On the numerical integration of a class of pressure‐dependent plasticity models with mixed hardening

Abstract

SUMMARYRadial return algorithms, for both three-dimensional and plane stress situations, are developed for a class of pressure-dependent plasticity models (formulated in state variables) with mixed hardening. The consistent tangent matrix has been developed which, among other advantages, does not require numerical inversion. The algorithms, for Gurson's mixed hardening model, are incorporated in a finite element program to solve several simple uniaxial tension problems. When compared with numerically integrated solutions, the results from the finite element analysis show excellent agreement. Finally, results of the axisymmetric necking problem, using Gurson's mixed hardening model, are presented as an example of application.

Implicit stress integration procedure for small and large strains of the Gurson material model

“…The same approach was followed by other authors, e.g. Lee and Zhang [29], Jha and Narasimhan [9], Doege et al [7], Zhang [30; 31], Lee and Zhang [6] and Brunet and Sabourin [8].…”

“…In comparison with a Newtontype procedure involving a system of equations with several unknowns and possible divergence in the solutions process (e.g. Lee and Zhang [29] formed the system of three equations), the proposed algorithm has the obvious advantages.…”

A Nonlocal Multiscale Fatigue Model

“…The evolution equations of the internal state variables (Eqs. (22), (29), (30), (32)- (34)) may be expressed in a general functional form as:Ḣ =h σ σ σ,λ, H (47) or in terms of the macro-and micro-chronological fieldṡ…”

“…The stress updates of the micro-and macro-chronological problems are carried out using a return mapping algorithm based on the method first proposed in [46] for isotropic hardening, and further extended to account for kinematic hardening in [47]. The aforementioned adaptive algorithm requires data transfer between the micro-and macrochronological problems at each time step.…”

A generalized approach to formulate the consistent tangent stiffness in plasticity with application to the GLD porous material model

“…They derived a tangent stiffness matrix for the J 2 material that is fully consistent with the backward Euler integration algorithm. Aravas (1987), Lee and Zhang (1991), Zhang (1995) and Muhlich and Brocks (2003) conducted detailed studies of the backward Euler method for numerical integration of a class of pressure-dependent plasticity laws and obtained the tangent moduli by consistent linearization of the elastoplastic constitutive equations.…”