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The present paper aims to explore a computational homogenisation procedure to investigate the full geometric representation of yield surfaces for isotropic porous ductile media. The effects of cell morphology and imposed boundary conditions are assessed. The sensitivity of the yield surfaces to the Lode angle is also investigated in detail.

The microscale of the material is modelled by the concept of Representative Volume Element (RVE) or unit cell, which is numerically simulated through three-dimensional finite element analyses. Numerous loading conditions are considered to create complete yield surfaces encompassing high, intermediate and low triaxialities. The influence of cell morphology on the yield surfaces is assessed considering a spherical cell with spherical void and a cubic RVE with spherical void, both under uniform strain boundary condition. The use of spherical cell is interesting as preferential directions in the effective behaviour are avoided. The periodic boundary condition, which favours strain localization, is imposed on the cubic RVE to compare the results. Small strains are assumed and the cell matrix is considered as a perfect elasto-plastic material following the von Mises yield criterion.

Different morphologies for the cell imply in different yield conditions for the same load situations. The yield surfaces in correspondence to periodic boundary condition show significant differences compared to those obtained by imposing uniform strain boundary condition. The stress Lode angle has a strong influence on the geometry of the yield surfaces considering low and intermediate triaxialities.

The exhaustive computational study of the effects of cell morphologies and imposed boundary conditions fills a gap in the full representation of the flow surfaces. The homogenisation-based strategy allows us to further investigate the influence of the Lode angle on the yield surfaces.

The purpose of this study is to evaluate the accuracy and numerical stability of the Generalized Finite Element Method (GFEM) for solving structural dynamic problems.

The GFEM is a numerical method based on the Partition of Unity (PU) concept. The method can be understood as an extension of the conventional Finite Element Method (FEM) for which the local approximation provided by the shape functions can be improved by means of enrichment functions. Polynomial enrichment functions are hereby used combined with an implicit time-stepping integration technique for improving the dynamical response of the models. Both consistent and lumped mass matrices techniques are tested. The method accuracy and stability are investigated through linear and nonlinear elastic problems.

The results indicate that the adopted strategies can provide stable and accurate responses for GFEM in dynamic analyses. Furthermore, the mass lumping technique provided remarkable reductions of the system of equation condition number, therefore leading to more stable numerical models.

The evaluated features of GFEM models for implicit time-stepping integration schemes represent new information of great deal of interest regarding linear and nonlinear dynamic analyses using such a method.