Nonlinear Deformation Research Articles

Modelling of water injection-induced shear stimulation and heat extraction in hot fractured reservoirs

Hydroshearing has been proposed as an effective technique for enhancing the permeability of fractured geothermal reservoirs. This approach involves complicated thermo-hydro-mechanical (THM) coupling, but the shear behaviour and its effect on flow and heat transfer are often simplified. In this study, Barton–Bandis (BB) joint behaviour is extended to include nonlinear rock joint deformation, shear dilation and post peak softening and healing behaviours. Two models of field-scale fractured geothermal reservoirs are considered. In addition, the widely used Mohr-Coulomb (MC) model is also incorporated into the THM coupled model for comparison. The results show that cold water injection-induced high-temperature rock contraction and fluid pressure increase, reducing the effective stress and promoting fracture shear deformation and irreversible slip. Moreover, shear dilation, shear softening, and nonlinear fracture opening notably alter reservoir permeability. The two models exhibit entirely different behaviours due to different pathway evolutions and consequent pressure build-up. The BB model displays a larger shear disturbance zone than the MC model, significantly enhancing the permeability and heat extraction within the fractured reservoirs. Accurate descriptions of the mechanical behaviour of rock fractures in hydroshearing models are crucial, suggesting the potential of these models to enhance fractured reservoirs and regulate fracturing for improved geothermal heat extraction.

Synthetic control of actin polymerization and symmetry breaking in active protocells.

Nonlinear biomolecular interactions on membranes drive membrane remodeling crucial for biological processes including chemotaxis, cytokinesis, and endocytosis. The complexity of biomolecular interactions, their redundancy, and the importance of spatiotemporal context in membrane organization impede understanding of the physical principles governing membrane mechanics. Developing a minimal in vitro system that mimics molecular signaling and membrane remodeling while maintaining physiological fidelity poses a major challenge. Inspired by chemotaxis, we reconstructed chemically regulated actin polymerization inside vesicles, guiding membrane self-organization. An external, undirected chemical input induced directed actin polymerization and membrane deformation uncorrelated with upstream biochemical cues, suggesting symmetry breaking. A biophysical model incorporating actin dynamics and membrane mechanics proposes that uneven actin distributions cause nonlinear membrane deformations, consistent with experimental findings. This protocellular system illuminates the interplay between actin dynamics and membrane shape during symmetry breaking, offering insights into chemotaxis and other cell biological processes.

An effective nonlinear dynamic formulation to analyze grasping capability of soft pneumatic robotic gripper

ABSTRACT Soft pneumatic robotic grippers have found extensive applications across various engineering domains, which prompts active research due to their splendid compliance, high flexibility, and safe human-robot interaction over conventional stiff counterparts. Previously simplified rod-based models principally focused on clarifying overall large deformation and bending postures of soft grippers from static or quasi-static perspectives, whereas it is challenging to elaborate grasping characteristics of soft grippers without considering contact interaction and nonlinear large deformation behaviors. To address this, based on absolute nodal coordinate formulation (ANCF), comprehensively allowing for structural complexity, geometric, material and boundary nonlinearities, and incorporating Coulomb’ friction law with a multiple-point contact method, we put forward an effective nonlinear dynamic modeling approach for exploring grasping capability of soft gripper. Moreover, we solved the established dynamic equations using Generalized-α scheme, and conducted thorough numerical simulation analysis on a three-jaw soft pneumatic gripper (SPG) in terms of grasping configurations, displacements and contact forces. The proposed dynamic approach can accurately both describe complicated deformed configurations along with stress distribution and provide a feasible solution to simulate grasping targets, whose effectiveness and precision were analyzed theoretically and verified experimentally, which may shed new light on devising and optimizing other multifunctional SPGs.

Modeling Analysis of Complex Deformation of Woven Coating Film during the Cyclic Tensile Process.

