The consistent tangent matrix for density-dependent plastic models within the theory of isotropic multiplicative hyperelastoplasticity is presented here. Plastic equations expressed as general functions of the Kirchhoff stresses and density are considered. They include the Cauchy-based plastic models as a particular case. The standard exponential return-mapping algorithm is applied, with the density playing the role of a fixed parameter during the nonlinear plastic corrector problem. The consistent tangent matrix has the same structure as in the usual density-independent plastic models. A simple additional term takes into account the influence of the density on the plastic corrector problem. Quadratic convergence results are shown for several representative examples involving geomaterial and powder constitutive models.
Abstract
The consistent tangent matrix for density-dependent plastic models within the theory of isotropic multiplicative hyperelastoplasticity is presented [...]
In this paper, a new approach for powder cold compaction simulations is presented. A density-dependent plastic model within the framework of finite strain multiplicative hyperelastoplasticity is used to describe the highly nonlinear material behaviour; the Coulomb dry friction model is used to capture friction effects at die-powder contact; and an Arbitrary Lagrangian–Eulerian (ALE) formulation is used to avoid the (usual) excessive distortion of Lagrangian meshes caused by large mass fluxes. Several representative examples, involving structured and unstructured meshes are simulated. The results obtained agree with the experimental data and other numerical results reported in the literature. It is shown that, contrary to other Lagrangian and adaptive h-remeshing approaches recently reported for this type of problems, the present approach verifies the mass conservation principle with very low relative errors (less than 1% in all ALE examples and exactly in the pure Lagrangian examples). Moreover, thanks to the use of an ALE formulation and in contrast with other simulations, the presented density distributions do not present spurious oscillations.
Abstract
In this paper, a new approach for powder cold compaction simulations is presented. A density-dependent plastic model within the framework of finite [...]