Force-displacement Curves Research Articles

Constitutive models for confined elastomeric layers: Effects of nonlinearity and compressibility

Elastomers tend to undergo large deformations accompanied by small volumetric changes. For elastomeric layers sandwiched between rigid plates, large deformations can be significantly limited by the constraints imposed by the plates. Further, those constraints can be enhanced by material’s inability to undergo large volumetric changes. From this perspective, it is appropriate to examine the validity of constitutive models, in which an elastomer is treated as incompressible, for analysis of the confined layers. Here, this issue is addressed by considering the mechanical response of sandwiched elastomeric layers using three constitutive models. The first one, referred to as compressible neo-Hookean, is regarded as exact. The other two models are regarded as approximations. Of those two, the first one neglects nonlinearity and the second one neglects compressibility. Accordingly, the modeling errors associated with the former are treated as measures of importance of nonlinearity, and the modeling errors associated with the latter are treated as measures of importance of compressibility. The modeling errors are evaluated using the force–displacement curve and the mean stress at the layer center as the quantities of interest. Numerical results are presented for rubber and polydimethylsiloxane (PDMS), characterized by Poisson’s ratios ν=0.4999 and ν=0.49, respectively. It is shown that, even when the forces applied to the plates are large, considering nonlinearity is important for thick but not for thin layers. In contrast, considering compressibility is important for thin layers. The need for considering compressibility is further assessed by introducing a competition parameter, which reinforces the notion that compressibility is important for modeling PDMS layers and thin rubber layers.

Phase field fracture in elasto-plastic solids: Considering complex loading history for crushing simulations

Phase field models have gained growing popularity in fracture analysis. However, phase field modelling remains lacking for complex real-life applications such as structural crushing analyses to date. The novelty of this study is to propose an explicit phase field modelling framework considering complex loading history to predict the crushing behaviour of additively manufactured metallic structures. First, the explicit phase field model is formulated by considering stress state dependent fracture initiations with non-proportional loading. Then, five types of material specimens with a wide range of stress states are experimentally tested to calibrate material parameters for additively manufactured 316L steel and Ti-6Al-4V titanium. Last, the square tubes are 3D-printed and tested under three-point bending and axial compression to demonstrate the capacity of the proposed model. The modelling results unveil that the crushing behaviour of both materials could be properly reproduced in terms of force-displacement curves and crack paths. Finally, the fracture mechanism of crushing deformation is analysed. For the three-point bending of Ti-6Al-4V tubes, cracks are mainly induced by the medium stress triaxiality tension and shear loading. For the axial compression of 316L tubes, the stress states of critical elements are relatively diverse yet slightly concentrated at the shear, compression-shear, and high stress triaxiality tension regions. Remarkably, non-proportional loading is significant in crushing deformation as a material point may experience a significant change in stress state with loading. By considering a non-proportional loading dependent threshold, the proposed phase field model can predict the crushing behaviour of structures even when the fracture initiations do not locate on the fracture locus. This study provides an effective explicit phase field framework featured with an insightful fracture mechanism for quasi-static crushing of additively manufactured metallic materials.

Experimental study on mechanical properties of corroded grouted sleeve splice

Grouted sleeve splices are widely used in precast-concrete (PC) structures. Although extensive tensile tests have been conducted on grouted sleeves, the force mechanism and changing rules of grouted sleeve connections as influenced by environmental corrosion have rarely been investigated. Accelerated corrosion and monotonic tensile tests were conducted on twenty-five grouted sleeves. The investigated variables of the sleeve splices were the degree of corrosion, rebar eccentricity, and geometrical sizes of the rebar and sleeve. Based on the test results, the three-dimensional corrosion characteristics of the sleeve were analyzed, and the influences of the corrosion distribution, rebar eccentricity, and sleeve size on the failure mode, force–displacement curve, and strain distribution of the sleeves were discussed. The results indicated that the surface roughness parameters Sz, Sa, and Sq of the sleeve increased with an increase in corrosion. As a result of sleeve corrosion, the failure mode of the grouted sleeve connection changed from rebar fracture to sleeve fracture, accompanied by an increase in the longitudinal and circumferential strains of the sleeve, and reductions in strength, deformation capacity, and energy dissipation ability. In addition, the rebar eccentricity led to an uneven strain distribution in the circumferential direction.

Investigation of the surface mechanical properties of functionalized single-walled carbon nanotube (SWCNT) reinforced PDMS nanocomposites using nanoindentation analysis.

