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Numerous studies have been carried out to characterize uncertainties of soil properties, and lots of multivariate databases have been compiled to make the characterization of uncertainties more realistic. However, when it comes to complex situations, that is, for complex critical state constitutive models and soil–structure interface properties, the uncertainty quantification becomes a challenge. This paper aims to quantify the uncertainties of the soil–structure interface properties from laboratory tests. A framework of uncertainty quantification based on a simplified two-dimensional Monte Carlo simulation is first proposed. To validate the performance of the framework, an enhanced hypoplastic interface model considering particle breakage is then proposed and employed in the uncertainty quantification framework. The CMA-ES algorithm is then used to calibrate the uncertainties based on the framework and the hypoplastic soil–structure interface model. The results showed the proposed framework with the enhanced model can capture the uncertainties of the soil–structure interface properties. In the studied experiments, 30 out of 42 experimental curves were found to be well calibrated based on the Kolmogorov–Smirnov normality test. Furthermore, to obtain acceptable results, based on the calibration-validation process, the effect of the selection of experiments on the calibration performance is discussed. Some suggestions on how to choose experiments to calibrate the soil–structure interface properties are summarized, which should be helpful in practice. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive approach aimed at developing a coupled process-structure simulation that integrates anisotropic and elastoplastic material behavior for plastic components manufactured through Fused Filament Fabrication (FFF) 3D printing. The simulation incorporates material orientation considerations, linking the process simulation with structural simulation. Subsequently, stress and strain values from the simulations are compared with the test results. Moreover, the fracture behavior of components manufactured in this way is also taken into account in relation to material orientation. The executed simulations have yielded successful outcomes, affirming the efficacy of the anisotropic and elastoplastic simulation across all strand orientations. Special attention is paid to the application of the method. Here, the simulation method introduced in this contribution with the approaches for describing the material behavior under mechanical load can be used in the future in the dimensioning of FFF manufactured plastic components to predict the deformation behavior and failure, especially under consideration of a well economic and efficient virtual product development. [ABSTRACT FROM AUTHOR]

The combined Finite–Discrete-Element Method (FDEM) has demonstrated significant advantages in simulating the fracture and fragmentation process of brittle materials. However, the use of simple elastic-damage model alone is insufficient to meet the requirements for simulating the deformation of materials with ductility, and the computational cost of the discrete-element makes it a bottleneck in further development of FDEM. In this work, the 3D elastoplastic-damage-fracture joint mechanical model is proposed, and a combined algorithm has been implemented in the new FDEM package, INterdisciplinary Finite–Discrete-Element Program (INFIDEP). To improve computational efficiency and scale, a universal General-Purpose Graphics Processing Unit (GPGPU) parallelization INFIDEP code has been developed using the Compute Unified Device Architecture (CUDA) in C/C + +. An improved parallel framework has been proposed, and a simplified contact detection algorithm that is more robust for non-uniform elements has been adopted. Using GPGPU-INFIDEP, we simulated Brazil's tensile strength (BTS) tests under quasi-static loading conditions and Taylor bar impact tests. The BTS tests demonstrated consistent stress–strain curves and accurate deformation trends. The speedup ratio stabilized at around 400–500 times on the NVIDIA A6000 GPU platform. The Taylor bar impact tests simulated based on the joint mechanical model well reflect the deformation trend of the specimen head and the impact fracture mode, which cannot be simulated by traditional FDEM and 2D plane-strain models. These results show that GPGPU-INFIDEP offers a valuable and powerful numerical tool for studying continuum–discontinuum deformation problems of brittle and elastoplastic materials in rock engineering. Highlights: The framework of 3D elastoplastic-damage-fracture joint mechanical model has been implemented in FDEM. An improved GPGPU parallel FDEM framework has been proposed, which improves the performance by a factor of 400 to 500 compared to a single-core CPU. The accuracy of the elastic-plastic model based on the FDEM framework has been verified, and GPGPU parallel acceleration has been implemented to improve its performance. The FDEM elastoplastic-damage-fracture joint model can better simulate the plastic deformation and cracking of ductile materials. [ABSTRACT FROM AUTHOR]

This work introduces a distributed memory machine and octree-based Finite Element (FE) framework for modeling metal Additive Manufacturing (AM) processes. In this sense, an Adaptive Mesh Refinement (AMR) is used to accurately capture the complex geometrical domain and the physical phenomena of AM processes for the part-scale analysis. AMR is used in conjunction with refinement criteria suitable for this problem: (1) a geometric criterion for refining the material deposition path, and (2) an accuracy criterion based on an a-posteriori error-indicator of the displacement field. As a consequence, the geometry and numerical solution are accurately captured whilst the number of FEs is kept controlled along the simulation. Numerical simulations involving growing domains are presented to assess the accuracy and computational efficiency of the framework with different octree-based and structured fixed mesh configurations. The overall performance of the framework is evaluated through a strong scalability analysis to track the evolution of the computational time along the simulation, where all steps composing the AM pipeline are independently analyzed. The strong scalability test consists of a discrete evolving domain with over 15 M active nodes, solved on a High-Performance Computer (HPC) using 2, 048 processors. [ABSTRACT FROM AUTHOR]

This paper aims to propose an improved constitutive model based on the classical Chaboche mixed hardening model to describe the cyclic elastoplastic behavior of 6082-T6 aluminum alloy. First, 16 specimens from 6082-T6 aluminum alloy were tested under monotonic and cyclic loads. The variation law of the backstress, yield surface size, elastic modulus, and peak stress with equivalent plastic strain was obtained and analyzed. The results show that the kinematic hardening before and after the load reversal had a significant difference. Meanwhile, the elastic modulus and yield surface radius experienced a rapid decay at the early stage of equivalent plastic strain growth and then tended to flatten out. Based on these phenomena, a modified constitutive model based on the classical Chaboche mixed hardening model was proposed. The evolutions of isotropic hardening/softening, backstress, and elastic modulus were introduced. Then, the model was introduced to the ABAQUS software by the user subroutine to define a material's mechanical behavior (UMAT) subroutine and corresponding parameters were provided. Finally, the proposed constitutive model was proven to capture the cyclic elastoplastic properties of 6082-T6 aluminum alloy well and had a significant improvement on the classical Chaboche mixed hardening model. Among them, the constitutive model can accurately describe the initial yield surface of 6082-T6, with an accuracy improvement of 26.6% compared to the Chaboche mixed hardening model, and an accuracy improvement of 7.44% in describing changes in elastic modulus. [ABSTRACT FROM AUTHOR]

