As stated in the introduction, the three main topics covered in this report are actual research fields. Different analyses and new developments related with these fields have been presented in the previous chapters. In the following, after a brief summary of the contributions, some directions for future research are outlined. Detailed presentations of the conclusions of each contribution are included in the corresponding sections and subsections. The most relevant contributions of this report are the following:
1. With respect to the treatment of large boundary displacements:
> Quasistatic and dynamic analyses of the vane test for soft materials using a fluid–based ALE formulation and different non-newtonian constitutive laws.
> The development of a solid–based ALE formulation for finite strain hyperelastic–plastic models, with applications to isochoric and non-isochoric cases.
2. Referent to the solution of nonlinear systems of equations in solid mechanics:
> The use of simple and robust numerical differentiation schemes for the computation of tangent operators, including examples with several non-trivial elastoplastic constitutive laws.
> The development of consistent tangent operators for substepping time–integration rules, with the application to an adaptive time–integration scheme.
3. In the field of constitutive modelling of granular materials:
> The efficient numerical modelling of different problems involving elastoplastic models, including work hardening–softening models for small–strain problems and density– dependent hyperelastic–plastic models in a large–strain context.
> Robust and accurate simulations of several powder compaction processes, with detailed analysis of spatial density distributions and verification of the mass conservation principle.