A variational constitutive model for porous metal plasticity

Abstract

This paper presents a variational formulation of viscoplastic constitutive updates for porous elastoplastic materials. The material model combines von Mises plasticity with volumetric plastic expansion as induced, e.g., by the growth of voids and defects in metals. The finite deformation theory is based on the multiplicative decomposition of the deformation gradient and an internal variable formulation of continuum thermodynamics. By the use of logarithmic and exponential mappings the stress update algorithms are extended from small strains to finite deformations. Thus the time-discretized version of the porous-viscoplastic constitutive updates is described in a fully variational manner. The range of behavior predicted by the model and the performance of the variational update are demonstrated by its application to the forced expansion and fragmentation of U-6%Nb rings.

A variational constitutive model for soft biological tissues

“…and the flow rules (0.13),(0.14) (Yang et al, 2006;Weinberg et al, 2006;Ortiz and Stainier, 1999;Fancello et al, 2006) that the Euler-Lagrange equations corresponding to the minimization problem (0.25) are the equations of motion…”

“…A discrete version of problem (0.22) is obtained by introducing the effective incremental strain-energy density (Weinberg et al, 2006)…”

“…The first Piola-Kirchhoff stress and consistent tangent can now be computed (Weinberg et al, 2006) as…”

“…By adopting a predictor-corrector strategy based on logarithmic elastic strains to solve the variational problem (0.30), the constitutive update is reduced to small-strains and purely kinematic steps (Cuitino and Ortiz, 1992;Ortiz and Stainier, 1999;Weinberg et al, 2006;Fancello et al, 2006). The corresponding elastic logarithmic strains at time t k+1 are e k+1 = e,pre …”

Nanovoid nucleation by vacancy aggregation and vacancy-cluster coarsening in high-purity metallic single crystals

“…The aim is to formulate a nucleation model that can be integrated into continuum multiscale descriptions of ductile fracture by void growth and coalescence. Such multiscale models often rely on porous plasticity methods to account for the macroscopic effect of the growing voids, [1][2][3][4][5][6][7][8][9][10][11][12][13] and on micromechanical or localization analyses in order to describe crack growth of the formation of spall planes. 5,[14][15][16][17][18] By design, micromechanical continuum models of porous plasticity either postulate an initial void size and density (e.g., when voids nucleate by decoherence of second-phase particles) or rely on a nucleation model in order to compute the initial void size and density.…”