The freeze–thaw (F-T) cycle is one of the weathering factors that can cause rapid deterioration of the mechanical properties of rocks and threaten the stability and durability of rock engineering in cold regions. To study the influence of F-T action on the mechanical and deformation characteristics of sandstone, triaxial compression tests were performed under four confining pressures (0, 1, 3, and 5 MPa) and five F-T cycles (0, 40, 80, 120, and 160). The experimental results show that the stress–strain curves of the sandstone after F-T cycles can be divided into four phases: compaction, elasticity, strain-hardening, and postpeak failure. According to the deformation behaviors of the sandstone with various F-T cycles, an elastoplastic damage constitutive equation was established considering the compaction effect and F-T action. The model parameters were determined, and the theoretical curves were calculated. The comparisons with theoretical and experimental stress–strain curves demonstrate that the formulated constitutive equation can reflect the key deformation stages and mechanical behaviors of sandstone with different F-T cycles. Because the damage variable is introduced in establishing the model, the proposed model can also provide a quantitative description of the macrodamage, which agrees well with the microdamage of the sandstone after many F-T cycles measured by acoustic emission (AE) technology. The formulated constitutive equation in this paper can well describe the experimental deformation curves of sandstone with various F-T cycles and is easy to embed into numerical analysis software. The results can provide a certain theoretical reference for the evaluation of the durability and stability of rock engineering structures impacted by F-T-induced damage in cold regions. [ABSTRACT FROM AUTHOR]

We carry out a variational study for integral functionals that model the stored energy of a heterogeneous material governed by finite-strain elastoplasticity with hardening. Assuming that the composite has a periodic microscopic structure, we establish the Γ -convergence of the energies in the limiting of vanishing periodicity. The constraint that plastic deformations belong to SL (3) poses the biggest hurdle to the analysis, and we address it by regarding SL (3) as a Finsler manifold. [ABSTRACT FROM AUTHOR]

Modeling of the soil–structure interface has been a critical issue in geotechnical engineering. Numerous studies have simulated complex soil–structure interface behaviors. These models usually are assessed by direct comparisons between the simulations and experiments. However, little work has been done to compare the specific interface behaviors simulated by different interface models. This paper evaluated some frequently recognized interface behaviors for six different interface models. These models either were adopted from the existing literature or modified from the existing soil models, including the exponential model, hyperbolic model, hypoplastic model, MCC model, SANISAND model, and SIMSAND model. Global comparisons and effects of the soil density, normal stiffness, and shearing rate were investigated to evaluate the interface models based on Fontainebleau sand–steel interface experiments and kaolin clay–steel interface experiments. The limitations and advantages of different models under different conditions were discussed. [ABSTRACT FROM AUTHOR]

This paper demonstrates a novel Eulerian computational framework for modeling anisotropic elastoplastic deformations of organic crystalline energetic materials (EM) under shocks. While Eulerian formulations are advantageous for handling large deformations, constitutive laws in such formulations have been limited to isotropic elastoplastic models, which may not fully capture the shock response of crystalline EM. The present Eulerian framework for high-strain rates, large deformation material dynamics of EM incorporates anisotropic isochoric elasticity via a hypo-elastic constitutive law and visco-plastic single-crystal models. The calculations are validated against atomistic calculations and experimental data and benchmarked against Lagrangian (finite element) crystal plasticity computations for shock-propagation in a monoclinic organic crystal, octahydro-1,3,5,7-tetranitro-1,3,5,7 tetrazocine (β-HMX). The Cauchy stress components and the resolved shear stresses calculated using the present Eulerian approach are shown to be in good agreement with the Lagrangian computations for different crystal orientations. The Eulerian framework is then used for computations of shock-induced inert void collapse in β-HMX to study the effects of crystal orientations on hotspot formation under different loading intensities. The computations show that the hotspot temperature distributions and the collapse profiles are sensitive to the crystal orientations at lower impact velocities (viz., 500 m/s); when the impact velocity is increased to 1000 m/s, the collapse is predominantly hydrodynamic and the role of anisotropy is modest. The present methodology will be useful to simulate energy localization in shocked porous energetic material microstructures and other situations where large deformations of single and polycrystals govern the thermomechanical response. [ABSTRACT FROM AUTHOR]

Brittle material Mode I fracture may be characterized by the double cleavage drilled compression test. For linear elastic materials, the critical energy release rate, or fracture toughness, can be estimated simply using the linear elastic fracture mechanics. For other types of constitutive behavior, the material parameter has to be determined with numerical fracture modeling. In this paper, we have used two approaches, the phase-field damage model and the cohesive elements, in order to estimate the critical energy release rate of an elastoplastic material. Firstly, we assessed the numerical models and discussed their parameters by comparison of available data from double cleavage drilled compression experimental tests run on a silica glass. Both phase-field damage and cohesive zone models were able to reproduce fracture initiation at the observed macroscopic stress for the linear elastic material. However, the material toughness could not be predicted by the phase-field approach due to the result dependence on the model regularization parameter. Secondly, an elastoplastic methyl methacrylate polymer was submitted to the compression test in our lab. Both models were then extended for elastic-perfectly plastic materials. Crack initiation was obtained at the observed macroscopic strain for similar critical energy release rate ranges for both approaches, providing good confidence in the estimated material toughness. [ABSTRACT FROM AUTHOR]

This study presents a numerical approach to an analysis of the mechanical behavior of double-layered tensegrity grids. We present a comparative study on the behavior of tensegrity grids through geometric nonlinear analysis (GNA) and combined nonlinear analysis (CNLA) (geometric and material), considering the possible effect of evolution in the elasto-plastic domain of the cable elements. The effect of the relaxation of cable on the amplification of the displacement of these grids was taken into account. The updated Lagrangian formulation, which modifies the Newton-Raphson iterative scheme with incremental loading, was adopted. We have developed a numerical computational model specific to tensegrity structures that simulates the geometric and material nonlinear behavior. The reliability of the calculation tool developed has been validated. Additionally, the results of the application of the numerical model on a grid, which was generated based on demi-cuboctahedral tensegrity cells, are presented. [ABSTRACT FROM AUTHOR]