It is difficult for the existing Burgers model to accurately depict the off-axis cyclic drawing process of woven coatings. In this paper, the mechanical deformation of woven PVC (polyvinyl chloride)-coated film at different temperatures is investigated. One-dimensional (1D) and two-dimensional (2D) constitutive models were established to characterize cyclic deformation processes. The 1D model is an improved Burgers model. The effects of the time dependence of the viscosity coefficient and the ratio of elastic to viscous deformation are considered simultaneously. The accuracy of the 1D model for predicting the cyclic nonlinear deformation at different temperatures and loading rates is improved. The 2D model is a nonlinear orthotropic model using polynomials. On the basis of the single-objective genetic algorithm, the inverse algorithm is used to obtain the shear polynomial coefficients in the tension phase and the shear modulus in the unloading phase, which circumvents performing the difficult shear test. UMAT subroutines of off-axis stretching and off-axis cyclic stretching are written separately. The intelligent inverse algorithm program consists of a single-objective genetic algorithm program, a finite element parametric modelling program, and a UMAT subroutine. The simulation results are compared with the off-axis cyclic tensile test data to validate the effectiveness and accuracy of the proposed 2D model for the analysis of the woven PVC-coated films in the tension-shear coupling state.

A refined model for the flexural behavior of reinforced UHPC members under sustained loading

The long-term behavior of reinforced Ultra-High Performance Concrete (UHPC) members is significantly influenced by UHPC’s creep properties. To predict the long-term performance of structural members, it is essential to have both a material-level creep model and a constitutive model for structural analysis. This paper presents a refined model for the long-term performance of UHPC, incorporating critical nonlinear deformation mechanisms: instantaneous damage, plastic strain, creep strain, and time-dependent damage. The constitutive model for instantaneous damage and plastic strain mechanisms is based on experimental data from short-term cyclic loading tests on UHPC specimens. Additionally, the creep strain components and time-dependent damage evolution laws are derived from well-established linear and nonlinear creep models, validated for cementitious materials through extensive research. The model parameters were meticulously calibrated using creep damage test results from UHPC. The validation process included linear and nonlinear creep tests on UHPC cylinders under sustained stress levels ranging from 0.2fc to 0.66fc, creep failure tests on UHPC cylinders under sustained stress levels from 0.85fc to 0.95fc, and long-term bending tests of reinforced UHPC beams under sustained load. In the linear and nonlinear creep tests, comparison between the calculated ultimate creep coefficients and the experimental results demonstrates the model’s validity under low and moderate stress levels. In the creep failure test, a comparative analysis of strain evolution and creep lifetime between experimental and model results confirms the model’s validity under high sustained stress levels. Similarly, during the long-term bending test, simulated time-dependent displacement and compressive strain show good agreement with the experimental data, confirming the model’s accuracy in predicting the long-term performance of reinforced UHPC members. Furthermore, to streamline the constitutive model, the instantaneous damage effect was simplified and ultimately neglected. A comparison of simulation results between the original model and the simplified version demonstrates that disregarding the instantaneous damage effect is a safe approach for practical engineering applications.

Design and Nonlinear Dynamic Response of a Steel Stack

AbstractIndustrial stacks are built in order to reduce atmospheric pollution and release gases to the higher level of the atmosphere. Since they are high and slender structures, they are significantly affected by lateral forces, in particular, induced by winds and earthquakes. This paper aims to summarize the design principles for steel stacks given in the international standards, codes and specifications considering the evaluation of the results from the investigation on nonlinear dynamic response of a typical steel stack subjected to the earthquake. For this purpose, a typical self-supporting steel stack has been designed and its performance under earthquake and wind forces has been investigated in terms of the applied design principles, such as the displacement limit and the potential plastic deformations. The study is accomplished by using finite element models employing nonlinear time history and pushover analyses. The numerical results are presented particularly by considering the design principles used for the model. The results show that wind loads considered are more pronounced in the design of industrial steel stacks than earthquake especially in terms of limiting top displacement. The flue openings which reduce strength and lateral stiffness of the stack web is significantly effective in the lateral behavior of the stack. Moreover, the principles considered are found applicable for the design of such steel stacks. Based on the results from nonlinear time history analyses, no yielding and plastic deformation are detected along the stack.

