Elastic-plastic Response Research Articles

Multi-scale finite element analysis of the strengthening and damage behavior of carbides with different characteristics in nickel-based superalloys

This study proposes a novel multi-scale numerical approach to explore the mechanical behavior and damage evolution in nickel (Ni)-based superalloys containing various carbide particles. At the nanoscale, the elastic properties of two distinct carbides are determined using first-principles calculations. At the microscale, finite element simulations (FEM) in ABAQUS are used to analyze the stress–strain relationship and local stress distribution within a three-dimensional representative volume element, as well as damage and fracture behavior. The model integrates the elastic–plastic response of the Ni matrix, the elastic-brittle fracture of micro-scale carbides, and the interface behavior between carbide and matrix. FEM findings are consistent with tensile test data, indicating that skeletal carbide promotes plasticity while blocky carbide elevates strength. The interface between blocky carbide and matrix is susceptible to cracking. When the carbide is oriented at 45° to the load direction, offering a balance of strength and plasticity. Stress concentration is reduced when carbides are uniformly distributed and present in high-volume fractions. The numerical method is well-suited for a thorough analysis of the comprehensive behavior of reinforced phase/metal-matrix composites.

Numerical investigation on bending characteristic and ductile fracture of AA7075 thin-walled beam using advanced orthotropic plasticity and fracture models

Thin-walled structures manufactured from the 7075 aluminum alloy are gaining tremendous attention in the automotive industry for their potential to reduce vehicle weight. However, the bending characteristics and rupture behavior of the AA7075 thin-walled beams under unexpected collision events have not been extensively studied. This study aims to fill that gap through a detailed numerical investigation of the bending deformation and failure mechanism of AA7075 thin-walled beams under quasi-static three-point bending at room temperature. Full-size, three-dimensional numerical simulations of laboratory-scale AA7075-T6 hat-shaped beam were conducted using the ABAQUS/Explicit solver. The material elastic–plastic response is described by a rate-independent constitutive description, incorporating advanced non-quadratic orthotropic plasticity and anisotropic ductile fracture criteria via VUMAT subroutines. Results indicate that the simulations accurately reproduced experimental observations, including the loading-displacement curves and deformation patterns. The bending behavior of the AA7075-T6 thin-walled beams aligns with typical bending collapse mechanisms, consistent with Kecman’s theory. The rupture process exhibits ductile fracture characteristics, with heterogeneous stress distribution across the material thickness affecting crack initiation rates between the upper and lower surfaces. Notably, the stress state at the fracture’s half-thickness section approximates an equi-biaxial tension condition. These findings provide essential insights into the bending deformation and failure mechanisms of AA7075 thin-walled structures under unexpected impact loading.

Analysis of Elastic-Plastic Lateral-Torsional Coupled Earthquake Response of Multilayer Bidirectional Stiffness Eccentric Frame Structure

Analysis of Elastic-Plastic Lateral-Torsional Coupled Earthquake Response of Multilayer Bidirectional Stiffness Eccentric Frame Structure

Base joint hysteresis model for reinforced concrete assembly columns with post-pouring area

In response to the problem of uncontrollable grouting quality of traditional grouting sleeves in the connection between prefabricated components, a column base joint with post pouring area connected by grouting sleeves (PCGS) is proposed. Both the sleeve and post pouring area could cause differences in hysteresis characteristics between prefabricated and cast-in-place components. In order to investigate the hysteresis model of PCGS column base joint, the cyclic load tests and finite element parametric analysis of PCGS column base joint were conducted. The theoretical calculation method for load and displacement of PCGS column base joint at yield, peak, and ultimate characteristic points was established based on equivalent rectangular stress and plastic hinge length in joint area. The average ratios of theoretical calculations to test results for load and displacement at the above three characteristic points are 0.997, 0.983, and 0.983, and 1.020, 1.041, and 0.970, respectively, indicating that the theoretical calculation method can accurately predict the strength and deformation of PCGS column base joint. The dimensionless skeleton curve model with double broken lines in the elastic and strengthening stages, and exponential function in descending stage has been established based on the test and simulated results. The degradation behavior of unloading stiffness and bearing capacity was quantitatively described using the regression fitting method, and the hysteresis rule was defined. The established hysteresis model can effectively reflect the strength and stiffness degradation under cyclic loading, which can provide guidance for the elastic-plastic seismic response analysis of PCGS column base joint.