The literature about the asymptotic numerical method (ANM) is reviewed in this paper as well as its application to hyperelasticity and elastoplasticity. ANM is a generic continuation method based on the computation of Taylor series for solving nonlinear partial differential equations. Modern techniques of high-order differentiation provide simple tools for computing these power series, the corresponding algorithms for finite strain elasticity and elastoplasticity being summarized here. Taylor series is not only a computation tool, but it contains also useful information about the structure of the considered solution curve. The paper ends with a short historical account about the development of this numerical method. [ABSTRACT FROM AUTHOR]

Solid deformation is always a crucial factor of gas transport in sedimentary rocks. While previous studies always adopt the assumption of isotropic poroelastic deformation, anisotropic poroelastoplastic deformation is rarely considered, despite anisotropy being a ubiquitous property of natural sedimentary rocks. In this work, an anisotropic poromechanical model is established to analyze the matrix porosity and apparent permeability evolutions during the process of gas migration. Using a thermodynamic formulation that treats the fluid–solid interface as an independent phase, we derive a rate form for matrix porosity and obtain the new dissipation function that contains three parts: dissipations from solid deformation, gas adsorption, and fluid flow. For gas adsorption, we justify the rationality of the adopted model; for fluid flow, the updated porosity can be substituted into sophisticated apparent permeability models for full‐scale analysis; and for solid deformation, a recently developed constitutive model appropriate for rocks exhibiting transverse isotropy in both the elastic and plastic responses is adopted in this work. Through the novel stress‐point simulation incorporating two effective stress measures and adsorption strain, new patterns of apparent permeability are obtained, which fit the experimental data quite well and cannot be reproduced from the assumption of isotropic poroelasticity. The advantages of our poromechanical model include thermodynamic consistency and the ability to employ finite‐element‐based formulation. Finally, an initial‐boundary value problem of gas production considering anisotropic plasticity is conducted, and the effects of the bedding plane and different adsorption models are highlighted. [ABSTRACT FROM AUTHOR]

Surface roughness emerges naturally during mechanical removal of material, fracture, chemical deposition, plastic deformation, indentation, and other processes. Here, we use continuum simulations to show how roughness which is neither Gaussian nor self-affine emerges from repeated elastic–plastic contact of rough and rigid surfaces on a flat elastic–plastic substrate. Roughness profiles change with each contact cycle, but appear to approach a steady-state long before the substrate stops deforming plastically and has hence “shaken-down” elastically. We propose a simple dynamic collapse for the emerging power-spectral density, which shows that the multi-scale nature of the roughness is encoded in the first few indentations. In contrast to macroscopic roughness parameters, roughness at small scales and the skewness of the height distribution of the resulting roughness do not show a steady-state. However, the skewness vanishes asymptotically with contact cycle. [ABSTRACT FROM AUTHOR]

This article presents a critical discussion of the repercussion of overshooting effects on element tests and finite-element simulations. For exemplification purposes, three advanced constitutive models for sands that had already achieved a certain level of accuracy in the simulation of monotonic and cyclic loading were carefully selected; namely, a bounding surface plasticity model, a hypoplastic model with intergranular strain, and a hypoplastic model with elastoplastic anisotropic intergranular strain. Cyclic loading laboratory data and scale tests on Karlsruhe fine sand were considered to support the analyses. The obtained results suggest that the overshooting issue is one of the most serious limitations of the selected models and has a major impact on elemental and finite-element simulations. Therefore, models' end-users should be aware of this drawback when performing simulations under certain conditions involving unloading–reloading episodes with different strain amplitudes. [ABSTRACT FROM AUTHOR]

The volumetric locking of the conventional finite element method (FEM) was investigated through the nearly incompressible elasto-plastic analysis, and the extra-DOF-free reinforcement function was introduced in the framework of the generalized finite element method (GFEM) for improvement of this problem. Through the introduction of the reinforcement function, a richer approximation space was obtained for the interpolation function, of which the ability of correctly reflecting structural deformations was promoted under the approximate volumetric invariance constraint. Furthermore, the construction of the reinforcement function is independent of the extra degrees of freedom, which eliminates the linear dependency in the traditional GFEM. Different triggering conditions and manifestations of volumetric locking of the conventional FEM were found in linear elastic, hyperelastic, and plastic analyses. Three classical numerical examples show that, the extra-DOF-free GFEM can effectively alleviate the volumetric locking in all analyses, and obtain accurate and reasonable results. [ABSTRACT FROM AUTHOR]

We perform via Γ-convergence a 2d-1d dimension reduction analysis of a single-slip elastoplastic body in large deformations. Rigid plastic and elastoplastic regimes are considered. In particular, we show that limit deformations can essentially freely bend even if subjected to the most restrictive constraints corresponding to the elastically rigid single-slip regime. The primary challenge arises in the upper bound where the differential constraints render any bending without incurring an additional energy cost particularly difficult. We overcome this obstacle with suitable non-smooth constructions and prove that a Lavrentiev phenomenon occurs if we artificially restrict our model to smooth deformations. This issue is absent if the differential constraints are appropriately softened. [ABSTRACT FROM AUTHOR]

We study the large-scale behavior of a small-strain lattice model for a network composed of elastoplastic springs with random material properties. We formulate the model as an evolutionary rate independent system. In an earlier work we derived a homogenized continuum model, which has the form of linearized elastoplasticity, as an evolutionary T-limit as the lattice parameter tends to zero. In the present paper we introduce a periodic representative volume element (RVE) approximation for the homogenized system. As a main result we prove convergence of the RVE approximation as the size of the RVE tends to infinity. We also show that the hysteretic stress-strain relation of the effective system can be described with the help of a generalized Prandtl--Ishlinskii operator, and we prove convergence of a periodic RVE approximation for that operator. We combine the RVE approximation with a numerical scheme for rate-independent systems and obtain a computational scheme that we use to numerically investigate the homogenized system in the specific case when the original network is given by a two-dimensional lattice model. We simulate the response of the system to cyclic and uniaxial, monotonic loading, and numerically investigate the convergence rate of the periodic RVE approximation. In particular, our simulations show that the RVE error decays with the same rate as the RVE error in the static case of linear elasticity. [ABSTRACT FROM AUTHOR]