MODELING THE DYNAMICS OF DEFORMABLE OBJECTS BASED ON VOLUMETRIC PATCHES OF FREE FORMS

A method for solving nonlinear implicit numerical integration problems based on volumetric patches of free forms for modeling deformable objects with high-speed dynamics is proposed. This method improves the accuracy, consistency and controllability of deformation modeling and animation. The method is characterized by speed, accuracy, stability and uses optimization with region decomposition. The method is well suited for modeling deformable bodies with a large time step, in a wide range of deformation dynamics. We propose decomposed optimization, an optimization method based on free-form patches with region decomposition to minimize incremental potentials at each time step. The method uses quadratic matrix decomposition to combine non-overlapping subregions. The Hessian is evaluated once at the beginning of the time step. The advantages of the method are as follows. Geometric primitives and their mathematical models are proposed, which allow the reasonable application of these primitives to solve problems of volume-oriented modeling. Such requirements are met by volumetric patches of free forms based on analytical perturbation functions relative to the base triangles. The decomposed Hessian is constructed for each subregion and calculated using a set of vertices taken from a complete non-decomposed grid. The weights add the missing second-order Hessian data to the vertices of the subregions from the neighbors along the decomposition boundaries. Thanks to this, the descent is performed along the grid coordinates. There is no need to add gradients. During the descent, the gradient is determined. The Hessians under the region are calculated and factorized in parallel once per time step. They are used as an initializer at each iteration. Then the results are mixed together. This ensures stable and continuous high-quality modeling. An automated and reliable optimization method adapted for modeling nonlinear materials, high-speed dynamics and large deformations is proposed.

Nonlinear vibration of five-layered functionally graded piezoelectric semiconductor nano-plate on Pasternak foundation

The vibration character of piezoelectric semiconductor nano-plate is important for understanding the multi-fields coupling and optimizing the serving behavior. In this article, the nonlinear vibration of five-layered functionally graded piezoelectric semiconductor nano-plate based on Pasternak foundation is studied, and the nonlocal theory is used to analyze the size-dependent dynamic response of nano-plate. Combining the Von karman’s nonlinear deformation theory and the constitutive of piezoelectric semiconductor layers, Hamilton’s principle is introduced to derive the nonlinear governing equations. To solve the nonlinear governing equations, the updated iteration method for this problem is proposed. Through numerical examples, it is found that the initial electron concentration in piezoelectric semiconductor layer, the nonlocal parameter, the functionally graded index in the plate, the elastic modulus of Pasternak foundation and the geometrical parameters can be designed to effectively tune the dynamic nonlinear frequency and damping of layered functionally graded piezoelectric semiconductor nanoplate. The interaction of these parameters is also analyzed in detail. Comparison with existing numerical results is also presented. A new way is provided to tune the nonlinear vibration of multi-layered piezoelectric semiconductor nano-plate.

An improved creep model for unsaturated reticulated red clay

Establishment of a creep model is an important method to analyze the relationship between soil creep deformation and time, and the element model is widely used for studying soil creep. However, the element creep model is employed for fitting saturated soil, and the mechanical element model is generally linear, which cannot well fit the nonlinear deformation of the soil with time in practice. The creep process of the soil is not only time-dependent, but also related to the deviatoric stress level. Therefore, the fractional calculus theory and a parameter n reflecting the effect of deviatoric stress level on the creep properties of the soil were introduced into the element model, and the fractional qBurgers creep model was established by using the fractional Koeller dashpot and Caputo fractional calculus. The proposed model was used to fit the triaxial test data of reticulated red clay under different net confining pressures and matric suctions by unsaturated triaxial apparatus. The proposed model can well describe the nonlinearity of unsaturated reticulated red clay, has memory and global correlation to the creep development process of unsaturated reticulated red clay, and has clear physical meaning. The functional relationships of the model parameters with the matric suction, net confining pressure and deviatoric stress level were deduced, so that the creep curves of unsaturated reticulated red clay can be obtained for any conditions, which is of great value for the study of unsaturated soils.

Theoretical prediction model for the compressive behavior of the hybrid tube considering compression angle

AbstractThe oblique collision happening in vehicle accidents poses a huge threat to passive safety, which causes great difficulties in the design of energy absorption (EA) structures and the prediction of EA capacity due to its highly nonlinear deformation characteristics. This study aims to establish a theoretical prediction model for the compression performance of Carbon Fiber Reinforced Polymer (CFRP)/Al hybrid tube considering the loading angle. First, a high‐precision FE model was established to obtain the influence laws of tube diameter, Al thickness, and CFRP thickness on the crashworthiness of CFRP/Al hybrid tubes, laying the foundation for subsequent theoretical model validation. Second, by summarizing the deformation modes of hybrid tubes generated by various parameter combinations, a modified global origami deformation assumption was proposed under multi‐angle compression conditions, and the key terms in energy composition are extracted based on the initial and final states of folding elements. Third, a theoretical model for predicting the mean crushing forces (MCFs) of hybrid tubes was established by revealing the correlation mechanism between energy composition terms and loading angle. Finally, the theoretical prediction model was validated by experiment and simulation results and the application premise was given. Results showed that the theoretical prediction model was proved to be of high accuracy, as the average absolute prediction errors of MCF under axial, 10°, 20°, and 30° compression conditions were 6.54%, 4.63%, 3.72%, and 3.93%, respectively. This study provides valuable guidance for the forward design and development of multi‐material hybrid structures facing complex crushing conditions.Highlights An analytical model of the hybrid circular tubes considering compression angle is newly proposed. Deformation mode and axial crushing response are analyzed by experiments. The major energy dissipation mechanism for hybrid circular tubes is explicitly derived. The Al thickness has the most significant impact on energy absorption. The recommendations for the design and development of hybrid tube are provided.

