions and in-plane vortex-like polarization patterns along domain walls, indicative of a network of polar merons and antimerons. Notably, the out-of-plane polarization exhibits three polarity reversals across a domain wall. Similar polar textures are identified in marginally twisted WSe2 and MoSe2 homobilayers. Our theoretical simulations attribute these unusual polarization reversals near the domain walls to the competition between moiré ferroelectricity and piezoelectricity. These results provide the experimental evidence of complex polar textures in moiré ferroelectrics, which may offer additional insights into the electronic band topology in twisted transition metal dichalcogenides.

Solar arrays are subjected to drastic thermal cycling in space orbits, which induces stress concentrations or even failure due to thermal expansion mismatches among the GaAs solar cell, aerospace silicone rubber, and substrate. Therefore, it is necessary to determine the mechanical properties of aerospace silicone rubber and design reasonable adhesive structure distribution at the joint to reduce the stress concentration of the solar arrays. Firstly, the viscoelasticity theory was employed, where the mechanical properties and viscoelastic parameters of aerospace silicone rubber are obtained by the Dynamic Mechanical Analysis (DMA) experiment. Then, a three-dimensional finite-deformation thermodynamic model of the Time–temperature superposition process of Thermo-rheological-simple polymers is constructed in Abaqus. Finally, the solid isotropic material with penalization (SIMP) method is utilized to determine the optimal distribution of materials in the design domain by topology optimization, and the microstructure of aerospace silicone rubber topology is reshaped. The results show that the finite element method can accurately predict the stress distribution of the solar arrays in the operating environment. In addition, the topological optimization design aids in reducing stress concentration in the structure and provides a theoretical basis for addressing such problems.

Fracture failure is a major concern in mechanical engineering, particularly for piezoelectric materials. In contrast to other numerical methods, phase field method has significant advantages in addressing fracture progress. It can automatically track crack surfaces through ordered parameter evolution, which is versatile for modeling complex fracture behaviors. However, previous studies on phase field fracture in piezoelectric solids have primarily focused on brittle ceramics with small deformation. In recent years, flexible piezoelectrics with high stretchability have already been achieved in industrial production. These materials exhibit obvious nonlinear characteristics during deformation, which renders the traditional assumption of small deformations inadequate for predicting their fracture behaviors. In this work, we propose a finite deformation phase field fracture model for flexible piezoelectric materials, building upon the established nonlinear electromechanical material model. The numerical framework is carried out in the commercial software ABAQUS via a user element subroutine. Both single–pass staggered algorithm (SPSA) and residual-controlled staggered algorithm with even-odd iteration split (RCSA-EO) are employed to solve coupled electro-mechanical-phase field governing equations. The proposed model is validated through comparisons with analytical solutions and existing literature. Moreover, the developed numerical framework effectively explains the nonlinear fracture behavior observed in experiments conducted on Polyvinylidene fluoride (PVDF), a flexible piezoelectric material with a large failure strain. Numerical simulations are also performed to demonstrate the influence of the applied electric field on electromechanical fracture behavior. The results highlight that the specific impact of electric fields depends on material parameters, geometric parameters, and boundary conditions. The developed model is capable of making accurate and realistic predictions of fracture in flexible piezoelectric materials. This is particularly important for evaluating the reliability and safety of flexible piezoelectric devices.

The applications of piezoelectric materials in the field of smart structures have received significant attention from both the communities of science and engineering. Numerous experimental studies have been carried out to endow smart structures with good flexibility. The flexible/stretchable piezoelectric materials are developed to fit this emerging trend. Generally, these materials undergo significant deformation before reaching fracture failure, and they often exhibit a stress-softening phenomenon during the deformation process. However, the traditional linear constitutive model, typically used for rigid piezoelectric ceramics, continues to dominate theoretical and modeling processes in many scenarios. Existing nonlinear constitutive models usually introduce additional coefficients besides elastic, piezoelectric, and dielectric coefficients. Determining these coefficients requires a substantial number of experiments. In this work, based on a Neo-Hookean material model and electromechanical theory, a novel model for flexible piezoelectric material considering large deformation has been established. In contrast with existing models, the present model describes the nonlinear behavior of flexible piezoelectric material without the need for introducing additional parameters. Furthermore, this model exhibits a quadratic dependence of stress on the electric field. To facilitate practical applications, the constitutive model has been implemented using the commercial simulation software ABAQUS through a user subroutine. The accuracy of the subroutine is validated by comparing simulations with analytical solutions for uniaxial stretching of a flexible piezoelectric ribbon. Several numerical examples are followed to demonstrate the robustness of the elements. The proposed model offers a valuable tool for the analysis and design of flexible piezoelectric material.