Fluid injection‐induced deformation around a cylindrical cavity is of particular interest in the area of subsurface energy extraction. In this study, a model is proposed to analyze the time‐dependent expansion of a cavity caused by fluid injection in an elastoplastic dry porous medium. This problem is characterized by the existence of two moving boundaries, a permeation front and an elastoplastic interface, which leads to distinct time‐dependent zones governed by different sets of equations. The interplay between these two boundaries leads to three phases of solution. The a priori unknown partitioning of the injection rate into the rate of change of cavity volume and infiltration in the porous medium necessitates the introduction of a time‐dependent permeation coefficient as one of the primary variables. The method of solution takes advantage of the quasi‐static and quasi‐stationary nature of the problem, which makes it possible to treat time as a parameter rather than a variable. It follows that the problem can be solved in two steps. In a first step, closed‐form expressions for the pore pressure, displacement, and stress fields in each zone are derived, with parameters in these expressions depending explicitly on four time‐dependent variables, namely the positions of the two interfaces, the cavity radius, and the permeation coefficient. In a second step, the rate equations governing the evolution of these variables during different phases are derived and solved numerically. The paper concludes with a parametric analysis of the influence of the stiffness and strength of the material on the solution. [ABSTRACT FROM AUTHOR]

Standard strength calculations for bearing units of extremely loaded structures, including nuclear power plants, allow an inelastic deformation of the materials of these units. At the same time, the calculations of the low-cycle fatigue require taking into account the factors that are not observed upon single loading, i.e., kinetics of cyclic strains, cyclic creep, and the effect of change in the modes of the inelastic cyclic deformation under normal operating conditions. It is known that, in this case, a material can be cyclically hardened, softened, or stable. For the first type of materials under soft loading with constant amplitude of stresses in cycles, the range of strains decreases with an increase in the number of cycles, but increases for the second one. Under hard loading with constant strain amplitude, the maximum stresses in a cycle increase for a hardened material and, on the contrary, decrease for a softened one. In addition, the soft loading of a softened material with an increased number of loading cycles results in one-sided accumulation of plastic deformations. These phenomena must be taken into account both in the analytical description of the kinetics of deformation diagrams and in the corresponding calculation equations used in the strength standards. At early stages of developing the calculation techniques for these conditions, the stresses were calculated under the assumption of perfect elasticity of a material. This approach was used owing to the lack of available calculation techniques for the problem of an inelastic cyclic deformation, which is complicated in the formulation. The subsequent development of the theory of the cyclic elastoplastic deformation and the analytical and numerical solutions of cyclic boundary-value problems and the development of numerical computational methods and powerful computer software codes fundamentally changed the situation, providing the possibility of analysis and modeling of the physically and geometrically nonlinear deformation processes. It is shown that the transition from the elastic adaptability (with an elastic deformation of the structure in a stable cycle) to a sign-alternating flow is smooth and continuous and is similar to the transition from the elastic to plastic deformation under a single loading. This mechanism is similar to the conditional boundary of the transition from low-cycle to high-cycle fatigue under a cyclic strain. In this case, we propose to use in calculations the existing rather simple models and experimentally determined parameters of the cyclic deformation diagrams of materials. In the modern formulation of the considered problems, it is of fundamental importance to take into account both the kinetics of cyclic and one-sided accumulated deformations and make allowance for the occurrence of creep effects in cycles. This approach also makes it possible to take into account the acceleration of unsteady cyclic creep as a result of the previous plastic deformation of the other sign, which can be rather significant. [ABSTRACT FROM AUTHOR]

The formulation of the Lamé–Gadolin problem on the equilibrium of a hollow sphere consisting of two parts, one of which is preliminarily deformed, is given for finite deformations. An analytical solution of the problem for the elastic potential of a special form is obtained. A numerical solution of the problem for an elastoplastic material is obtained. When modeling plastic deformations, the Drucker–Prager plasticity condition is used, and the plastic flow is described using an unassociated law. [ABSTRACT FROM AUTHOR]

This paper describes a study of deformation of an ideal elastoplastic adhesive layer of a sample in the form of an elastic double-cantilever beam. The integral values are determined for a number of adhesives with account for all diagonal stress tensor components in the layer. It is shown that the integral value is significantly affected by the plane problem type in the case where an elastic-plastic model of layer deformation is applied. As demonstrated in the study, compressive stresses may be present during normal fracture in the irreversible deformation region of the adhesive in a plane stressed state. [ABSTRACT FROM AUTHOR]

Natural gas hydrates have potential economic and environmental significance. However, wellbore instability likely occurs during drilling due to the deterioration in the geomechanical properties of formation caused by hydrate dissociation. In this study, a time-dependent elastoplastic analytical model for wellbore stability is proposed under overbalanced and underbalanced drilling, considering the hydrate dissociation-induced changes in the geomechanical properties and full coupling between hydraulic–mechanical fields. The analytical solutions are verified with the finite element results under the same conditions and validated with the results from complex numerical simulations. According to the analytical solutions, the difference in pore pressure relative to the initial pore pressure decreases, and accordingly, the incremental displacement decreases (by approximately 39.54% for the maximum displacement) after the influence of the mechanical field on pore pressure is considered. The influence is greater far from the wellbore and smaller around the wellbore due to the constant drilling fluid pressure. The risk of wellbore instability increases with time, and the safe drilling window of drilling fluid pressure will be narrowed by hydrate dissociation (by −5.90%), the increase in the drilling fluid temperature (by −12.64% from the temperature of 20 °C to 30 °C) and the reduction in cohesion (by −47.43% at most). [ABSTRACT FROM AUTHOR]

This paper develops a modeling method with an incremental stress–strain–environment constitutive model to predict the change in the plastic mechanical behavior of concrete caused by environmental action. The model regards the environmental factor as a constitutive variable, similar to stress and strain. The yield condition of the model is a function of stress, the plastic internal variable, and the environmental variable. The loading–unloading criterion is established in the space constructed by the strain and the environmental variable to determine the contribution of mechanical loads and environmental factors to plastic deformation. By considering the strain rate as an environmental factor and applying the proposed method, a stress–strain–strain rate constitutive model of concrete is developed to describe the plastic flow caused by the combined action of stress and strain rate. In addition, constant- and variable-strain rate loading tests are performed to evaluate the performance of the established model. In particular, the model's capabilities are further highlighted by comparing the simulation results of the dynamic stress–strain model and the proposed model under loading conditions with rapidly decreasing strain rates. [ABSTRACT FROM AUTHOR]

