Two-scale space-time methods for computational solid mechanics

Abstract

The efficient, robust and accurate assessment of structures in large deformation simultaneously requires: i) the resolution of micro-scale states to avoid the use of empirical material laws and assess reliability, ii) the availability of sufficiently light models to enable optimal structure design and uncertainty quantification.

The present work contributes to the first objective by the use of variational integrators, a non-conforming space discretization in the sense of mortar methods and the design of optimal coarse grids to enhance traditional domain decomposition methods. The second issue is handled by an homogenized problem iteratively improved by accurate subgrid models in space and time. Several aspects of the method are analyzed and some examples are displayed as an illustration.