Observations on additive plasticity in the logarithmic strain space at excessive strains

Toward robust scalar-based gradient plasticity modeling and simulation at finite deformations

“…As summarized in [44], finite strain formulations for strain gradient plasticity lead to distinct regularization operators. Non-coaxial deformations, such as simple glide, reveal significant differences between finite strain formulations, as recently discussed for the micromorphic approach of plasticity in [45]. In particular, the formulation based on additive logarithmic strain decomposition under non-coaxial deformation yields a softer response and eventually leads to early strain localization compared to the multiplicative elastoplasticity.…”

Efficient gradient enhancements for plasticity with ductile damage in the logarithmic strain space

“…Numerically, an augmented Lagrange formulation (Fortin and Glowinski, 2000) is utilised, requiring additional degrees of freedom for a Lagrange multiplier field. We assume their observed plastic localisation to directly originate from the loss of ellipticity at large non-coaxial plastic strains for ln-space plasticity, as shown in (Friedlein et al, 2022). Even though the critical strains in (Friedlein et al, 2022) are excessive for modelling purely plastic material responses, they can become reality in the simulation of ductile damage, where the softening effect of damage causes substantial strain localisation.…”

“…We assume their observed plastic localisation to directly originate from the loss of ellipticity at large non-coaxial plastic strains for ln-space plasticity, as shown in (Friedlein et al, 2022). Even though the critical strains in (Friedlein et al, 2022) are excessive for modelling purely plastic material responses, they can become reality in the simulation of ductile damage, where the softening effect of damage causes substantial strain localisation. Thus, although ln-space-based plasticity -gradient-damage can regularise the softening effect of damage, the results might still be mesh-dependent due to loss of ellipticity of plasticity as will be shown in Section 4.1.…”

“…This makes it tempting to use algorithmically simple frameworks, such as the logarithmic strain space, as for instance done in Holthusen et al (2022) for finite plasticity -anisotropic gradientdamage. However, such advanced constitutive models can suffer from different sources of localisation, e. g. softening plasticity (Dimitrijevic and Hackl, 2011;Anand et al, 2012), non-associative plasticity (Sabet and de Borst, 2019;Neuner et al, 2020) or the plasticity formulation itself (Friedlein et al, 2022). Therefore, it is desirable to regularise as many phenomena as possible by a single gradient-enhancement, in order to reduce computational effort and model complexity, also with respect to subsequent parameter identification.…”

“…A gradient-enhancement of the plasticity model is -on the other hand -beneficial for several reasons. On the one hand, gradient-plasticity can resolve or lessen many of the observed localisation phenomena (Anand et al, 2012;Sabet and de Borst, 2019;Friedlein et al, 2022). Moreover, gradient-plasticity also smoothes the plastic strains, which are the dominant contribution to the total strains for metals.…”