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This work addresses the computational aspects of a model for elastoplastic damage at finite strains. The model is a modification of a previously established model for large strain elastoplasticity described by Perić et al. which is here extended to include isotropic damage and kinematic hardening. Within the computational scheme, the constitutive equations are numerically integrated by an algorithm based on operator split methodology (elastic predictor—plastic corrector). The Newton—Raphson method is used to solve the discretized evolution equations in the plastic corrector stage. A numerical assessment of accuracy and stability of the integration algorithm is carried out based on iso‐error maps. To improve the stability of the local N—R scheme, the standard elastic predictor is replaced by improvedinitial estimates ensuring convergence for large increments. Several possibilities are explored and their effect on the stability of the N—R scheme is investigated. The finite element method is used in the approximation of the incremental equilibrium problem and the resulting equations are solved by the standard Newton—Raphson procedure. Two numerical examples are presented. The results are compared with those obtained by the original elastoplastic model.

In this paper an interface is derived between arbitrary three‐dimensional material laws and finite elements which include special stress conditions. The mechanical models of beams and shells are usually based upon zero‐stress conditions. This requires a material law respecting the stress condition for each finite element formulation. Complicated materials, e.g. finite strain models are often described in the 3D‐continuum. Considering the zero‐stress condition requires a reformulation of these material laws, which is often complicated. The subject of this paper is to incorporate physically non‐linear 3D‐material laws in beam and shell elements. To this effect a local algorithm will be developed to condense an arbitrary 3D‐material law with respect to the zero‐stress condition. The algorithm satisfies the stress condition at each integration point on the element level.

The purpose of this paper is to investigate the stress distribution in shape memory alloy (SMA) composite due to phase transformations in the fiber in view of the applied boundary conditions on the matrix.

A consistent homogenization of a SMA wire‐reinforced polymer composite volume element undergoing quasi‐static deformation was performed and SMA wire‐matrix interface behaviour was presented. For the SMA wire, a one‐dimensional phenomenological constitutive model was used. Eshelby's inclusion theory was employed for homogenization. A strain averaging approach was reviewed in which the average strain was substituted back to obtain the expressions for the effective stiffness, the inelastic strain, and the average stresses in the constituent phases. In order to study the stress distribution in SMA composite and constituent phases (fiber and matrix) as a consequence of the SMA wire‐matrix interface effect, interfacial stress model was derived. Interfacial axial and shear stress distribution is characterized for forward and reverse phase transformations. Finally, the thermomechanical behaviours were computed by applying strain energy approach incorporating the interface effects.

The results presented show that due to the difference between the shear modulus of matrix and SMA wire, and because of the strain non‐uniformity at the SMA wire‐matrix interface, shear stress is developed within the matrix under the axial loading of the representative volume element (RVE). The shear stress increases more rapidly as the SMA wire radius is increased but not with increase in the length. However, the axial stress does not increase much with increase in the SMA wire radius and length. Further, the average stress equation of the RVE at the SMA wire‐matrix interface is effectively addressed. The modeling approach is successfully validated extensively for different geometric and volumetric parameters for different loading conditions. It is evident that the interface effect of SMA wire composites is SMA stiffness dominated due to the fact that the geometric parameters do not influence much the stresses as compared to the change in SMA wire stiffness.

The approach is based on modeling the fiber matrix interface effect using homogenization scheme. Further, the strain energy approach is applied to compute the stress‐strain response. This indicates the importance of modeling the SMA wire‐matrix interface effect, and in particular, the energy exchange between the constituent phases. The results have been compared for different geometric parameters as well as volume fractions of the constituent phases under different loading conditions.

This paper proposes a unified original general framework, designed to theoretically develop and to extremely easily implement elastoplastic constitutive laws defined in the so called two-invariants space, both in small and finite strain regime.

A general return mapping algorithm is proposed, and particularly a standard procedure is developed to compute the two algorithmic tangent operators, required to solve the Newton–Raphson scheme at the local and global level and thus cast the elastoplastic algorithm within a FEM code.

This work demonstrates that the proposed procedure is fully general and can be applied whatever is the elastic law, the yield surface, the plastic potential function and the hardening law. Several numerical examples are reported, not only to demonstrate the accuracy and robustness of the algorithm, but also explain how to use this general algorithm also in other applications.

The proposed algorithm and its numerical implementation into a FEM code is new and original. The usefulness and the value of the algorithm is twofold: (1) it can be implemented in a small and finite strain simulation FEM code, in order to handle different types of constitutive laws in the same modular way, thus fully leveraging on modern object-oriented coding approach; (2) it can be used as a framework to develop (and then to implement) new constitutive models, since the researcher can simply define the relevant functions (and its main derivatives) and automatically get the numerical algorithm.

The purpose of this paper is to suggest an implicit integration method for updating the constitutive relationships in the newly proposed anisotropic egg-shaped elastoplastic (AESE) model and to apply it in ABAQUS.

The implicit integration algorithm based on the Newton–Raphson method and the closest point projection scheme containing an elastic predictor and plastic corrector are implemented in the AESE model. Then, the integration code for this model is incorporated into the commercial finite element software ABAQUS through the user material subroutine (UMAT) interface to simulate undrained monotonic triaxial tests for various saturated soft clays under different consolidation conditions.

The comparison between the simulated results from ABAQUS and the experimental results demonstrates the satisfactory performance of this implicit integration algorithm in terms of effectiveness and robustness and the ability of the proposed model to predict the characteristics of soft clay.

The rotational hardening rule in the AESE model together with the implicit integration algorithm cannot be considered.