Fundamental influence of irreversible stress–strain properties in solids on the validity of the ramp loading method

The widely used quasi-isentropic ramp loading technique relies heavily on back-calculation methods that convert the measured free-surface velocity profiles to the stress–density states inside the compressed sample. Existing back-calculation methods are based on one-dimensional isentropic hydrodynamic equations, which assume a well-defined functional relationship P(ρ) between the longitudinal stress and density throughout the entire flow field. However, this kind of idealized stress–density relation does not hold in general, because of the complexities introduced by structural phase transitions and/or elastic–plastic response. How and to what extent these standard back-calculation methods may be affected by such inherent complexities is still an unsettled question. Here, we present a close examination using large-scale molecular dynamics (MD) simulations that include the detailed physics of the irreversibly compressed solid samples. We back-calculate the stress–density relation from the MD-simulated rear surface velocity profiles and compare it directly against the stress–density trajectories measured from the MD simulation itself. Deviations exist in the cases studied here, and these turn out to be related to the irreversibility between compression and release. Rarefaction and compression waves are observed to propagate with different sound velocities in some parts of the flow field, violating the basic assumption of isentropic hydrodynamic models and thus leading to systematic back-calculation errors. In particular, the step-like feature of the P(ρ) curve corresponding to phase transition may be completely missed owing to these errors. This kind of mismatch between inherent properties of matter and the basic assumptions of isentropic hydrodynamics has a fundamental influence on how the ramp loading method can be applied.

Numerical examination on seismic response behavior of a piping system considering the plastic deformation of supports

A previous study proposed a passive safety structure to mitigate severe damage to crucial components under the beyond design basis event (BDBE). To examine the applicability of this concept to the piping system, the effect of the elastic-plastic behavior of the piping support structure on the seismic response of the piping system was investigated through elastic-plastic time history response analyses on a piping system model with multiple support structures. The numerical analyses considered the elastic-plastic behavior of supports and/or the inelastic characteristics of pipe material. The analysis results confirmed that the response of the piping system can be suppressed by adequately introducing the inelastic behavior of support structures. The results show the possibility of realizing of passive safety structure in piping systems and addressing some issues, such as changing vibration modes due to the elastic-plastic deformation of the support or the order of generation of inelastic behavior of pipe material and supports.

An interface constitutive model of plastic tensile–compressive damage under impact loading based on continuous–discontinuous framework

Bullet penetration test is a classic impact loading test, which involves complex dynamic elastic–plastic response. Conventionally, this process was often described using a single high-strain-rate constitutive model, which could only capture a specific type of failure during the impact damage process. Furthermore, these constitutive models were mostly defined on element and posed the risk of computational divergence(element distortion). In this work, a novel constitutive model for combined tensile–compressive damage in interface element was developed within a Continuous–Discontinuous Element Method(CDEM) framework. This model successfully captures the processes of pit formation and target collapse during projectile penetration. The tension and compression damage parts of the developed interface constitutive model were validated through Brazilian splitting test and interface direct shear test. Subsequently, bullet penetration test is simulated and the post-penetration velocity is compared with published results from other studies, with computational errors found to be within 2.56%, thus validating the accuracy of the developed interface constitutive model.

Exact solutions for the elastic-plastic response of functionally graded pipe under external pressure

This study investigates the influence of material gradient on the elastoplastic response of functionally graded (FG) thick-walled pipes subjected to external pressure. Closed-form solutions are derived for radial and circumferential stresses across various stages: purely elastic, partially plastic, and post-unloading from plastic regimes. Both the elastic modulus and yield stress exhibit radial variation defined by power-law functions, while Poisson's ratio remains constant. The stress distribution within the pipe depends not only on the external pressure but also on the material gradient index and the geometric dimensions of the pipe. A method is presented to accurately determine the first yielding position in a thin-walled tube based on the material gradient index by employing Tresca's yield criterion. Plastic zones nucleate at one or both surfaces as external pressure increases. The propagation of elastoplastic interfaces and stress distributions within each zone are examined in detail. Notably, following plastic deformation and complete unloading, FG thick-walled pipes may exhibit re-emergence of plastic deformation, depending on the pre-unloading stress state and the gradient of the elastic modulus. The conclusions of this work expected to aid in the design of FG pressure vessels and improve their load-carrying capacity and safety.

