A reduced strain gradient crystal plasticity theory which involves the gradient of a single scalar field is presented. Rate-dependent and rate-independent crystal plasticity settings are considered. The theory is then reformulated following first the micromorphic approach and second a Lagrange multiplier approach. The finite element implementation of the latter is detailed. Computational efficiency of the Lagrange multiplier approach is highlighted in an example involving regularization of strain localization. The numerical performance improvement is shown to reach up to two orders of magnitude in computation time speedup. Then, size effects predicted by micromorphic and Lagrange multiplier based formulations of strain gradient plasticity are assessed. First of all numerical comparisons are performed on single crystal wires in torsion. Saturation of the size effects induced by the micromorphic approach and absence of saturation with the Lagrange multiplier approach when sample size is decreased are demonstrated. The Lagrange multiplier based formulation is finally applied to characterize size effects predicted for the ductile growth of porous unit-cells at imposed stress triaxiality. Excellent agreement with micromorphic results is obtained.

No 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.