The singularity problem existing in most elastoplastic models is eliminated by the closed, smooth and flexible anisotropic egg-shaped yield surface form in the AESE model. In addition, this notion leads to an efficient implicit integration algorithm for updating the highly nonlinear constitutive equations for unsaturated soft clay.

Under restriction of an isotropic elastic response of deformed lattice, develops a covariant theory of finite elastoplasticity in principal axes of a pair of deformation tensors. In material description, the tensor pair consists of the plastic deformation tensor and the total deformation Cauchy‐Green tensor. Applies the proposed theory to elastoplastic membrane shells, whose references and current configurations can be arbitrary space‐curved surfaces. Pressure‐insensitive von Mises yield criterion with isotropic hardening and a quadratic form of the strain energy function given in terms of elastic principal stretches are considered as a model problem. Through an explicit enforcement of the plane stress condition we arrive at a reduced two‐dimensional problem representation, which is set in the membrane tangent plane. Numerical implementation of the presented theory relies crucially on the operator split methodology to simplify the state update computation. Presents a set of numerical examples in order to illustrate the performance of the presented methodology and indicate possible applications in the area of sheet metal forming.

Many practical problems in engineering require fast, accurate numerical results. In particular, in cyclic plasticity or fatigue simulations, the high number of loading cycles increases the computation effort and time. The purpose of this study is to show that the return mapping technique in the framework of unconventional plasticity theories is a good compromise between efficiency and accuracy in finite element analyses.

The accuracy of the closest point projection method and the cutting plane method implementations for the subloading surface model are discussed under different loading conditions by analyzing the error as a function of the input step size and the efficiency of the algorithms.

Monotonic tests show that the two different implicit integration schemes have the same accuracy and are in good agreement with the solution obtained using an explicit forward Euler scheme, even for large input steps. However, the closest point projection method seems to describe better the evolution of the similarity centre in the cyclic loading analyses.

The purpose of this work is to show two alternative implicit integration schemes of the extended subloading surface method for metallic materials. The backward Euler integrations can guarantee a good description of the material behaviour and, at the same time, reduce the computational cost. This aspect is particularly important in the field of low or high cycle fatigue, because of the large number of cycles involved.

A detailed description of both the cutting plane and closest point projection methods is offered in this work. In particular, the two integrations schemes are compared in terms of accuracy and computation time for monotonic and cyclic loading tests.

This paper aims to develop a finite element analysis strategy, which is suitable for the analysis of progressive failure that occurs in pressure-dependent materials in practical engineering problems.

The numerical difficulties stemming from the strain-softening behaviour of the frictional material, which is represented by a non-associated Drucker–Prager material model, is tackled using the Cosserat continuum theory, while the mixed finite element formulation based on Hu–Washizu variational principle is adopted to allow the utilization of low-order finite elements.

The effectiveness and robustness of the low-order finite element are verified, and the simulation for a real-world landslide which occurred at the upstream side of Carsington embankment in Derbyshire reconfirms the advantages of the developed elastoplastic Cosserat continuum scheme in capturing the entire progressive failure process when the strain-softening and the non-associated plastic law are involved.

The permit of using low-order finite elements is of great importance to enhance computational efficiency for analysing large-scale engineering problems. The case study reconfirms the advantages of the developed elastoplastic Cosserat continuum scheme in capturing the entire progressive failure process when the strain-softening and the non-associated plastic law are involved.

The purpose of this paper is to extend the bridge scale method (BSM) developed for granular materials with only the solid phase to that taking into account the effects of wetting process in porous continuum. The granular material is modeled as partially saturated porous Cosserat continuum and discrete particle assembly in the coarse and fine scales, respectively.

Based on the mass and momentum conservation laws for the three phases, i.e. the solid skeleton, the pore water and the pore air, the governing equations for the unsaturated porous Biot-Cosserat continuum model in the coarse scale are derived. In light of the passive air pressure assumption, a reduced finite element model for the model is proposed. According to the decoupling of the fine and coarse scale calculations in the BSM, the unsaturated porous Cosserat continuum model using the finite element method and the discrete element model using the discrete element method for granular media are combined.

The numerical results for a 2D example problem of slope stability subjected to increasing rainfall along with mechanical loading demonstrate the applicability and performance of the present BSM. The microscopic mechanisms of macroscopic shear band developed in the slope are demonstrated.

Do not account for yet the effects of unsaturated pore water in the fine scale.

The novel BSM that couples the Biot-Cosserat porous continuum modeling and the discrete particle assembly modeling in both coarse and fine scales, respectively, is proposed to provide a micro-macro discrete-continuum two-scale modeling approach for numerical simulations of the hydro-mechanical coupling problems in unsaturated granular materials.

This paper aims at the problem of surrounding rock excavation damage zone of tunneling in the rich water region, this paper aims to propose a new seepage-stress-damage coupling model and studied the numerical algorithm. This reflects the characteristics of rock damage evolution, accompanied by plastic flow deformation and multi-field interaction.

First of all, rock elastoplastic damage constitutive model based on the Drucker–Prager criterion is established, the fully implicit return mapping algorithm is adopted to realize the numerical solution. Second, based on the relation between damage variation and permeability coefficient, the rock stress-seepage-damage model and multi-field coupling solving iterative method are presented. Finally, using the C++ language compiled the corresponding programs and simulated tunnel engineering in the rich water region.

Results show that difference evolution-based back analysis inversed damage parameters well, at the same time the established coupling model and calculating program have more advantages than general conventional methods. Multiple field coupling effects should be more considered for the design of tunnel support.

The proposed method provides an effective numerical simulation method for the construction of the tunnel and other geotechnical engineering involved underground water problems.