As a composite structure, the single fixed clamp (SFC) is an important supporting component of the aeroengine piping system. The dynamic parameters (stiffness and damping) of SFC have significant differences in bolt direction and opening direction. Accurately identifying the dynamic parameters of an SFC in both directions is of great significance for the study of pipeline system dynamics. At present, there is very little research on the identification of dynamic parameters for such SFC. Therefore, an SFC-straight pipe structure for identifying the dynamic parameters of an SFC is proposed in this paper. In this structure, one end of the straight pipe is completely fixed, and the other end is supported by an SFC. This structure can better reflect the working state of the SFC. A dynamic model of this structure is established based on the finite element method for parameter identification of SFC. In the finite element model (FEM), the constraint effect of the SFC is simplified into two identical spring-damping groups. Considering the structural asymmetry, spring and damping parameters for bolt direction and opening direction are separately set in each spring damping group. Next, based on the Pareto multi-objective genetic algorithm, an identification algorithm and procedure for the stiffness and damping of the SFC using modal test data as input parameters are proposed. Through experimental testing, parameter identification is carried out for DK8 type SFC, and a straight pipe experimental structure completely supported by two SFCs is constructed to verify the correctness of the identification results.

Flexible piezoelectric materials have gained considerable attention due to their remarkable properties, including electromechanical coupling and high stretchability. These characteristics make them valuable in the realm of flexible electronic devices. However, the issue of fracture in these materials cannot be ignored. In general, these flexible/stretchable materials experience fractures when subjected to significant deformation, unlike brittle piezoelectric materials with low failure strain which have been extensively studied. There is a pressing need to investigate the fracture behavior of flexible piezoelectrics under finite deformation conditions. Within the framework of the phase field method, this work addresses the fracture of flexible piezoelectrics utilizing a nonlinear electromechanical material model. To investigate the influence of electrical boundary conditions on fracture behavior, a function related to the electric permittivity ratio and phase field variable is employed to degrade the electric energy density. By adjusting the electric permittivity ratio, the analysis encompasses the fracture behavior of flexible piezoelectric materials under the assumptions of electrically impermeable, semi-permeable, and permeable conditions, respectively. In order to solve the coupled governing equations, a residual controlled staggered algorithm (RCSA) is employed in the user element subroutine of commercial software ABAQUS. The simulation results indicate that fracture behavior in flexible piezoelectric materials is influenced by several factors, including material parameters, geometry, polarization direction, and the external electric field. Notably, when the poling direction is perpendicular to the electric field direction, variations in the external electric field have a minimal impact on fracture behavior. In contrast, when the poling direction is parallel to the electric field direction, the influence on fracture behavior is pronounced. These findings provide valuable insights for developing strategies to enhance the fracture resistance and durability of flexible piezoelectric materials in practical applications.

During long-term service in space, Gallium Arsenide (GaAs) solar cells are directly exposed to electron irradiation which usually causes a dramatic decrease in their performance. In the multilayer structure of solar cells, the germanium (Ge) layer occupies the majority of the thickness as the substrate. Due to the intrinsic brittleness of semiconductor material, there exist various defects during the preparation and assembly of solar cells, the influences of which tend to be intensified by the irradiation effect. In this work, first, Ge specimens for mechanical tests were prepared at scales from microscopic to macroscopic. Then, after different doses of electron irradiation, the mechanical properties of the Ge specimens were investigated. The experimental results demonstrate that electron irradiation has an obvious effect on the mechanical property variation of Ge in diverse scales. The four-point bending test indicates that the elastic modulus, fracture strength, and maximum displacement of the Ge specimens all increase, and reach the maximum value at the irradiation dose of 1 × 1015 e/cm2. The micrometer scale cantilever and nanoindentation tests present similar trends for Ge specimens after irradiation. Atomic Force Microscope (AFM) also observed the change in surface roughness. Finally, a fitting model was established to characterize the relation between modulus change and electron irradiation dose.