Functionalizing single-walled carbon nanotubes (SWCNT) with different chemical functional groups directly enhances their chemical adhesion and dispersion in viscous polymeric resins such as polydimethylsiloxane (PDMS). Nevertheless, the ideal surface polarity (hydrophilic or hydrophobic) for SWCNT to foster stronger chemical bonding with PDMS remains uncertain. This investigation delves into the impact of enhanced SWCNT dispersion within PDMS on the surface mechanical characteristics of this flexible composite system. We use carboxylic acid-functionalized SWCNT (COOH-SWCNT) and silane-functionalized SWCNT (sily-SWCNT), recognized for their hydrophilic and hydrophobic surface polarities, respectively, as reinforcing agents at ultra-low weight percentage loadings: 0.05 wt%, 0.5 wt%, and 1 wt%. We perform quasi-static nanoindentation analysis employing a Berkovich tip to probe the localized mechanical behavior of PDMS-SWCNT films at an indentation depth of 1 μm. Plastic deformation within the samples, denoted as plastic work (Wp), as well as the elastic modulus (E), hardness (H), and contact stiffness (Sc) of the composites are examined from the force-displacement curves to elucidate the enhancement in the surface mechanical attributes of the composite films.

Variable Stiffness and Damping Mechanism for CPR Manikin to Simulate Mechanical Properties of Human Chest.

This study introduces a novel system that can simulate diverse mechanical properties of the human chest to enhance the experience of CPR training by reflecting realistic chest conditions of patients. The proposed system consists of Variable stiffness mechanisms (VSMs) and Variable damper (VD) utilizing stretching silicone bands and dashpot dampers with controllable valves to modulate stiffness and damping, respectively. Cyclic loading was applied with a robot manipulator to the system. Compression force and displacement were measured and analyzed to evaluate the system's mechanical response. Long-term stability of the system was also validated. A non-linear response of the human chest under compression is realized through this design. Test results indicated non-linear force-displacement curves with hysteresis, similar to those observed in the chest of patients. Controlling the VSM and VD allowed for intentional changes in the slope and area of curves that are related to stiffness and damping, respectively. Stiffness and damping of the system were computed using performance test results. The stiffness ranged from 5.34 N/mm to 13.59 N/mm and the damping ranges from 0.127 N[Formula: see text] s/mm to 0.511 N[Formula: see text] s/mm. These properties cover a significant portion of the reported mechanical properties of the human chests. The system demonstrated satisfactory stability even when it was subjected to maximum stiffness conditions of the long-term compression test. The system is capable of emulating the mechanical properties and behavior of the human chests, thereby enhancing the CPR training experience.

Interface Mechanics of Double-Twisted Hexagonal Gabion Mesh with Coarse-Grained Filler Based on Pullout Test.

The interface friction mechanics of reinforcement material with filler is an essential issue for the engineering design of reinforced soil structure. The interface friction mechanics is closely associated with the properties of filler and reinforcement material, which subsequently affects the overall stability. In order to investigate the interface mechanism of a double-twisted hexagonal gabion mesh with a coarse-grained filler derived from a weathered red sandstone, a large laboratory pullout test was carried out. The pullout force-displacement curve was obtained by fully mobilizing the gabion mesh to reach the peak shear stress at the interface between the gabion mesh and the coarse-grained filler. The change of force-displacement characteristics and the distribution of tensile stress in gabion mesh during the pullout process were obtained. A 3D numerical model was established based on the pullout test model, and the model for analyzing the interface characteristic between the gabion mesh and the coarse-grained filler was modeled using the FLAC3D 6.0 platform. The interface characteristics were further analyzed in terms of the displacement of soil, the displacement of reinforcement, and the shear stress of soil. The strength and deformation behaviors of the interface during the entire pullout process were well captured. The pullout force-displacement curve experiences a rapid growth stage, a development transition stage and a yielding stabilization stage. The critical displacement corresponding to peak pullout stress increases with the increase in normal stress. The normal stress determines the magnitude of shear stress at the reinforcement and soil interface, and the displacement distribution of a gabion mesh is not significantly affected by normal stress when the applied normal stress is within a range of 7-20 kPa. The findings are beneficial to engineering design and application of a gabion mesh-reinforced soil structure.

