The LATIN-PGD methodology to nonlinear dynamics and quasi-brittle materials for future earthquake engineering applications

Abstract

This paper presents a first implementation of the LArge Time INcrement (LATIN) method along with the model reduction technique called Proper Generalized Decomposition (PGD) for solving nonlinear low-frequency dynamics problems when dealing with a quasi-brittle isotropic damage constitutive relations. The present paper uses the Time-Discontinuous Galerkin Method (TDGM) for computing the temporal contributions of the space-time separate-variables solution of the LATIN-PGD approach, which offers several advantages when considering a high number of DOFs in time. The efficiency of the method is tested for the case of a 3D bending beam, where results and benchmarks comparing LATIN-PGD to classical time-incremental Newmark/Quasi-Newton nonlinear solver are presented. This work represents a first step towards taking into account uncertainties and carrying out more complex parametric studies imposed by seismic risk assessment.