Elastic-plastic response of tunnel in GZZ-based constitutive model

Investigating the stress redistribution characteristics after tunneling is critical for designing and constructing deeply buried tunnels. Three-dimensional stresses are more prominent in deep than in shallow tunnels, resulting in nonlinear strength. The generalized Zhang–Zhu (GZZ) criterion captures the nonlinear strength well. Therefore, this study established a 2D plane-strain numerical model using a GZZ-based constitutive model. The effects of the axial stress and rock properties on the stress redistribution and plastic zone are discussed. The initial axial stresses changed the axial stress distribution after excavation and had little effect on the radial and tangential stress distributions. The size of the plastic zone decreases with decreasing geological strength index and increasing rock mass mi . However, with increasing dilation coefficient, the stress distributions remained almost unchanged, whereas the radial deformation gradually increased.

Irradiation Effects on Tensile Properties of Reduced Activation Ferritic/Martensitic Steel: A Micromechanical-Damage-Model-Based Numerical Investigation

The tensile properties of reduced activation ferritic/martensitic (RAFM) steels are significantly influenced by neutron irradiation. Here, a mechanism-based model taking account of the typical ductile damage process of void nucleation, growth, and coalescence was used to study the temperature and irradiation effects. The elastic–plastic response of RAFM steels irradiated up to 20 dpa was investigated by applying the GTN model coupled with different work hardening models. Through a numerical study of tensile curves, the GTN parameters were identified reasonably and satisfying simulation results were obtained. A combination of Swift law and Voce law was used to define the flow behavior of irradiated RAFM steels. The deformation localization could be adjusted effectively via setting the nucleation parameter εn close to the strain where necking occurs. Because εn changed with uniform elongation, εn decreased with the testing temperature and rose with an irradiation temperature above 300 °C. The nucleation parameter fn increased with the testing temperature for RAFM steels before irradiation. For irradiated RAFM steels, fn barely changed when the irradiation temperature was below 300 °C and then it rose at a higher irradiation temperature. Meanwhile, the ultimate strength of the simulated and experimental curves showed good agreement, indicating that this method can be applied to engineering design.

Large deformation response of a novel triply periodic minimal surface skeletal-based lattice metamaterial with high stiffness and energy absorption

Triply periodic minimal surface (TPMS) lattice metamaterials present superior mechanical performance over traditional strut-based lattice metamaterials due to their unique structural characteristics. However, the high stiffness–stable plastic response trade-off dilemma is still the major challenge for skeletal-based metamaterials. Herein, a novel TPMS skeletal lattice metamaterial is proposed. Finite element simulations are conducted to reveal its elastic properties and plastic response under compression. Afterwards, validation experiments are performed on the lattice specimens fabricated by the most common Fused Deposition Modeling (FDM) process. The nominal stress–strain curves and collapse mode of the lattice materials are obtained accordingly. Both the numerical simulations and experiments demonstrate that the proposed TPMS lattice metamaterial exhibits high specific modulus, strength and energy absorption, together with a smooth and elongated stress plateau, thereby overcoming the strength-efficiency trade-off. Different from the rigid nodal region in traditional strut-based lattices, the strut connection parts in the novel TPMS lattices experience shear and twisting, which avoids the catastrophic failure of the struts and enhances the loading efficiency of the structure under compression. Meanwhile, the numerical results indicate that the stable plastic response of the designed architecture is insensitive to the plastic flow behavior of the bulk material, which is also supported by the experimental results. It is also demonstrated that the novel TPMS lattice metamaterial presents several times higher stiffness as well as energy absorption simultaneously than the current strut-based lattice materials, which can be potentially applied as load-bearing components and impact energy absorbers.

A novel constitutive model for S30408 stainless steel considering strain memory effect: Formulation and implementation

To predict seismic behavior of steel structures and conduct performance-based seismic design, a precise constitutive model to accurately reflect the elastic-plastic response of structural steel under various loading protocols is always needed, so that the strength, deformation capacity, and energy dissipation capacity of a steel component or system in case of a severe earthquake can be reasonably evaluated. On the other hand, the constitutive model should be convenient for practical engineering implementation and application. Previous studies show that certain type steel like stainless steel S30408 shows complex features under various strain ranges such as pronounced strain memory effect, unsaturated cyclic softening/hardening under small/large strain amplitudes, which differ from mild steel and low yield point steel. Therefore, the stainless steel S30408 is taken as the research object in this study to develop a new constitutive model to describe structural steels with such complex mechanical properties. First, a new nonlinear isotropic and kinematic hardening rule is extended based on the classical Chaboche model and a functional relationship between the hardening rate (defined as the variation value of peak stress in every adjacent cycle during cyclic loading) and the applied strain amplitude is established through a logistics function to describe the coupling effects. Second, the numerical implementation technique for three-dimensional is elaborated in detail. Third, the numerical implementation technique is extended to plane stress cases by the improved P projection method. Using the numerical integration algorithm, the proposed constitutive model can be successfully incorporated into ABAQUS/Standard through the UMAT subroutine interface which is suitable for both solid and shell elements.