The influence of particle shape on crushing pattern and energy dissipation within a pressurized sand damper

A discrete element method (DEM) model was introduced to examine the crushing pattern, energy dissipation, force–displacement curves, and stresses within a pressurized sand damper (PSD). Simulations were carried out with various particle shapes, including elongated, triangle, pyramid, cube, and hexagon. While monitoring the force–displacement curves, it was observed that the hexagon-shaped particles yielded the highest forces, while the triangle-shaped particles resulted in the lowest forces. Altering the particle shapes did not significantly impact the overall shape of the force–displacement curves, suggesting that dynamic force generation remains unaffected by the particle shape. Particle crushing was closely examined for all particle shapes, and it was concluded that all shapes exhibit relatively similar crushing locations and patterns. In the analysis of normal stress, hexagon- and elongated-shaped particles were found to experience the highest and lowest stresses, respectively. Observing the energy dissipation revealed that, among the shapes studied, triangle-shaped particles had the lowest cumulative dissipated energy over five loading-unloading cycles, whereas hexagon-shaped particles had the highest. The calculation of specific damping capacity showed a large loss angle, indicating the presence of large strains inside the model.

Theoretical model of energy absorption for square tubes under transverse loading with variable axial constraint condition

Thin-walled tubes in the actual engineering structure (e.g., autobody) are usually connected to other structure, and the boundary constraint condition at both ends of tubes are usually very complex when bending deformation occurs under transverse loading. This paper aims at the effect and mechanism of axial constraint on the bending energy absorption effect of thin-walled tube under limited and variable axial constraint condition at both ends. A typical of thin-walled tube, square tube, is taken as an example. Firstly, we compare the experiment results of square tube under transverse loading with three-point-bending condition and fully clamped condition, revealing that the axial constraint force has a significant effect on the energy absorption effect. After that, a FE model of the square tube under variable axial constraint condition at both ends is established and validated based on experiment. Based on the validated FE model, the effect of different sizes of axial constraint stiffness on the bending energy absorption of square tube are investigated, and it is found that it has a significant effect on the deformation mode and bending energy absorption. With the increase of axial constraint stiffness, it will mainly affect the latter segment of the force–displacement curve in the bending process, which increases the bending energy absorption. Finally, theoretical models are developed to predict the force–displacement curves and bending energy absorption of the square tube under three different types of variable axial constraint properties: linear axial constraint, unequal linear axial constraint and nonlinear axial constraint.

Study on seismic behavior of prefabricated shear walls with steel double tube connections

The joints are crucial for influencing the overall mechanical performance of precast shear wall constructions under seismic actions. The existing joint connections are complex and not efficient enough. To maximize the potential of prefabricated structures, this study proposed innovative prefabricated shear walls with steel double tube connections. Two pseudo-static tests were conducted to investigate the influence of axial compression ratio on the seismic behavior of the innovative shear walls. The failure modes were all bending failures, and it had been discovered that increasing the axial compression ratio can improve the carrying capacity and energy dissipation capacity. Seven models with different axial pressure ratios were established to conduct nonlinear finite element analysis. The result showed that as the axial compression ratios raised, the carrying capacity and stiffness of the models increased, but the decreasing trend of force–displacement curves were also more distinct. Therefore the recommended axial pressure ratio of the models did not exceed 0.4. Finally, the calculation method of the loading capacity of novel shear walls was proposed, which provided the basis for the design of innovative shear walls.

Device for determination of internal pressure in beer cans by measuring the force-displacement curves

Microbiological contamination of beer is usually manifested by the production of CO2 and, hence, an increase in its concentration. The increased concentration of CO2 in a closed package leads to an increase of internal pressure, which can cause a destruction of the package and have dangerous consequences. A device for non-destructive monitoring of the internal pressure in beer cans based on measurement of force-displacement curve has been developed and characterized in this study.