This paper provides the solution of a homogenization model that simultaneously considers the plastic and elastic strain fields in a single analytical formulation. In addition, the authors aim to decouple plastic flows triggered in the inclusions, in the matrix at the interfaces with the inclusions, and in the matrix at a large distance from the inclusions. The authors propose an admissible displacement field containing elastic and anelastic contributions in series. This field provides a new strain homogenization formula in which the plastic deformations in the inclusions, at the interface between the matrix and the inclusions, and in the matrix far from the inclusions appear explicitly. Applications allow to evaluate the pertinence of the approximation provided by this field, and show that this new formulation is able to create macroscopic work hardening while all the elementary phases have elastic‐perfectly plastic behaviour without resorting to expensive numerical simulations (such as mesoscopic finite element modelling). This is the consequence of the simultaneous presence of elasticity and plasticity on the one hand and, on the other, the possibility of triggering plastic flows independently on the surface of each type of inclusion and in the matrix at a large distance from the inclusions. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to present a direct analysis to demonstrate why markedly different tensile and compressive behaviors of concretes could not be simulated with the Drucker–Prager yield criterion. Design/methodology/approach: This study proposed an extended form of the latter for establishing a new elastoplasticity model with evolving yield strengths. Findings: Explicit closed-form solutions to non-symmetric tensile and compressive responses of uniaxial specimens at finite strain are for the first time obtained from hardening to softening. Originality/value: With such exact solutions, the yield strengths in tension and compression can be explicitly prescribed by uniaxial tensile and compressive stress-strain functions. Then, the latter two are further provided in explicit forms toward accurately simulating tensile and compressive behaviors. Numerical examples are supplied for meso-scale heterogeneous concrete (MSHC) and high-performance concrete (HPC), etc. Model predictions are in good agreement with test data. [ABSTRACT FROM AUTHOR]

A large part of fractures found in nature are offset or unmated. The closure behavior of unmated rock fractures under a normal load is critical for the stability analysis of fractured rock masses and the associated coupling process. Local contacted asperities undergone plastic deformation are gradually flattened and dwarfed during a fracture closure, combined with the emergence of new contacts, resulting in the rapid growth of fracture stiffness. The effect of this morphological change on fracture deformability has not been quantitatively characterized, if any. A contact analysis based on the geometrical change of a sphere was put forward to simulate the closure of unmated fractures, validated by fracture closure experiments on three unmated rock fractures. A square-covering fractal method was then employed to characterize the distribution of contacts between two rough surfaces and to quantify fracture morphology variations. A modified exponential model incorporating two new parameters, a fractal dimension and a mixed regime length, was established by regression analysis to quantify the elastoplastic deformation of unmated rock fractures. The results suggest that the elastic and plastic deformation of contacted asperities happens most significantly in the initial loading stage, with a successive growth of the proportion of the plastic deformation in the total deformation. The degradation of fracture morphology leads to a rapid increase in the contact area and fracture stiffness, enhancing the ability of asperities to resist deformation. The modified exponential model yields precise predictions to the experimental data, offering a quick and accurate assessment method for the closure behavior of unmated rock fractures. [ABSTRACT FROM AUTHOR]

In this article, a pseudo-stress for local residual and an algebraically derived consistent tangent are applied to elastic–plastic boundary value problems of shells. The authors define a coupled problem of the weak form of the equilibrium equation for the overall structure and the constrained equations for stress state, which include the yield condition and the plane stress condition, at every material point. Since the pseudo-stress for the residuals of yield criterion and plane stress state is incorporated into the linearized weak form of the equilibrium equation, the proposed scheme does not have any local iterative calculations and enables us to decrease the residuals in the coupled boundary value problems simultaneously. Some numerical examples using shell elements demonstrate the validity and effectiveness of the procedures in complex situation with material and geometrical nonlinearities. [ABSTRACT FROM AUTHOR]

The Dou-Gong bracket is a key transition component between the roof and the column in ancient Chinese wooden structures. In this paper, the static structural behavior of Qing-style 'one bucket three liters' Column-cap Dou- Gong Bracket (third-class material) full-scale test model was studied by simulation. The simulation of monotonic static loading was carried out in the vertical (Z-axis) direction, and the simulation of quasi-static loading under horizontal low-cycle reciprocating load was carried out in the horizontal direction (Y-axis, X-axis). The material of the simulation was P. sylvestris, and the setting of its material parameters referred to the results obtained from the material property tests. An anisotropic constitutive model suitable for the properties of wood materials was selected, and the elastoplasticity of wood in the simulation was defined by the Hill yield rule. The static structural behavior of the component in the Z-axis could be described by the variable stiffness linear elastic mechanical model. The static structural behavior of the component in the Y-axis and X-axis could be described by a multi-linear restoring force model. According to the simulation results, the key mechanical indexes of Dou-Gong bracket component in the Z, Y, and X axes were calculated from three aspects of strength, deformation, and energy. [ABSTRACT FROM AUTHOR]

As complex and heterogeneous materials, the mechanical properties of rocks are still in need of further investigation regarding the mechanisms of the effects of water. In engineering projects such as goaf foundation treatment and ecological restoration, it is particularly important to describe the fracturing process of non-uniform water-containing sandstone media. The study utilized the theory of continuum mechanics to adopt an elastoplastic strain-softening constitutive relationship and develop a numerical model for analyzing the uniaxial compressive strength and failure characteristics of non-uniform water-containing sandstone. The results indicate that, compared with the reference rock sample, the shorter the capillary path of water entering the rock sample's internal pores or the larger the contact area with water, the shorter the time required for the rock sample to be saturated. Increasing the water content causes a rapid decline in the rock sample's elastic modulus and intensifies its brittleness. Group D2 and D3 samples exhibited a decrease in average peak strength to 70.4% and 62.1%, respectively, along with a corresponding decrease in the elastic modulus to 90.78% and 76.55%, indicating significant strain softening. While the failure mode of the rock sample remains consistent across different water contents, the homogeneity of failure shows significant variation. Increasing volumetric water content raises the likelihood of interconnecting cracks between rock samples, resulting in a progressive decline in macroscopic mechanical properties such as peak strength, critical strain, and elastic modulus. This research is significant in advancing the theory and construction technology for ecological restoration in goaf areas. [ABSTRACT FROM AUTHOR]