An SPH formulation for general plate and shell structures with finite deformation and large rotation

In this paper, we propose a reduced-dimensional smoothed particle hydrodynamics (SPH) formulation for quasi-static and dynamic analyses of plate and shell structures undergoing finite deformation and large rotation. By exploiting Uflyand–Mindlin plate theory, the present surface-particle formulation is able to resolve the thin structures by using only one layer of particles at the mid-surface. To resolve the geometric non-linearity and capture finite deformation and large rotation, two reduced-dimensional linear-reproducing correction matrices are introduced, and weighted non-singularity conversions between the rotation angle and pseudo normal are formulated. A new non-isotropic Kelvin-Voigt damping is proposed especially for the both thin and moderately thick plate and shell structures to increase the numerical stability. In addition, a shear-scaled momentum-conserving hourglass control algorithm with an adaptive limiter is introduced to suppress the mismatches between the particle position and pseudo normal and those estimated with the deformation gradient. A comprehensive set of test problems, for which the analytical or numerical results from literature or those of the volume-particle SPH model are available for quantitative and qualitative comparison, are examined to demonstrate the accuracy and stability of the present method.

Mechanical heterogeneity in a soft biomaterial niche controls BMP2 signaling

The extracellular matrix is known to impact cell function during regeneration by modulating growth factor signaling. However, how the mechanical properties and structure of biomaterials can be used to optimize the cellular response to growth factors is widely neglected. Here, we engineered a macroporous biomaterial to study cellular signaling in environments that mimic the mechanical stiffness but also the mechanical heterogeneity of native extracellular matrix. We found that the mechanical interaction of cells with the heterogeneous and non-linear deformation properties of soft matrices (E < 5 kPa) enhances BMP-2 growth factor signaling with high relevance for tissue regeneration. In contrast, this effect is absent in homogeneous hydrogels that are often used to study cell responses to mechanical cues. Live cell imaging and in silico finite element modeling further revealed that a subpopulation of highly active, fast migrating cells is responsible for most of the material deformation, while a second, less active population experiences this deformation as an extrinsic mechanical stimulation. At an overall low cell density, the active cell population dominates the process, suggesting that it plays a particularly important role in early tissue healing scenarios where cells invade tissue defects or implanted biomaterials. Taken together, our findings demonstrate that the mechanical heterogeneity of the natural extracellular matrix environment plays an important role in triggering regeneration by endogenously acting growth factors. This suggests the inclusion of such mechanical complexity as a design parameter in future biomaterials, in addition to established parameters such as mechanical stiffness and stress relaxation.

Comparison between DInSAR and Stacking in Deformation Monitoring Using LuTan-1

Abstract. LuTan-1 (LT-1) satellite constellation is used to conduct surface deformation monitoring. Following the successful launch of two satellites, we began to use the independently developed LandSAR software for differential interferometric data processing and application at the beginning of 2022. In this paper, we tested the LandSAR software by assessing the DInSAR and stacking modules. We used 21 LT-1 single look complex (SLC) images from December 2022 to May 2023 to conduct DInSAR and stacking processing of Datong City, Shanxi Province. DInSAR revealed more subsidence funnels and larger relative deformation values compared to stacking. We tested the DInSAR technology with different parameter combination. Results show that multi-looking factor is the most important to detect the deformation details because of the phase gradient limitation of DInSAR. Compared multi-looking ratios of 2×2 and 4×4, the subsiding funnels that were detected decreased from 60 to 47. After deep testing and assessment, we found that the linear model used by stacking affects the result severely, meaning that most of the subsidence of coal mines were not linear. Stacking only found 32 subsidence funnels which were active coal mines during our observation time. The test result show that LandSAR was compatible for DInSAR and stacking. And it is useful to observe linear and nonlinear deformation in the coal mine regions.