Buckling and fracture characterization of pristine bundles of vertically aligned carbon nanotubes using quantitative in situ TEM axial compression

This work investigates the mechanical deformation and fracture characteristics of pristine bundles of vertically aligned multi-walled carbon nanotubes (MWCNTs) subjected to axial compression in situ transmission electron microscope (TEM). Accurate measurements of force-displacement data were collected simultaneously with real-time TEM videos of the deformation process. Two distinct regimes were observed in the force-displacement curve: (1) an initial elastic section with a linear slope, followed by (2) a transition to a force plateau at a critical buckling force. Morphological data revealed coordinated buckling of the pristine bundle, indicating strong van der Waals (VdW) forces between the nanotubes. The experimental setup measured an effective modulus of 83.9 GPa for an MWCNT bundle, which was in agreement with finite element analysis (FEA) simulations. FEA also highlighted the significant role of VdW forces in the bundle mechanical reactions. Furthermore, we identified nickel nanoparticles as key players in the fracture behavior of the bundles, acting as nucleation sites for defects. The direct mechanical measurements of MWCNT bundles provide valuable insights into their mechanical deformation and fracture behavior, while correlating it to the morphology of the bundle. Understanding these interactions at the bundle level is crucial for improving the reliability and durability of VACNTs-based components.

Micromechanical analysis of the suction bucket-granular soil interactions under the pull action of anchor lines: Embedded length effect

The micro-mechanism of interactions between suction buckets and granular soil under different embedded lengths remains unclear. This study investigates the micro-to-macro interactions between suction buckets and granular soil under an inclined pull action of anchor lines, taking the embedded length effect into consideration. The granular soil was modeled using the discrete element method (DEM), while the suction bucket was modeled using the finite element method (FEM). The peak pull force in DEM-FEM simulations was validated using model test results, while macro and micro behaviors of the structure-soil interaction were analyzed. The findings demonstrated that the embedded length effect shaped the pull force-displacement curve by influencing the interaction modes between structures and granular soil. Discontinuity and large soil deformation occurrences can be successfully simulated using the DEM-FEM method and the relationships to embedded lengths were discovered. Besides, clear relationships among bucket rotation angles, the effective supporting areas, vertical pull-out displacement, shear wear, and deformation of buckets, were established. Furthermore, a detailed investigation of particle-scale behaviors led to an identification of mechanical failure modes of suction bucket-granular soil interaction. The findings suggest that ignoring the embedded length effect could lead to misestimating the uplift capacity and failure modes of the suction buckets.

Mode II and mode III delamination of carbon fiber/epoxy composite laminates subjected to a four-point bending mechanism

Accurate determination of mode III interlaminar fracture toughness is paramount in composite materials due to its critical role in edge delamination, which nonetheless remains a significant challenge encountered. As such, this study focused on the investigation of mode II and III interlaminar fracture behavior of carbon fiber (CF)/epoxy composite laminates using four-end notched flexure (4ENF) tests and four-point bending plate (4PBP) tests, respectively. In particular, a cohesive zone model was employed for the simulation of the delamination process via finite element analysis (FEA). The mode II fracture toughness of CF/epoxy composites was determined to be 1.41 N/mm in experimental work. Additionally, experimental data in relation to force-displacement curves were in good agreement with numerical simulation results, which validated this simulation approach to successfully capture the mechanical response of composite laminates. In a similar manner, mode III delamination fracture toughness for CF/epoxy composites was numerically estimated to be 2.1 N/mm. Microscopic analysis indicated shear cusps were observed in both mode II and III specimens, as opposed to existing flakes discovered in mode III specimens only. Overall, this research enlightens a simple and effective way to estimate pure mode III fracture toughness and corresponding delamination behavior with respect to crack initiation and propagation.

A mechanically-derived contact model for adhesive elastic-perfectly plastic particles, Part II: Contact under high compaction—modeling a bulk elastic response

In Part I of this two part series (Zunker and Kamrin, 2024), we presented a multi-neighbor dependent contact model for adhesive elastic–plastic particles built upon the method of dimensionality reduction that is valid for the elastic and fully-plastic contact regimes. In this Part II, we complete the contact model by proposing a treatment for the bulk elastic contact regime which is characterized by a rapid stiffening in the force–displacement curve as interstitial pore spaces vanish. A simple formulation is presented for an additional bulk elastic force. A novel criterion for triggering this force (i.e. detecting the bulk elastic regime) related to the remaining free surface area of the particle is also given. This bulk elastic force is then superimposed with the force response given in Part I to achieve a contact model capable of capturing a variety of complex loadings. In this way, the methodology for treating the bulk elastic regime presented here stands independent of Part I and could be appended to any contact model. Direct comparison is made to finite element simulations showcasing bulk elastic responses, revealing the accurate predictive capabilities of the contact model. Notably, the contact model is also demonstrated to detect and evolve contacts caused purely by outward displacement of the free surface with good precision. A numerical implementation suitable for the discrete element method is provided.

