Regularization of shear banding and prediction of size effects in manufacturing operations: A micromorphic plasticity explicit scheme

Abstract

Good quality manufacturing operation simulations are essential to obtain reliable numerical predictions of the processes. In many cases, it is possible to observe that the deformation localizes in narrow areas, and since the primary deformation mode is under shear, these areas are called shear bands. In classical continuum mechanics models, the deformation localization may lead to spurious mesh dependency if the material locally experiences thermal or plastic strain softening. One option to regularize such a non-physical behavior is to resort to non-local continuum mechanics theories. This paper adopts a scalar micromorphic approach, which includes a characteristic length scale in the constitutive framework to enforce the plastic strain gradient theory to regularize the solution. Since many manufacturing process simulations are often assessed through finite element methods with an explicit solver to facilitate convergence, we present an original model formulation and procedure for the implementation of the micromorphic continuum in an explicit finite element code. The approach is illustrated in the case of the VPS explicit solver from ESI GROUP. According to the original formulation, we propose an easy way to implement a scalar micromorphic approach by taking advantage of an analogy with the thermal balance equation. The numerical implementation is verified against the analytical solution of a semi-infinite glide problem. Finally, the correctness of the method is addressed by successfully predicting size effects both in a cutting and a bending tests.

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

“…The micromorphic approach can also be useful to ease numerical implementation of phase field models as demonstrated recently for twinning plasticity in [93]. Note finally that the micromorphic approach is also suitable for explicit finite element simulation schemes used in metal forming as recently shown in [16,94].…”

“…Many regularization methods are intrusive regarding their FE implementation. The advantage of scalar micromorphic approaches involving one additional degree for freedom lies in its relative simplicity of implementation as illustrated by its use in explicit codes [14][15][16].…”