A gradient model for finite strain elastoplasticity coupled with damage

Abstract

This paper describes the formulation of an implicit gradient damage model for ÿnite strain elastoplasticity problems including strain softening. The strain softening behavior is modeled through a variant of Lemaitre's damage evolution law. The resulting constitutive equations are intimately coupled with the ÿnite element formulation, in contrast with standard local material models. A 3D ÿnite element including enhanced strains is used with this material model and coupling peculiarities are fully described. The proposed formulation results in an element which possesses spatial position variables, nonlocal damage variables and also enhanced strain variables. Emphasis is put on the exact consistent linearization of the arising discretized equations.A numerical set of examples comparing the results of local and the gradient formulations relative to the mesh size in uence is presented and some examples comparing results from other authors are also presented, illustrating the capabilities of the present proposal. ?

Analysis of 3D problems using a new enhanced strain hexahedral element

“…Even complex implicit gradient models for modelling strain softening behaviour have been implemented with success with a variant of the present element (see Reference [51]). In terms of linear elastic accuracy, if mesh is regular, the element behaviour is very good as the tests performed in this paper illustrate.…”

“…The extension to plasticity is carried out through the introduction of a scalar internal variable, which is the plastic multiplier, but the internal forces and consistent tangent sti ness matrix retain the form presented for the conservative system (see References [51,52] for further details).…”

“…Motivations to use this function are discussed in Reference [22]. A 3D element based on this function was published recently [51]. The ÿrst 9 shape functions in Table I are a simple extension of the ones proposed for the 2D case in a recent publication [22] and applied for the ÿrst time in a 3D case in Reference [51].…”

“…The elasto-plastic model adopted in several problems has been described in References [51,52] and is a variant of the one adopted in other sources [49,54,55]. For the purely elastic analysis, the Hencky hyperelastic model is adopted, with exception of the silicone rubber tension test where the Yeoh hyperelastic model is employed (see Reference [47]).…”

Algorithms for the analysis of 3D finite strain contact problems

“…Various material models are employed to represent the material behaviour of the bulk solids (for an accounting of the elastoplastic model employed, please consult References [67,68]). Another point is that the applicability of the previous framework in the dissipative context is that plasticity algorithms do not allow, in a given point, both loading and unloading during the same time-step.…”