Jerzy Pamin

On coupled gradient-dependent plasticity and damage theories with a view to localization analysis

Combinations of gradient plasticity with scalar damage and of gradient damage with isotropic plasticity are proposed and implemented within a consistently linearized format. Both constitutive models incorporate a Laplacian of a strain measure and an internal length parameter associated with it, which makes them suitable for localization analysis. The theories are used for finite element simulations of localization in a one-dimensional model problem. The physical relevance of coupling hardening/softening plasticity with damage governed by different damage evolution functions is discussed. The sensitivity of the results with respect to the discretization and to some model parameters is analyzed. The model which combines gradient-damage with hardening plasticity is used to predict fracture mechanisms in a Compact Tension test.

Dispersion analysis and element‐free Galerkin solutions of second‐ and fourth‐order gradient‐enhanced damage models

Gradient-dependent damage formulations incorporate higher-order derivatives of state variables in the constitutive equations. Different formulations have been derived for this gradient enhancement, comparison of which is difficult in a finite element context due to higher-order continuity requirements for certain formulations. On the other hand, the higher-order continuity requirements are met naturally by element-free Galerkin (EFG) shape functions. Thus, the EFG method provides a suitable tool for the assessment of gradient enhanced continuum models. Dispersion analyses have been carried out to compare different gradient enhanced models with the non-local damage model. The formulation of the additional boundary conditions is addressed. Numerical examples show the objectivity with respect to the discretization and the differences between various gradient formulations with second- and fourth-order derivatives. It is shown that with the same underlying internal length scale, very different results can be obtained. Copyright

On gradient-enhanced damage and plasticity models for failure in quasi-brittle and frictional materials

Gradient-enhanced damage and plasticity approaches are reviewed with regard to their ability to model localization phenomena in quasi-brittle and frictional materials. Emphasis is put on the algorithmic aspects. For the purpose of carrying out large-scale finite element simulations efficient numerical treatments are outlined for gradient-enhanced damage and gradient-enhanced plasticity models. For the latter class of models a full dispersion analysis is presented at the end of the paper. In this analysis the fundamental role of dispersion in setting the width of localization bands is highlighted.

Mixed mode fracture in plain and reinforced concrete : some results on benchmark tests

Three different models for concrete based on local and non-local approaches have been adopted to investigate the mechanical behaviour of plain and reinforced concrete when undergoing mixed-mode fracture. The purpose of the research is to understand the results of some benchmark tests, to compare the models with each other and with experiments, and to estimate the reliability of the modelling. To create a sound basis for the comparison, the discretizations, the boundary conditions and the material data are considered, when possible, as unified parameters for the different models in each benchmark test.

Two gradient plasticity theories discretized with the element-free Galerkin method

Abstract In this paper, the element-free Galerkin method is exploited to analyze gradient plasticity theories. The use of this discretization method has the advantage that higher-order continuity, which can be required for the plastic multiplier field, is provided for. In passing, we show that the regularization properties of the higher-order gradients are necessary, since, similar to finite element methods, a severe discretization sensitivity is encountered otherwise. The mesh-free discretization method is first applied to an established, stress-space gradient plasticity theory. Next, a strain-space gradient plasticity theory, which employs an implicit averaging of an invariant strain measure, is proposed and elaborated. This theory is insensitive to the order of the interpolation polynomials and, as a result, the convergence of the Newton–Raphson procedure is better. The performance of both gradient plasticity models is examined for the mesh-free discretization scheme. A comparative study is carried out for a one-dimensional bar in tension, while the influence of the discretization in biaxial compression is studied next, including that of the numerical parameters of the discretization scheme and that of the internal length scale contained in the gradient plasticity theories.

Some future directions in computational failure mechanics

Continuum approaches are reviewed which can properly model localised deformations that act as a precursor to final fracture in quasi-brittle materials. Next, one such higher-order damaging continuum model is combined with a stochastic approach to describe the heterogeneity in quasi-brittle materials.

Numerical analysis of ellipticity condition for large strain plasticity

This paper deals with the numerical investigation of ellipticity of the boundary value problem for isothermal finite strain elasto-plasticity. Ellipticity can be lost when softening occurs. A discontinuity surface then appears in the considered material body and this is associated with the ill-posedness of the boundary value problem. In the paper the condition for ellipticity loss is derived using the deformation gradient and the first Piola-Kirchhoff stress tensor. Next, the obtained condition is implemented and numerically tested within symbolic-numerical tools AceGen and AceFEM using the benchmark of an elongated rectangular plate with imperfection in plane stress and plane strain conditions.

Damage Processes in Solids and Structures and their Numerical Computation

A concise overview is given of some recent developments, mainly by the Delft group, of numerical modelling of damage processes. Attention is paid to discrete methods, where all damage is lumped into interface elements, and to enhanced continuum theories, where higher-order terms, either in time or in space, are added to preserve well-posedness of the rate boundary value problem after the onset of softening.