Anisotropic plasticity‐damage material model for sheet metal — Regularised single surface formulation

Abstract

Sheet metal forming as well as mechanical joining demand increasingly accurate and efficient material modelling to capture large deformations, the inherent sheet orthotropy and even process‐induced damage, which is expected to be influential. To account for large strains the additive logarithmic strain space is utilised that enables a straightforward incorporation of plastic anisotropy, herein modelled by a Hill48 yield function. A gradient‐enhancement is used to equip the ductile damage model with an internal length scale curing the damage‐induced localisation. An affine combination of the local and non‐local softening variable is derived enabling a more efficient single surface formulation for the regularised plasticity‐damage material model.

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

“…However, it also requires a higher computational effort. With the affine damage combination proposed in (Friedlein et al, 2021a), a single-surface formulation is sufficient even for gradient-damage.…”

“…This paradox is explained by the back coupling of the local and non-local variable inside the material model making the local variable a function of the non-local variable. This relation has been unfolded for gradient-damage (ϑ = d) from a dual-surface model in (Friedlein et al, 2021a). Separating the parts affected by the non-local damage variable d from the ones being identical to a local model, denoted as "truly" local damage d loc , reveals an affine combination of the damage variables stating that…”

“…with the penalty parameter β d for gradient-damage (Friedlein et al, 2021a). On the material point level, first the truly local damage is computed from Eq.…”

“…Many approaches directly introduce the gradient-enhancement on the softening damage variable (gradient-damage), using a flexible two-surface approach such as (Sprave and Menzel, 2020;Brepols et al, 2020), or an efficient single-surface coupling (Langenfeld et al, 2019;Friedlein et al, 2021a). Such gradient-damage models are appealing for several reasons.…”

On the Influence of Fatigue Damage in Short-Fibre Reinforced Thermoplastic PBT GF30 on Its Residual Strength under High Strain Rates: An Approach towards Simulative Prediction

“…The edge lengths in the parallel area are 2 mm and thus correspond to the meshing with which the undamaged material model was also calibrated. This method eliminates the effects of mesh dependence, which would otherwise falsify the comparison of simulations of damaged and undamaged samples, as well as the comparison of simulation and experiment [23,24]. The specimen is secured by a rigid beam spider in the moving upper area and by securing all nodes in the lower jaw area.…”