Computational anisotropic hardening multiplicative elastoplasticity based on the corrector elastic logarithmic strain rate

Abstract

Highlights • New computational framework for multiplicative anisotropic elastoplasticity. • Based on a six-dimensional additive corrector update for elastic logarithmic strains. • No hypothesis needed for the plastic spin in order to integrate the symmetric flow. • Yields a fully symmetric finite element formulation parallel to the infinitesimal one. • Overcomes the so-called "rate issue" from a computational standpoint.

Fast, Rate-Independent, Finite Element Implementation of a 3D Constrained Mixture Model of Soft Tissue Growth and Remodeling

“…(33), which drives changes in volume via mass growth, resembles a pressure-sensitive yield function in rate-independent elastoplasticity, which triggers changes in volume via inelastic mechanisms, generally coupled with plastic distortions but without mass exchange (such as for geomaterials, metallic foams, or filled polymers [16]). Since the present G&R formulation contains other noticeable differences when compared to classical elastoplasticity (e.g., mixture theory describing different behaviors of different constituents, rather than a homogenized material; pre-stresses with evolving natural configurations; and a multiplicative decomposition without explicit consideration of an elastic gradient), elastic predictor / inelastic corrector integration schemes typically used in computational plasticity [17,18] do not seem well suited for integrating the present rateindependent constrained-mixture equations. Rather, we solved this set of nonlinear equations exactly using a different stress-point resolution procedure (Box 1), whose consistent linearization for efficient finite element implementations is addressed next.…”

Extension of the sensitivity-based virtual fields to large deformation anisotropic plasticity

“…By choosing more complex models that account for e.g. multiplicative decomposition of deformation gradient [27], hyperelasticity [42], anisotropic hardening [10] or even complete anisotropic elastoplasticity [40] more complex material description could be reached, but this has not been considered in this work.…”

Computational Algorithms for Cyclic Plasticity Based on Prager's Translation Rule

“…where we used the usual assumption that tr R e ≈ t+∆t 0 R e [75], [73], [76], [69]. By systematic use of the chain rule, the tangent of the small strains algorithm may be converted to the typical tangent employed in finite element codes which relates second Piola-Kirchhoff stresses with Green-Lagrange strains in the reference configuration.…”

“…We defined the trial and corrector partial derivative contributions trε e ≡ε e |ε p=0 and ctε e ≡ε e |ε =0 . In the new formulation of large strain elasto-plasticity presented in [69] and [70], this framework based on the chain rule remains additive and unaltered at large strains even when using the multiplicative decomposition. The stored energy is -see Figure 2.1 Ψ (ε e , ξ, γ) = W (ε e ) + H (ξ, γ) = 1 2 ε e : C : ε e + H (ξ, γ)…”

“…The latter is the rate of the stress tensor during plastic flow which produce the maximum dissipation. Note that this novel continuum framework presented in [69], [70] mimics the usual algorithmic implementation, even at large strains, but it is just an immediate application of the chain rule when considering the dependencies…”