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An implicit type algorithm for the integration of hypoelastic constitutive equations is proposed for large strain and large rotation conditions. Constitutive relations are derived in a deformation‐neutralized form. This provides the basis for integration in time resulting in an incremental tensor relation. Proposed algorithm can be considered as a generalization of the closest‐point‐projection method in the sense that the projection property applies to a ‘midstep’ rather than the final stress state. Hill's yield criterion under plane stress conditions suitable for metal‐forming applications is used in presented benchmark problems. Numerical results are discussed illustrating the accuracy of the algorithm for different values of the midstep parameter.

Finite element implementations of the classical (stick‐slip) and a regularized (elastic‐slip) friction laws are compared for a class of non‐linear slip criteria. The fully implicit method is used for integrating the friction law. A novel implementation of the stick‐slip law, that involved transformation to a non‐orthogonal coordinate system at each contact point, is assessed. A numerical comparison is carried out for a simple problem, that has previously been analysed in the literature. The convergence of the elastic‐slip law for increasing stiffness is evaluated in addition to convergence behaviour of the adopted Newton iterations for a given law.

In this work a gradient‐based optimization method is applied in order to determine material parameters for a viscoplastic model with dynamic yield surface coupled to damage as presented in 1997. To this end a sensitivity analysis consistent with the integration scheme presented previously is performed in a systematic manner, both for strain and stress controlled experiments. The algorithm is tested in two numerical examples: first, simulated data are used, in order to re‐obtain parameters for the case of damage under monotonic loading. In the second example material parameters are obtained based on experimental data for lcf‐testing of an austenetic stainless steel, thus showing a very good agreement with respect to hardening, rate and damage effects.

Presents a computational algorithm for the numerical integration of triaxial concrete plasticity formulations. The specific material formulation at hand is the so‐called extended leon model for concrete. It is based on the flow theory of plasticity which entails isotropic hardening as well as fracture energy‐based softening in addition to non‐associated plastic flow. The numerical algorithm resorts to implicit integration according to the backward Euler strategy that enforces plastic consistency according to the closes‐point‐projection method (generalized radial‐return strategy). Numerical simulations illustrate the overall performance of the proposed algorithm and the significant increase of the convergence rate when the algorithmic tangent is used in place of the continuum operator.

As known from nearly incompressible elasticity, selective reduced integration (SRI) is a simple and effective method of overcoming the volumetric locking problem in 2D and 3D solid elements. This method of finite elastoviscoplasticity is discussed as are its well‐known limitations. In this context, an isochoric‐volumetric decoupled material behavior is assumed and thus the additive deviatoric‐volumetric decoupling of the consistent algorithmic moduli tensor is essential. By means of several numerical examples, the performance of elements using selective reduced integration is demonstrated and compared to the performance of other elements such as the enhanced assumed strain elements. It is shown that a minor modification, with little numerical effort, leads to rather robust element behaviour. The application of this process to so‐called solid‐shell elements for thin‐walled structures is also discussed.

The formulation of finite elements with incompatible discontinuous modes is examined rigorously. Both weak and strong discontinuities are considered. Starting from a careful elaboration of the kinematics for both types of discontinuities a comprehensive finite element formulation is derived based on a three‐field variational statement. Similarities and differences are highlighted between the various formulations which ensue.

Numerical solutions in computational plasticity are severely challenged when concrete and geomaterials are considered with non‐regular yield surfaces, strain‐softening and non‐associated flow. There are two aspects that are of immediate concern within load steps which are truly finite: first, the iterative corrector must assure that the equilibrium stress state and the plastic process variables do satisfy multiple yield conditions with corners, Fi(σ, q) = 0, at discrete stages of the solution process. To this end, a reliable return mapping algorithm is required which minimizes the error of the plastic return step. Second, the solution of non‐linear equations of motion on the global structural level must account for limit points and premature bifurcation of the equilibrium path. The current paper is mainly concerned with the implicit integration of elasto‐plastic hardening/softening relations considering non‐associated flow and the presence of composite yield conditions with corners.

The purpose of this paper is to present several methods on how to deal with yield surface discontinuities. The explicit formulations, first presented by Koiter (1953), result in multisingular constitutive matrices which can cause numerical problems in elasto-plastic finite element calculations. These problems, however, are not documented in previous literature. In this paper an amendment to the Koiter formulation of the constitutive matrices for stress points located on discontinuities is proposed.

First, a review of existing methods of handling yield surface discontinuities is given. Examples of the numerical problems of the methods are presented. Next, an augmentation of the existing methods is proposed and its robustness is demonstrated through footing bearing capacity calculations that are usually considered “hard”.

Previous studies documented in the literature all present “easy” calculation examples, e.g. low friction angles and few elements. The amendments presented in this paper result in robust elasto-plastic computations, making the solution of “hard” problems possible without introducing approximations in the yield surfaces. Examples of “hard” problems are highly frictional soils and/or three-dimensional geometries.

The proposed method makes finite element calculations using yield criteria with corners and apices, e.g. Mohr-Coulomb and Hoek-Brown, much more robust and stable.

The purpose of this paper is to model the strain localization in J₂ materials with damage evolution using embedded strong discontinuity modes.

In this procedure, an heuristic bandwidth scale is adopted to model the damage evolution in the shear bands. The bifurcation triggering conditions and band growth directions are studied for these materials.

The resulting formulation does not require a specific mesh refinement to model a localization, provides mesh independent results also insensitive to element distortions and allows calibration of the model response using experimental data. The formulation capability is shown embedding the strong discontinuity modes into quadrilateral and higher order elements.

The work described in this paper extends the use of strong discontinuity modes to materials with damage evolution.

The implementation of the finite element solution of Biot's consolidation theory on a low‐cost microcomputer is described. A two‐dimensional linear elastic model is solved using bilinear rectangular elements and a fully implicit timestepping algorithm. The machine used is the Acorn Computers model B, BBC microcomputer, a popular low‐cost engineering applications machine. The program is written in Basic but to increase speed of computation certain sections of the solution procedure involving matrix manipulation are written in Assembly language. The results obtained are encouraging from the point of view of accuracy, problem size and computational time. It is concluded that there is scope for the use of the present generation of low‐cost microcomputer, as typified by this machine, in the numerical solution of the more straightforward, but still realistic, consolidation problems.