Dynamic Analysis of an FGM Beam Undergoing Large Overall Motion in Temperature Field

The dynamic analysis of a functionally gradient material (FGM) beam undergoing large overall motion based on meshless methods is studied in the variable temperature field environment. Considering the high-order terms of nonlinear coupling deformation which were often ignored in previous studies, the high-order rigid–flexible coupled (HOC) dynamic model of a rotating FGM beam with a lumped mass in a temperature field is established by employing Lagrange’s equations of the second kind. Compared with the first-order approximate coupled (FOAC) dynamic model, the HOC dynamic model is more accurate and has a wider scope of application. The validity of the point interpolation (PIM) method and radial point interpolation method (RPIM) in this paper is verified by comparison with simulation results of the assumed mode method (AMM) and the finite element method (FEM). On this basis, the factors affecting the dynamic characteristics of the FGM beam such as the form of temperature field, the functionally gradient index, and the location of added lumped mass are discussed. In this paper, the meshless method with higher computational efficiency and the HOC dynamic model with more accurate results are adopted. This study will provide guidance and reference for dealing with problems in engineering, machinery, aerospace, and other fields in complex environment.

Fracture toughness evolution and failure mechanisms of two-dimensional SiCf/SiC composites at temperatures up to 1500 °C in air

Silicon carbide fiber reinforced silicon carbide composites (SiCf/SiC) are of the few most promising materials for high-temperature structural applications. In this study, two-dimensional (2D) plain-woven SiCf/SiC composites were prepared by chemical vapor infiltration process and subjected to single-sided notched beam three-point bending tests from room temperature (RT) to 1500 °C in air. The temperature-dependent bending load–deflection curves and fracture toughness were obtained. The results show that the SiCf/SiC composites exhibit linear deformation characteristics initially, followed by nonlinear deformation behavior which become more pronounced with increasing temperature. The fracture toughness decreases in the range of RT to 1000 °C due to the evolution of components properties, and increases at 1200 °C due to the interface property degradation and fiber pull-out. Above 1200 °C, it decreases with increasing temperature owing to the serious high-temperature oxidation. Further, the failure mechanisms of the 2D plain-woven SiCf/SiC composites at different temperatures was analyzed through macro and micro analysis. The evolution of components properties affected by high temperature and oxidation as well as fiber pull-out play a leading role in fracture toughness of composites. The findings of this study provide important support for the mechanical behavior and failure mechanisms of SiCf/SiC composites at ultra-high temperatures in air.

A Self-Optimized Machine Learning Approach for Constitutive Parameters Identification of Aortic Walls

The accurate identification of constitutive parameters is considered the key challenge for the study of mechanical properties of biological soft tissues. The popular machine learning (ML)-based inverse identification frameworks always require large amounts of training datasets. This work proposes an ML framework called self-optimized ML for accurate identifying the constitutive parameters of aortic walls under few training datasets conditions. The self-optimized ML includes three steps: Step 1: the forward physical FEM models first simulate the nonlinear deformation of aortic walls subject to uniaxial tension tests and are used to establish the nonlinear relationship datasets, Step 2: the carefully designed inverse random forest (RF) of the ML model can offer rapid identification by learning the established nonlinear relationship datasets, and Step 3: forward physical FEM models are recalled to evaluate the error between the identification results in Step 2 and real values, and then the accuracy are embedded into RF for guiding optimization directions to ensure that the final identification results are accurately and physically reasonable. The accuracy and robustness validation of proposed framework was conducted by constitutive parameters identification of uniaxial tension experiment samples of bovine aortic walls. The approach proposed achieves the R-squared exceeding 96.90% in longitudinal direction and 98.30% in circumferential direction, which is better than directly ML approach and gradient-based approach under the same amounts of datasets, respectively. The comparison results show that self-optimized ML can not only achieve accurate identification of the constitutive parameters of aortic walls, but also can decrease the identification results dependency of the initial number of sampling data effectively. The identification approach developed herein provides a common and convenient framework for constitutive parameters identification of biological soft tissues.