Bending behavior of diamane and twisted bilayer graphene: Insights from four-point bending deformation

The intriguing physical properties of two-dimensional (2D) nanomaterials make them promising building blocks for flexible electronics. Using a four-point bending approach, this work establishes a comprehensive understanding of the bending behavior of diamane – a 2D diamond nanostructure, from elastic deformation to structural failure through atomistic simulations. The four-point bending method accurately reproduces the pure bending of the sample, and the obtained force-displacement curve fit well with the classical Euler beam theory. Structural failure is observed from diamane under bending when its thickness or the number of layers increases. Atomic insights reveal that the crack initiates from the tension side of the sample, resulting in a tension-induced bending failure. Specifically, the bending limit is found to be slightly larger than the fracture strain under tensile deformation. Additionally, the bending behaviour of the diamane analogous – twisted bilayer graphene with interlayer-bonding (TBGIB), has been investigated. Different from diamane, TBGIB bends elastically at the initial stage and then experiences structural failures with increasing bending strain. Higher interlayer bonding density is observed to result in a higher bending stiffness. Meanwhile, significant interlayer shear strain is detected during bending, which leads to interlayer bond breakage, rippling, and buckling of the graphene layer. This work provides a full description of the pure bending behavior of diamane and its analogous structure, which could be beneficial for their applications in flexible electronics.

The effect of halloysite nanotubes reinforced epoxy filler on the crushing behavior of aluminum tubes

AbstractCrash box is one of the equipment to minimize the damage that may occur during an accident in vehicles. Many studies are conducted to improve the performance of crash boxes. Some of these studies were aimed at filling thin‐walled crash boxes. Halloysite nanotubes (HNT) were used as filling material in this study. HNT can be found in nature and is in nanotube structure by nature. For this reason, it is inexpensive compared to other nanotubes like carbon nanotube. Within the scope of the study, epoxy‐based mixtures with 0%, 5%, 10%, and 15% HNT were prepared and filled into aluminum tubes. The powders used were ~20–100 nm in size and in the form of cylindrical tubes. Investigated were the effects of the HNT ratio and the thin‐walled aluminum construction. Nine diverse types of specimens were created. The vacuuming principle was used as the production method. The reason for this is to minimize the air bubbles that may occur during mixing. The effect of aluminum tube and HNT ratio on energy absorption and mechanical strength was investigated. For this, quasi‐static tests were conducted. The absorbed energies of the specimens were determined by integrating the acquired contact force–displacement curves, and the specific absorbed energy was determined by dividing the absorbed energy by the specimen weights. SEM images were taken for internal structure characterization. In addition, FTIR analysis was performed to determine whether the composite was cured. According to the results obtained, the mechanical characteristics and specific absorbed energy of the filled specimens were superior to those of the unfilled ones. Specimen containing 5% HNT showed maximum energy absorption and mechanical strength. Although the HNT additive has a positive effect on the mechanical and energy absorption in general, it has been determined that the HNT additive affects the performances negatively from 10%.

Crashworthiness analysis of gradient branch circular tubes inspired by the structure of leaf vein

The gradient branch circular tubes (GBCTs) were proposed based on the structure of leaf vein. Crashworthiness performances of GBCTs are investigated via finite element simulation. The results show that the specific energy absorption (SEA) of GBCTs is much higher than the conventional circular tube, and it increases with the increase of hierarchical level under the condition of the same mass. GBCTs with large wall thickness have better energy absorption performance, but they also increase the fluctuation of the force-displacement curve. Moreover, the branch point location and gradient wall thickness of GBCTs have a great impact on their crashworthiness performance.

Biomechanical comparison of open Bankart repair vs. conjoint tendon transfer in a 10% anterior glenoid bone loss shoulder instability model