Anisotropy characteristics of electrical conductivity and compressive strength of 3D carbon fiber/epoxy angle-interlock woven composites

Electrical and compressive performances are important in 3D carbon fiber/epoxy angle-interlock woven (AIW) composites for mechanical-electrical coupling behaviors. Here we investigate the electrical conductivity and compressive strength of.3D AIW composites both in in-plane and out-of plane. Four-probe method is conducted to measure the volume resistance along different directions. Damage evolution and failure modes are recorded with a high-speed camera during compressive test. Electrical conductivity and compressive strength exhibit obvious anisotropic characteristics due to fiber orientation and yarn waviness. The curved warp yarns result in the compromise of the X-direction conductivity by extending the current transmission length and increase of the Z-direction conductivity by forming more contact points to expand the current flow paths. Because of different yarn arrangements, the compressive failure mechanisms of 3D AIW composites in the X, Y and Z directions are buckling failure, double shear bands and indirect tensile failure, individually. Yarn undulation in the X-direction causes premature buckling and exhibits elastic-plastic nonlinear response, resulting in the lowest compressive strength and modulus. The 3D AIW composites have the lowest electrical conductivity and highest compressive strength in the Z-direction, which is suitable for high strength stress-sensing elements.

Elastic-plastic response for the foam-filled sandwich circular tube under internal blast loading

The dynamic response and the blast resistance of an aluminum foam-filled sandwich circular tube under internal blast loading was investigated theoretically. The deformation of the structure is decoupled into three phases corresponding to blast loading interacting with the internal tube, foam core crushing and external tube deformation. During the process, the theoretical model includes both the circumferential membrane forces and the axial moment components and considers an elastic-plastic strengthening model for internal/external tubes. The proposed model is tested against the experimental results for the mid-point deflection of the external/internal tubes. The influence of the physical and geometrical parameters of the structure on their deformation is investigated. It is shown that the dimensionless mid-point deflection of the external tube decreases as the tangent modulus of the internal/external tube increases, while the tangent modulus of the internal tube has a larger effect on the mid-point deflection of the external tube. The minimum mass of a sandwich circular tube can be found when the deformation of the external tube is specified. The research results can provide theoretical basis for lightweight structure design.

Theoretical and numerical analysis on elastic-plastic bending responses of honeycomb beams

Cellular honeycomb beams are widely encountered in nature and engineering applications. The mechanical responses of them under various loads are critical to their applications. However, theoretical analyses and predictions of these mechanical responses are quite challenging. In this paper, theoretical studies are carried out to predict their large deformation bending responses. Theoretical expressions are derived for bending moment responses of honeycomb beams under both pure bending and three-point bending by considering the bending theory of solid beams and incorporating the relative density ρ* of the cellular honeycomb beams. Numerical simulations are performed to demonstrate the effectiveness and accuracy of the proposed theories by using the numerical model validated by experiment. Rectangular honeycomb beams with the relative density 0 < ρ* ≤ 1 are selected by Latin hypercube sampling. The theoretical bending moment curves of these beams predicted by the proposed theories agree well with the numerical results for both pure bending and three-point bending. In addition, the proposed theories are also validated to be effective in predicting the bending responses of honeycomb beams with different sectional cell shapes.

Accurate Finite Element Simulations of Dynamic Behaviour: Constitutive Models and Analysis with Deep Learning.

Owing to the challenge of capturing the dynamic behaviour of metal experimentally, high-precision numerical simulations have become essential for analysing dynamic characteristics. In this study, calculation accuracy was improved by analysing the impact of constitutive models using the finite element (FE) model, and the deep learning (DL) model was employed for result analysis. The results showed that FE simulations with these models effectively capture the elastic-plastic response, and the ZA model exhibits the highest accuracy, with a 26.0% accuracy improvement compared with other models at 502 m/s for Hugoniot elastic limit (HEL) stress. The different constitutive models offer diverse descriptions of stress during the elastic-plastic response because of temperature effects. Concurrently, the parameters related to the yield strength at quasi-static influence the propagation speed of elastic waves. Calculation show that the yield strength at quasi-static of 6061 Al adheres to y = ax + b for HEL stress. The R-squared (R2) and mean absolute error (MAE) values of the DL model for HEL stress predictions are 0.998 and 0.0062, respectively. This research provides a reference for selecting constitutive models for simulation under the same conditions.