Investigation on the damage model of rock subjected to freeze-thaw cycles considering its fracture voids compaction

The investigation on the mechanical properties and damage model of rock subjected to freeze-thaw cycles (FTCs) holds significant theoretical for assessing the deformation of rock mass engineering in cold regions. When the rocks subjected to FTCs, the fracture voids of rocks increase with increasing number of FTCs, and the rocks exhibit nonlinear deformation characteristics as its fracture voids compaction. Based on the dissipation energy evolution law and distribution characteristics of rocks under loading, the critical point of rock compaction deformation was determined. A constitutive model for rock subjected to FTCs considering its fracture voids compaction was established based on macroscopic and microscopic damage levels. The rationality of the model was validated using experimental results, and a comparison was made between the calculation results of proposed model and model that not consider fracture voids compaction. The evolution properties of rock damage variable and stress under different FTCs were analyzed. The variation of model parameters with the FTCs and the influence of model parameters on the deformation characteristics of rock was analyzed.

Identifying the origin of inhomogeneous degradation and irreversible swelling inside cylindrical 21700 high-energy lithium-ion cells

Cylindrical cells are gaining market volume in the production of batteries for electric vehicles among others due to high flexibility with regard to space utilization. However, the internal winding structure can be prone for inhomogeneities regarding current distribution, electrode degradation, and mechanical stress. In this study, 27 cylindrical SDI INR21700 50E cells with a nickel-rich NCA cathode and a Si/C composite anode were subjected to five individual aging procedures. Computed tomography scans were conducted at 100%, 90% and 80% capacity retention to investigate internal swelling and deformation of the jelly roll non-destructively. The cells were disassembled at 80% capacity retention for post-mortem analysis on coin half-cells harvested from different locations of the jelly roll to quantify inhomogeneous aging and electrode swelling.Increased cycle depth and discharge current exacerbated inhomogeneous degradation across the electrode length. In comparison to 860 equivalent full cycles (EFC) at 0.5C and 100% cycle depth, limiting the SoC range between 20% to 80% at 25°C increased cycle life to 4150EFC despite a high discharge current of 2C. Minimizing utilization of the silicon content and avoiding lithium plating, the cathode and the anode retained around 4% and 2% increased capacity at the inner winding area in comparison to the outer area, presumably due to increased mechanical pressure at the inner area. At the same time, the inner area displayed reduced swelling, further suggesting increased mechanical pressure at the inner area. Overall, the irreversible swelling measured 6% to 16% and 8% to 20% for the cathodes and the anodes after disassembly, depending on the operating conditions and the location on the electrode. To prevent non-linear capacity fade and deformation of the jelly roll, the results suggest to restrict utilization of the silicon content and to avoid high charging currents at low temperature.

Cut layout optimization for design of kirigami metamaterials under large stretching

Kirigami metamaterials have gained increasing attention due to their unusual mechanical properties under large stretching. However, most metamaterial designs obtained with trial-and-error approaches tend to lose their desirable properties under large tensile strains due to occurrence of instability caused by out-of-plane buckling. To cope with this limitation, this paper presents a systematic approach of cut layout optimizing for designing kirigami metamaterials working at large tensile strains by fully exploiting their out-of-plane buckling behaviors. This method can also mitigate the local stress concentration issue at the hinges of conventional kirigami designs working at in-plane deformation modes. The effectiveness of the proposed method is demonstrated through several examples regarding metamaterial design with negative Poisson's ratio and specified flip angle pattern. It is shown that the proposed method is capable of addressing the highly nonlinear deformation impacts on the mechanical performance under large stretching, to meet the growing and diverse demands in the field of kirigami metamaterials.

Measuring traction–separation relationships of bonded Fe-SMA double cantilever beam joints

Adhesively bonded strengthening systems using self-prestressing iron-based shape memory alloys (Fe-SMA) have demonstrated significant potential. However, the premature nonlinear behavior of Fe-SMA during debonding failure presents challenges in ensuring the integrity of the adhesive joint. A recent study indicated that this behavior may lead to premature joint failure, and a similar conclusion can be drawn concerning plasticity in thin adherends. To characterize the failure process of Fe-SMA bonded joints, a method capable of measuring traction–separation relationships of thin adherends bonded with tough adhesives is essential. An algorithmic method, supported by an analytical nonlinear beam-on-foundation model and a minimization scheme, is shown to offer a solution. To benchmark the method against the J-integral approach, experiments are conducted using two types of adherends: thick steel with thickness-limiting plasticity and Fe-SMA with material behavior that inevitably leads to nonlinear deformation. Comparison of methods shows both measurement method are valid and allow for proper predictive modeling using the finite element method. The proposed method can be readily employed to characterize various thin adherends with elasto-plastic material behavior.