Background: Accurate measurements of material constitutive model parameters are of great significance for design optimization and reliability analysis. Objective: In this paper, to characterize the anisotropic elastoplastic parameters of single-crystal metal materials at the nanoscale, a high-throughput inversion method of anisotropic elastoplastic constitutive parameters of single-crystal metal materials using a neural network and bicrystalline indentation load-depth curve is proposed. It addresses the limitations of indentation technology in the characterization of anisotropic material parameters. Methods: A large number of finite-element simulation results were used to build a sample dataset. A neural network was used to build a mapping relationship model between the characteristics of the indentation load-depth curve and the parameters of the material elastic–plastic constitutive model. Results: The parameter inversion method based on the neural network reduced the iterative optimization link, improved the parameter inversion efficiency, and realized high-throughput parameter inversion of the nonupdated intelligent material constitutive model. Conclusion: The effectiveness of the method was verified by inversion experiments of anisotropic elastic–plastic parameters of a single-crystal copper material. The accuracy and universality of the method were further verified by an error analysis, demonstrating the engineering application prospects of the proposed method. [ABSTRACT FROM AUTHOR]

The concept of concurrent material and structure optimization aims at alleviating the computational discovery of optimum microstructure configurations in multiphase hierarchical systems, whose macroscale behavior is governed by their microstructure composition that can evolve over multiple length scales from a few micrometers to centimeters. It is based on the split of the multiscale optimization problem into two nested sub-problems, one at the macroscale (structure) and the other at the microscales (material). In this paper, we establish a novel formulation of concurrent material and structure optimization for multiphase hierarchical systems with elastoplastic constituents at the material scales. Exploiting the thermomechanical foundations of elastoplasticity, we reformulate the material optimization problem based on the maximum plastic dissipation principle such that it assumes the format of an elastoplastic constitutive law and can be efficiently solved via modified return mapping algorithms. We integrate continuum micromechanics based estimates of the stiffness and the yield criterion into the formulation, which opens the door to a computationally feasible treatment of the material optimization problem. To demonstrate the accuracy and robustness of our framework, we define new benchmark tests with several material scales that, for the first time, become computationally feasible. We argue that our formulation naturally extends to multiscale optimization under further path-dependent effects such as viscoplasticity or multiscale fracture and damage. [ABSTRACT FROM AUTHOR]

In deep shale gas reservoir exploration, elastoplastic embedment plays an increasingly important role in analyses of the conductivity of fracture networks because it is affected by high temperature, high in-situ stress. To obtain a full understanding of proppant embedding behavior, an analytical model of the embedment depth of a single spherical proppant was developed based on the Drucker–Prager (D–P) yield criterion and shale elastoplastic mechanical behavior. Shale indentation tests with rigid balls with diameters of 0.8 mm and 1.0 mm were conducted to validate the reliability of the theoretical model. Compared with the Hertz, Thornton and non-linear models, the new model developed in this paper was in better agreement with embedment experimental data. Each parameter of the new model has clear physical meaning and can be obtained by a series of triaxial compression tests. An Analysis of Variance (ANOVA) method was applied to discuss the sensitivity of the model to the parameters, and the results showed that the strength parameters α and Y contributed the most to, and had nonlinear effects on, the proppant embedment depth. Highlights: According to the shale mechanical properties, the contact area between a single spherical particle and a semi-infinite space can be divided into elastic, strain hardening and fully plastic region approximately. An analytical elastoplastic embedment depth model for a single rigid spherical particle was developed based on the Drucker-Prager yield criterion and total strain theory. The yielding parameters have a dominant and nonlinear effects on the proppant embedment depth. It is more appreciated that applying a suitable yield criterion which can accurately describe the yielding process of rock-like materials to discuss the interaction between proppant and shale. [ABSTRACT FROM AUTHOR]

The possibility of modeling elastoplastic deformations in materials characterized by anisotropy of elastic and plastic properties without restrictions on the anisotropy magnitude of linear compressibility of the material is shown. The mathematical model of elastoplastic deformation of anisotropic materials is applicable for symmetry cases when it is possible to decompose the elastic deformation energy into the volume change energy and the shape change energy. To simulate the processes of deformation of anisotropic materials by the dynamic finite element method, the anisotropic pressure caused by uniform volumetric deformation is introduced into the difference scheme instead of the isotropic pressure. In this case, the total stress tensor is uniquely decomposed into the anisotropic pressure tensor and the total stress tensor deviator. A criterion is given for the possibility of using the anisotropic pressure when modeling the elastic-plastic deformation in anisotropic materials instead of the spherical part of the stress tensor within the framework of the model of a volume-isotropic material. [ABSTRACT FROM AUTHOR]

• Two unified numerical algorithms of periodic boundary condition are proposed. • The proposed algorithms predict accurate thermo-mechanical properties of composites. • The proposed algorithms are available for RVEs with periodic and nonperiodic meshes. • The proposed algorithms can be used for simple and complicated nonradial loadings. This work emphasizes on the Periodic Boundary Condition (PBC) utilized in the Finite Element Homogenization (FEH) method to numerically determine the Thermo-mechanical (T-M) properties of composites. The unified numerical implementation algorithms of the PBC used for accurately predicting the elastic properties, coefficients of thermal expansion and elasto-plastic behaviors of composites and available for representative volume elements with conformal and non-conformal surface meshes, respectively, are proposed and detailed. Regarding not only the thermo-elastic properties of composites, but also the elasto-plastic behaviors of composites under both simple uniaxial tensile, shear, uniaxial cycle loading paths and complex non-radial loading paths, the unified numerical implementation algorithms are verified to accurately predict the T-M properties of composites, through comparison with the results of the analytical models, the DIGIMAT-FE method, the experimental test and the results from the literature. The unified numerical implementation algorithms of the PBC can be extended to the predictions of other properties of various composites. This work provides a comprehensive insight into the PBC used for predicting the T-M properties of composites and benefits development of future FE codes implemented in commercial software packages. [ABSTRACT FROM AUTHOR]