Controlling the balance between piezoelectric and flexoelectric effects is crucial for tailoring the electromechanical responses of a material. In twisted graphene, it is found that the electromechanical response near the domain walls (DWs) is dominated by either the flexoelectric effect as in twisted bilayer graphene (tBLG) or the piezoelectric effect as in twisted monolayer–bilayer graphene (tMBG). The codominance of both effects in a single system is rare. Here, utilizing lateral piezoresponse force microscopy (LPFM), we show that piezoelectric and flexoelectric effects can coexist and are equally important in twisted double bilayer graphene (tDBG), termed as the piezo-flexoelectric effect. Unlike tBLG and tMBG, distinctive two-step LPFM spatial profiles are captured across the moiré DWs of tDBG. By decomposing the LPFM signal into axisymmetric and antisymmetric components, we find that the angular dependence of both components satisfies sinusoidal relations. Quantitatively, the in-plane piezoelectric coefficient of DWs in tDBG is determined to be 0.15 pm/V by dual AC resonance tracking (DART) LPFM measurement. The conclusion is further supported by continuum mechanics simulations. Our results demonstrate that the stacking configuration serves as a powerful tuning knob for modulating the electromechanical responses of twisted van der Waals materials.

The coupling of mechanical deformation and electrical stimuli at the nanoscale has been the subject of intense investigation in the realm of materials science. Recently, twisted van der Waals (vdW) materials have emerged as a platform for exploring exotic quantum states. These states are intimately tied to the formation of moiré superlattices, which can be visualized by directly exploiting the electromechanical response. However, the origin of the response, even in twisted bilayer graphene (tBLG), remains unsettled. Here, employing lateral piezoresponse force microscopy (LPFM), we investigate the electromechanical responses of marginally twisted graphene moiré superlattices with different layer thicknesses. We observe distinct LPFM amplitudes and spatial profiles in tBLG and twisted monolayer-bilayer graphene (tMBG), exhibiting effective in-plane piezoelectric coefficients of 0.05 and 0.35 pm/V, respectively. Force tuning experiments further underscored a marked divergence in their responses. The contrasting behaviors suggest different electromechanical couplings in tBLG and tMBG. In tBLG, the response near the domain walls is attributed to the flexoelectric effect, while in tMBG, the behaviors can be comprehended within the context of the piezoelectric effect. Our results not only provide insights into electromechanical and corporative effects in twisted vdW materials with different stacking symmetries but may also offer a way to engineer them at the nanoscale.

A wide variety of photo-cured materials have recently been developed with the rapid advancement of three-dimensional (3D) printing technology. However, most of these materials are designed as soft functional materials, and their failure mechanisms have received little attention. This work studies the mesoscale residual stress defects of photo-cured materials that are generated due to non-uniform curing and volume shrinkage during the manufacturing process. The defects are simplified as uncured inclusions embedded within a fully cured, infinite matrix which are then additionally cured. A large deformation model, validated against finite element analysis, is established to determine the nonlinear elastic field induced by the curing of inclusions with different Poisson’s ratio and shape (i.e., sphere and prolate spheroid), and is shown to outperform the infinitesimal strain model. This large deformation model, which includes a phase evolution constitutive model to describe the inclusion’s behavior and a compressible neo-Hookean model to describe the matrix’s behavior, is derived based on the same elastic field distribution as that in the infinitesimal strain solution and an ellipsoid-ellipsoid transformation kinematics assumption. The final solution is expressed in a discrete formulation and is exact for the spherical inclusion and approximate for the prolate spheroid inclusion. The prediction results of the theoretical model are compared with the finite element analysis, and reasonable agreement is obtained. This study may lay a foundation for investigating the effects of mesoscale residual stress defects on the mechanical behavior of 3D printing materials.

Porous elastomeric materials have wide applications in aerospace, electronics, biomedicine, and other fields. However, closed-form analytical solutions for macroscopic strain energy density of high-order porous elastomers have not been well resolved. In this work, we propose a new approach for constitutive modeling of porous elastomeric materials under large deformation, mainly relying on expressing the macroscopic strain energy density function of the composite material as a function of the strain energy of elastomer matrix via a strain-amplification relation. Such amplification relation, as constructed through a thick-walled sphere volume element model, is utilized in a mapping of the macroscopic deformation to the average deformation of elastomer matrix in the sense of the first invariant by a scaling coefficient–amplification factor, which depends on both the initial void volume fraction and the macroscopic volumetric deformation ratio. The analytical stress–stretch relation is then derived and given in simple form of only three material parameters. Discussions on how the factors affect the amplification factor are made and the behavior of the model is shown in several deformation simulations. The prediction results of this model are compared with those of existing models, and reasonable agreement is obtained.