The treatment of shoulder instability in patients with subcritical glenoid bone loss poses a difficult problem for surgeons as new evidence supports a higher failure rate when a standard arthroscopic Bankart repair is used. The purpose of this study was to compare a conjoint tendon transfer (soft-tissue Bristow) to an open Bankart repair in a cadaveric instability model of 10% glenoid bone loss. Eight cadaveric shoulders were tested using a custom testing system that allows for a 6-degree-of-freedom positioning of the glenohumeral joint. The rotator cuff muscles were loaded to simulate physiologic muscle conditions. Four conditions were tested: (1) intact, (2) Bankart lesion with 10% bone loss, (3) conjoint tendon transfer, and (4) open Bankart repair. Range of motion, glenohumeral kinematics, and anterior-inferior translation at 60° of external rotation with 20 N, 30 N, and 40 N were measured in the scapular and coronal planes. Glenohumeral joint translational stiffness was calculated as the linear fit of the translational force-displacement curve. Force to anterior-inferior dislocation was also measured in the coronal plane. Repeated measures analysis of variance with a Bonferroni correction was used for statistical analysis. A Bankart lesion with 10% bone loss increased the range of motion in both the scapular (P=.001) and coronal planes (P=.001). The conjoint tendon transfer had a minimal effect on the range of motion (vs. intact P=.019, .002), but the Bankart repair decreased the range of motion to intact (P=.9, .4). There was a significant decrease in glenohumeral joint translational stiffness for the Bankart lesion compared with intact in the coronal plane (P=.021). The conjoint tendon transfer significantly increased stiffness in the scapular plane (P=.034), and the Bankart repair increased stiffness in the coronal plane (P=.037) compared with the Bankart lesion. The conjoint tendon transfer shifted the humeral head posteriorly at 60° and 90° of external rotation in the scapular plane. The Bankart repair shifted the head posteriorly in maximum external rotation in the coronal plane. There was no significant difference in force to dislocation between the Bankart repair (75.8±6.6 N) and the conjoint tendon transfer (66.5±4.4 N) (P=.151). In the setting of subcritical bone loss, both the open Bankart repair and conjoint tendon transfer are biomechanically viable options for the treatment of anterior shoulder instability; further studies are needed to extrapolate these data to the clinical setting.

Experimental evaluation of the out-of-plane behavior of a traditional timber frame with mud and rubble infill wall strengthened by a polypropylene band mesh on one side

The structural integrity of traditional Chinese village residences may be compromised due to inadequate connections between the timber frame and infill walls, coupled with the weak cohesiveness of clay mud. Among the various damage mechanisms resulting from earthquakes, the out-of-plane collapse of infill walls is a recurrent and significant concern. The goal of this research is to investigate the feasibility and effectiveness of a polypropylene (PP) band mesh reinforcement approach for a traditional timber frame with mud and rubble infill walls. The ultimate goals are to prevent out-of-plane collapse, improve the collaborative performance of the structure, reduce seismic vulnerability, and safeguard the architectural heritage of traditional dwellings. With careful consideration of their aesthetics, the study centers on timber frames with mud and rubble infill walls strengthened by a polypropylene (PP) band mesh and cement mortar on one side. A series of experiments were conducted based on out-of-plane cyclic one-way tests of four full-scale specimens. Different loading surfaces and reinforcing PP grid sizes with and without window openings were investigated to characterize the out-of-plane behavior of the reinforced hybrid walls. The damage evolution, failure modes, force–displacement curves, out-of-plane profile characteristics, stiffness, strength, and energy dissipation were described. All the reinforced walls exhibited marked improvements out-of-plane lateral capacity, with enhancements of approximately 120% and 162%, and stiffness increases of approximately 105% and 200%, compared to the unreinforced walls. The minimal out-of-plane displacement observed on the reinforcement side was also accompanied by significant increase in integrity and ductility.

Damage and fracture behavior under non-proportional biaxial reverse loading in ductile metals: Experiments and material modeling

This paper deals with a modified anisotropic stress-state-dependent plastic-damage continuum model incorporating combined hardening and softening rules to predict the plastic, damage, and fracture behavior of ductile metals under monotonic and reverse loading conditions. In the experimental part, a newly designed biaxially loaded cruciform flat HC-specimen of aluminum alloy EN AW 6082-T6 was subjected to biaxial non-proportional loading to generate a wide range of stress triaxialities during experiments. Thus, it is enabled to perform shear monotonic and reverse loading superimposed by various preloads without unloading processes. The experimental data reveal the Bauschinger effect, the strength-differential (SD) effect, and the change in the hardening ratio after shear reverse loading. This is captured by a Drucker–Prager-type yield criterion with an extended Voce isotropic hardening and modified Chaboche’s kinematic hardening rule. In addition, the damage surface is assumed to be translated in the direction of the rate of the damage strain. The numerically predicted global force–displacement curves and local strain fields are verified in terms of the digital image correlation (DIC) technique. Moreover, the scanning electron microscopy (SEM) is used to examine the fracture surfaces and to validate the proposed damage constitutive model.