A numerical-analytic structural model of thermoelastoplastic deformation of a composite material cross-reinforced with fibers in arbitrary directions is developed on the basis of the time-steps algorithm. The materials of constituents of the composition are isotropic; their plastic deformation is described by the theory of flow with isotropic hardening taking into account the dependence of the loading function on temperature. Conditions determining thermoelastic deformation, unloading, neutral and active loading of thermosensitive constituents of the composition are obtained. The coupled problems of the thermophysical and mechanical behavior of reinforced materials are considered. Structural relationships that are necessary for solving the thermophysical component of the investigated problem are presented. The developed structural model is focused on the use of explicit numerical integration schemes for both elastoplastic and thermophysical problems. [ABSTRACT FROM AUTHOR]

This contribution discusses surrogate models that emulate the solution field(s) in the entire simulation domain. The surrogate uses the most characteristic modes of the solution field(s), in combination with neural networks to emulate the coefficients of each mode. This type of surrogate is well known to rapidly emulate flow simulations, but rather new for simulations of elastoplastic solids. The surrogate avoids the iterative process of constructing and solving the linearized governing equations of rate-independent elastoplasticity, as necessary for direct numerical simulations or (hyper-)reduced-order-models. Instead, the new plastic variables are computed only once per increment, resulting in substantial time savings. The surrogate uses a recurrent neural network to treat the path dependency of rate-independent elastoplasticity within the neural network itself. Because only a few of these surrogates have been developed for elastoplastic simulations, their potential and limitations are not yet well studied. The aim of this contribution is to shed more light on their numerical capabilities in the context of elastoplasticity. Although more widely applicable, the investigation focuses on a representative volume element, because these surrogates have the ability to both emulate the macroscale stress-deformation relation (which drives the multiscale simulation), as well as to recover all microstructural quantities within each representative volume element. [ABSTRACT FROM AUTHOR]

A novel quadrature element for performing plane stress elastoplastic analysis is introduced in this paper. Differing from the popular finite-element method, the quadrature-element method (QEM) first evaluates the integration in the weak-form statement of the problem by an integral quadrature scheme, and then approximates the differentiation at the discrete integration points by the differential quadrature analog. As a result, the QEM avoids construction of shape functions and obtains higher-order elements easily by just increasing the order of integration. The usage of higher-order elements leads to more accurate solutions and coarser geometric meshes without detriment to the computational scale because the number of degrees of freedom is maintained. In addition, the element nodes in the QEM are the same as the integration points that possess physical meanings such as strains and stresses, which is crucial in the elastoplastic analysis for determining the elastic/plastic state of the nodes. A straightforward elastoplastic quadrature-element formulation is developed. Incremental-iterative and return mapping solution schemes are adopted to implement the quadrature element for the elastoplastic analysis. Numerical examples are presented to demonstrate the effectiveness and high accuracy of the proposed approach. [ABSTRACT FROM AUTHOR]

Based on the permeability-based hydraulic fracture (PHF) model， a statistical fracture model (SFM) is introduced to capture the influence of the micro non-uniform distribution of rock materials on the macroscale characteristics of hydraulic fracture. The Weibull probability model is adopted to account for the discreteness of characteristics of these characteristics. By assuming that the permeability of rock material is a function of the mean effective stress， the PHF-SFM model is proposed based on the Biot consolidation theory. The model incorporates the Mohr-Coulomb elastoplastic constitutive model and Darcy’s law to represent mechanical behaviors for the solid and liquid phase of rock material in pre- and post-failure part. The verification is carried out by comparing the simulated results with those of the KGD model. Breakdown pressure， equivalent fracture height and fracture width were studied by varying the Weibull modulus and scale parameters in the SFM model and material properties of rock. The simulation results indicate that including the SFM model does not affect the breakdown pressure， but does vary the fracture geometry. When the Weibull modulus decreases or the scale parameter increases， the discreteness of fracture geometry features increases. [ABSTRACT FROM AUTHOR]

Elastoplasticity is observed in a wide range of materials like metals that have real-world applications. The design and optimization process of such materials depends strongly on elastoplastic analysis for the prediction of displacement and stress. However, elastoplastic simulation is computationally expensive and often requires the use of parallel computers in real-world applications like crashworthiness and metal forming. This paper presents a novel parallel framework for finite element analysis of elastoplastic problems on massively parallel Graphics Processing Units (GPUs) architecture. We propose GPU-based parallel algorithms for all expensive steps in elastoplastic analysis, namely the computation of elemental matrices and their assembly, the computation of stress using the well-known radial-return method and the computation of internal force vectors and their assembly. Since GPUs have limited memory, assembly is done directly into a sparse storage format that can be seamlessly integrated with a GPU-based linear solver. The proposed algorithms are optimized for efficient memory access and fine-grain parallelism and prefer computation over data storage and reuse. In the proposed framework, all the computations are performed on the GPU and expensive data transfers to the CPU are avoided to achieve the best performance. Numerical experiments are conducted over three benchmark examples in three dimensions (3D) considering 8-noded hexahedral elements to demonstrate the performance of the proposed framework. The comparison of execution timings with sequential CPU implementation reveals speedups in the range 20.4 × –69.7 × for computation of elemental matrices and assembly, 47.2 × –66.1 × for computation of stress using radial-return method, 53.7 × –67.3 × for computation of internal force vectors and their assembly. A comparison of wall-clock timings shows 1.4 × to 7.2 × speedup by the proposed GPU implementation. The proposed framework is able to solve up to 5.1 million degrees of freedom (DOFs) elastoplasticity problem on a single GPU. [ABSTRACT FROM AUTHOR]

Experimental results provide strong evidence that the deformation and strength of rocks are closely related to the damage suffered during loading. The classic constitutive models such as Mohr–Coulomb criterion and the Drucker–Prager criterion are usually unable to describe the non-linear deformation behavior of rocks, including strain hardening and softening. Their applications in numerical analysis and practical engineering are limited. For this purpose, an elastoplastic damage constitutive model that takes into account the competition mechanism between damage and strain hardening or softening during rock compression is proposed herein. This model is used to investigate the deformation behaviors and damage evolution of rocks. More importantly, this model has been implemented by finite element programming code and verified by a series of triaxial compression tests. The comparison results between theoretical analysis and experimental data indicate that this model can well describe the stress–strain curves and damage–strain curves of the investigated rocks (sandstone and salt rock), especially the characteristics of softening, hardening and residual strength. Based on parametric analysis, the influence of confining pressure, scale parameter and shape parameter on rock damage is revealed. It is found that the rock scale parameter in this model has a power function relationship with confining pressure. The ultimate plastic deformation that rocks can withstand is related to the scale parameter. The shape parameter controls the residual strength and deformation of rocks. Model results demonstrate that the strength and deformation vary with rock properties, and are strongly dependent on the stress-induced damage and strain characteristics. [ABSTRACT FROM AUTHOR]

