A new class of plastic flow evolution equations for anisotropic multiplicative elastoplasticity based on the notion of a corrector elastic strain rate

Abstract

In this paper we present a new general framework for anisotropic elastoplasticity at large strains. The new framework presents the following characteristics: (1) It is valid for non-moderate large strains, (2) it is valid for both elastic and plastic anisotropy, (3) its description in rate form is parallel to that of the infinitesimal formulation, (4) it is compatible with the multiplicative decomposition, (5) results in a similar framework in any stress-strain work-conjugate pair, (6) it is consistent with the principle of maximum plastic dissipation and (7) does not impose any restriction on the plastic spin, which must be given as an independent constitutive equation. Furthermore, when formulated in terms of logarithmic strains in the intermediate configuration: (8) it may be easily integrated using a classical backward-Euler rule resulting in an additive update. All these properties are obtained simply considering a plastic evolution in terms of a corrector rate of the proper elastic strain. This formulation presents a natural framework for elastoplasticity of both metals and soft materials and solves the so-called rate issue.

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

“…A recent publication considering the numerics of the multiplicative decomposition, including combined isotropic-kinematic hardening models, can be found in [48]. However, the most controversial aspect of the theory is arguably associated with the derivation of continuum evolution equations for the plastic flow [49] and with their numerical integration [50], i.e. the "rate issue" as coined by Simo [11].…”

“…In Ref. [49] we present a new class of flow rules valid for anisotropic elastoplasticity and large elastic strains consistent with the Lee multiplicative decomposition. Generalizing Simo's approach [11], internal elastic strain variables are taken as the basic variables, so the evolution equations become entirely formulated in terms of corrector elastic strain rates rather than plastic ones.…”

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

“…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. Since the large strains pre-and post-processors are unchanged from the well-established classical plasticity and the experimental data used below are in the range of small strains, we refer for example to [75], [73] (Table 7.3.1), [76], [70], [69] for further details on the large strain numerical implementation using geometrical mappings.…”

“…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…”