Abstract:

This report identifies key ingredients necessary for developing a robust numerical framework capable of performing full-field simulations of polymer base lattice materials. Direct simulation of components manufactured out of lattice materials is not deemed suitable on account of high computational cost. The remedy is suggested by employing a computational homogenization framework. It is shown that the conventional multiscale homogenization framework, based on the standard continuum, cannot capture the intricacies of size effect and local instabilities that play a significant role in the behavior of lattice materials.

Higher-order and micromorphic homogenization frameworks based on enriched order continua are presented, which can model lattice size effects and local instabilities. Based on experimental observations, it is further argued that the full-field simulation framework should accommodate rate-dependent inelastic constitutive law for realistic modeling. In this regard, a thermodynamically consistent viscoelastic- viscoplastic constitutive model is developed, and material parameters are identified for polymer PA-12.

Some intermediate results are presented using the developed material model for the bulk response of PA-12 as well as lattice-material employing the first-order computational homogenization scheme. Finally, instability analysis is performed on unit lattices to obtain instability modes, alongside showcasing Bloch waves’ capability to determine the periodicity of the underlying RVE.