Experimental investigation of seismic response of precast concrete panels with castellated keys support pillar connections under in-plane cyclic loading

The reliable joint connection between precast members is vital to resisting earthquake loads in precast concrete structures. To further improve the convenience of precast construction, this paper presents a new horizontal joint of precast concrete panels with castellated keys supports pillar connections based on the stable mechanical properties of the wet concrete joint. To examine the seismic response of this connection type, a series of in-plane cyclic loading tests were carried out using six full-size precast specimens and one cast-in-place specimen for comparison. The influences of axial compression ratio, joint width, and joint concrete strength on the seismic indicators of the precast concrete panel were considered in the design of specimens. The test results showed all specimens had the same damage process, and the ultimate failure modes combined compression and bending. The precast specimens exhibited similar seismic performance to the cast-in-place specimen, especially whose joint concrete strength is higher than the precast concrete panel. Based on the load–displacement test curve, a hysteretic curve model that included both the envelope curve and the stiffness degradation law was proposed. The predictions from the model showed good compatibility with the experimental results, and the model can be used as a reference for analyzing the elastic–plastic response of the precast concrete panels with castellated keys supporting pillar connections.

Experimental characterization and numerical analysis of CFRPs at cryogenic temperatures

The thermo-mechanical performance of carbon fiber reinforced polymers (CFRPs) is affected by temperature changes due to the dissimilar nature of the constituents and dissimilar properties. For instance, under cryogenic conditions, the effective mechanical performance of the composite system can be significantly reduced. In this work, dynamic mechanical analysis (DMA) tests and coupon mechanical tests at room and cryogenic temperatures (through immersion in liquid nitrogen), are combined with computational micromechanics to analyze the development of micro-residual stresses from curing to cryogenic conditions, and their influence on the mechanical performance of a unidirectional CFRP. The results confirm the stiffness increase in the matrix and in the composite under cryogenic conditions, but the high tensile triaxial stress state that is developed during cooling reduces the overall composite strength, despite the increase of the matrix strength with decreasing temperature. To capture the failure modes and the evolution of the properties appropriately, the elastic-plastic response and the pressure dependent failure model are formulated to appropriately represent the shear response of the composite system and matrix failure under complex triaxial stress states, enabling a complete analysis and the identification of effective material properties, based on a reduced number of simple tests on the neat resin and on the composite system at different temperatures, which otherwise would be impossible to obtain considering the dimensional and technological restrictions of performing mechanical tests at cryogenic conditions.

Numerical and theoretical modeling of the elastic-plastic bulging deformation of UHMWPE composite laminate under high-speed impact

The bulging test is crucial for evaluating the ballistic resistance of ultra-high molecular weight polyethylene laminate. However, the underlying deformation mechanism and the quantitative description of the bulging deformation, including the apex displacement and the location of the boundary of the deformation region (traveling hinge), are still lacking due to the complex dynamic elastic-plastic response under impact. In this paper, the bulging deformation of UHMWPE laminates is computationally and theoretically studied. First, an orthotropic elastic-plastic damage model considering the strain rate effect is established, which can describe the dynamic response of UHMWPE laminates in agreement with the experimental results. Secondly, the results show that the apex displacement increases linearly with the increase of impact velocity but decreases nonlinearly with the thickness. In contrast, the traveling hinge moves outward at a constant speed, independent of the thickness and impact velocity. It can be explained that the membrane stretching dominates the bulging deformation. Based on these results, an analytical model is proposed to quantitatively predict the bulging deformation, which can be used to predict the effects of the mass and the impact velocity and thickness on the bulging deformation. The work is meaningful for the design of UHMWPE laminates with high-impact resistance.

A SDoF Response Model for Elastic–Plastic Beams under Impact at Any Point on the Span

This study aims to investigate the elastic–plastic response of a clamped-clamped beam struck by a rigid heavy mass with a low velocity at any point on the span. The impact system is simplified as a single-degree-of-freedom (SDoF) mass-spring model to formulate the beam’s equations of motion during loading and unloading. With the consideration of material elasticity and large deflection, elastic–plastic analytical solutions are derived to predict the global deformation behavior of the beam. Validation and comparison are conducted against numerical simulations performed using ABAQUS, and satisfactory agreement is achieved for the predictions of the structural dynamic behavior. Meanwhile, a parametric study is presented to assess the influence of the impact location on the characteristic response parameters, which suggests that the structural stiffness increases as the impact location approaches the beam’s support. The findings drawn from analytical and numerical studies can be useful in the anti-impact design of engineering structures.