On a finite-strain viscoplastic law coupled with anisotropic damage: theoretical formulations and numerical applications

Abstract

Based on a dissipation inequality at finite strains and the effective stress concept, a Chabochetype infinitesimal viscoplastic theory is extended to finite-strain cases coupled with anisotropic damage. The anisotropic damage is described by a rank-two symmetric tensor. The constitutive law is formulated in the corotational material coordinate system. Thus, the evolution equations of all internal variables can be expressed in terms of their material time derivatives. The numerical algorithm for implementing the material model in a finite element programme is also formulated, and several numerical examples are shown. Comparing the numerical simulations with experimental observations indicates that the present material model can describe well the primary, secondary and tertiary creep. It can also predict the anisotropic damage modes observed in experiments correctly.

Model Describing Material-Dependent Deformation Behavior in High-Velocity Metal Forming Processes

“…This is a problem that many authors have considered, e.g. Lin and Brocks (2006), Simo and Miehe (1992) and Tugcu (1996). The geometry of the model is shown in Fig.…”

An elastoplastic damage-induced anisotropic constitutive model at finite strains

“…In their work, the remarkable influence of damage on the behavior of the material, especially within necking and localization computations, has been emphasized. Lin and Brocks (2006) extended a Chaboche-type infinitesimal viscoplastic theory to the finite strain coupled with anisotropic damage in order to describe the creep responses of different hightemperature materials as well as to predict the location of creep damage in the materials. Soyarslan and Tekkaya (2010) presented an orthotropic finite plasticity model coupled with a Lemaitre-type isotropic ductile damage based on the logarithmic strain and its conjugate stress measure.…”

Finite Element Analysis for the Problem of Tunnel Excavation Successive Phases and Lining Mounting

“…For instance, tunneling using FEM for viscoplastic materials has been investigated widely, as well, e.g. [9] approaches the problem with outstanding results in computational geomechanics, with special reference to earthquake engineering, in numerical modeling of dynamic soil and pore fluid interaction and earthquake-induced liquefaction and multiphase pollutant transport in partially saturated porous media; Zienkiewicz provides outstanding numerically approaches in a wide range of problems, e.g., [10] is devoted to computational geomechanics; [11] focuses a great interest in the multi-disciplinarily aspect of the problem, taking into account also adjacent phenomenon occurring at the rock-support interaction; [12] deals with ductile damage and fracture FE modeling of viscoplastic voided materials for high strain rate problems, [13] provides a finite-strain viscoplastic law coupled with anisotropic damage both theoretical and numerical approach, [14] develops a FE procedure to model the tunnel installation and the liner to predict the likely extent of damage to surface structures caused by nearby shallow tunneling, [15] deals with FE modelling of excavation and advancement process of a shield tunnelling machine, [16] develops a FE micromechanical-based model for hydromechanical coupling for tunnelling application, [17] applies a model based on plastic damage evolution and permeability to excavation-disturbed zone simulation of the mudstone shield tunnel; [18] analyses tunnel depth effect on the stress and strain state around the tunnel; [19], [20] studies the face tunnel influence in the analysis of a circular tunnel with a time-dependent behaviour, etc.…”