Traditional machining in micro-scale still presents many challenges associated with bad chip formation, presence of high burrs, elevated tool wear and low surface quality. Most problems in micro-machining are a consequence of the size effect, which is the similarity in the scale sizes of the cutting-edge radius of the tool and the minimum uncut chip thickness (MUCT). Micro-machining tends to be even more challenging for low-machinability alloys, such as Inconel 718. Through the finite element method (FEM), it is possible to estimate the minimum uncut chip thickness of a material providing that the constitutive model that describes its elastoplastic behavior is known. Therefore, the objective of this contribution is to analyze the chip formation in orthogonal micro-cutting of Inconel 718 using numerical FEM simulations and the Johnson–Cook plasticity model in an explicit scheme. Two cutting tools were modelled with different edge radius in order to represent a sharp tool and a tool that suffered rounding of the tip because of wear. Simulations were carried out with different values of feed per tooth in order to determine which value is closest to MUCT. The Mises stress and accumulated plastic strain were monitored, as well as the cutting forces. The results show that the rounded tool, with an edge radius of 5 µm, leads to higher forces, worse chip formation and worse surface quality when compared to the sharp tool, with an edge radius of 1 µm. [ABSTRACT FROM AUTHOR]

We study the development of plastic deformations in a body with thin inclusion subjected to shear loading under the conditions of unilateral contact with perfectly elastoplastic medium. We determine the shape of a continual plastic zone from the solution of an elastoplastic problem and analyze the development of a plastic layer along the inclusion–medium boundary. Continually distributed plastic deformations cover less than 40% of the surface of inclusion, while the model of localized deformations predicts the complete exfoliation of the inclusion. [ABSTRACT FROM AUTHOR]

It is well known that the use of a consistent tangent stiffness matrix is critical to obtain quadratic convergence of the global Newton iterations in the finite-element simulations of problems involving elasto-plastic deformation of metals, especially for large-scale metallic structure problems. In this article, we derive an exact consistent stiffness matrix for a porous material model, the GLPD model developed by Gologanu, Leblond, Perrin, and Devaux for ductile fracture of porous solids based on generalized continuum mechanics assumptions. Full expressions for the derivatives of the Cauchy stress tensor and the generalized moments stress tensor the model involved are provided and implemented into a finite-element code. The effectiveness and robustness of the proposed tangent stiffness moduli are assessed by applying the formulation in the finite-element simulations of typical ductile fracture problems. Comparisons between the performance of our stiffness matrix and the standard ones are also provided. [ABSTRACT FROM AUTHOR]

Argillaceous rocks are candidate host and/or cap formations for the geological disposal of nuclear wastes in many countries, including Canada, France and Switzerland. The understanding of the long term mechanical behaviour of such rocks is an essential requirement for the assessment of their performance as a barrier against radionuclide migration. Due to the existence of bedding, argillaceous rocks are inherently anisotropic and the development of stress-strain models for their mechanical behaviour needs to take this anisotropy into account. This paper presents two examples of the practical implementation of stress-strain relationships in finite element models to simulate the excavation damage zones (EDZ) in bedded argillaceous rocks. The first example concerns the EDZ around a micro-tunnel in Opalinus Clay, in Switzerland. The second example relates to the EDZ around the century-old tunnel in Tournemire shale, in France. Both examples show the importance of developing robust stress-strain models that can replicate inherent anisotropy of the rock, and of calibrating and validating the models with a comprehensive set of laboratory experiments. The second example shows the additional influence of dessication and fault zone on the extent and shape of the EDZ. [ABSTRACT FROM AUTHOR]

Experimental data are often costly to obtain, which makes it difficult to calibrate complex models. For many models an experimental design that produces the best calibration given a limited experimental budget is not obvious. This paper introduces a deep reinforcement learning (RL) algorithm for design of experiments that maximizes the information gain measured by Kullback–Leibler divergence obtained via the Kalman filter (KF). This combination enables experimental design for rapid online experiments where manual trial-and-error is not feasible in the high-dimensional parametric design space. We formulate possible configurations of experiments as a decision tree and a Markov decision process, where a finite choice of actions is available at each incremental step. Once an action is taken, a variety of measurements are used to update the state of the experiment. This new data leads to a Bayesian update of the parameters by the KF, which is used to enhance the state representation. In contrast to the Nash–Sutcliffe efficiency index, which requires additional sampling to test hypotheses for forward predictions, the KF can lower the cost of experiments by directly estimating the values of new data acquired through additional actions. In this work our applications focus on mechanical testing of materials. Numerical experiments with complex, history-dependent models are used to verify the implementation and benchmark the performance of the RL-designed experiments. [ABSTRACT FROM AUTHOR]

A generalization of the physically nonlinear Maxwell-type constitutive equation with two material functions for non-aging rheonomic materials, whose general properties and area of application have been studied analytically in previous articles, was suggested. To extend the set of basic rheological phenomena simulated, a third strain component expressed as the Boltzmann–Volterra linear integral operator governed by an arbitrary creep function was added. For generality and convenience of managing the constitutive equation and its fitting to various materials and lists of effects simulated, a weight factor (degree of nonlinearity) was introduced into the constitutive relation, which enabled to combine the primary physically nonlinear Maxwell-type model with the linear viscoelasticity equation in arbitrary proportion to construct a hybrid model and to regulate the prominence of different phenomena described by the two constitutive equations. A general expression for creep and recovery curves produced by the constitutive equation proposed was derived and analyzed. The general properties of creep and recovery curves were studied assuming three material functions are arbitrary. New properties were established, which enabled the generalized model to adjust the form of creep and recovery curves and to simulate additional effects (in comparison with the primary Maxwell-type model) observed in creep and recovery tests of various materials at different stress levels. [ABSTRACT FROM AUTHOR]