Semi-implicit finite strain constitutive integration of porous plasticity models

• The combination of relative Green-Lagrange strains with the exact corotational method.
• The use of L¨owdin algorithm based on the Jacobians of configurations Ωb and Ωa.
• Replacement of the complementarity condition by the Chen-Mangasarian function.
• GTN and Rousselier constitutive models, with the determination of intersections with axes of pressure-shear diagram (p − q).
• The use of MINI element in triangles and tetrahedra to avoid locking due to quasi-incompressibility.

Two porous plasticity models, Rousselier and Gurson–Tvergaard–Needleman (GTN), are integrated with a new semi-implicit integration algorithm for finite strain plasticity. It consists of using relative Green–Lagrange during the iteration process and incremental frame updating corresponding to a polar decomposition. Lowdin׳s method of orthogonalization is adopted to ensure incremental frame-invariance. In addition, a smooth replacement of the complementarity condition is used. Since porous models are known to be difficult to integrate due to the combined effect of void fraction growth, stress and effective plastic strain evolution, we perform a complete assessment of our semi-implicit algorithm. Semi-implicit algorithms take advantage of different evolution rates to enhance the robustness in difficult to converge problems. A detailed description of the constitutive algorithm is performed, with the key components comprehensively exposed. In addition to the fully detailed constitutive algorithms, we use mixed finite strain elements based on Arnold׳s MINI formulation. This formulation passes the inf–sup test and allows a direct application with porous models. Isoerror maps for two common initial stress states are shown. In addition, we extensively test the two models with established benchmarks. Specifically, the cylindrical tension test as well as the butterfly shear specimen are adopted for validation. A 3D tension test is used to investigate mesh dependence and the effect of a length scale. Results show remarkable robustness.