Multi-temporal decomposition for elastoplastic ratcheting solids

2023/08/22 by Ulloa, Jacinto, Degrande, Geert, Andrade, José E. +1
#FOS: Mathematics #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2308.11821

Abstract

This paper presents a multi-temporal formulation for simulating elastoplastic solids under cyclic loading. We leverage the proper generalized decomposition (PGD) to decompose the displacements into multiple time scales, separating the spatial and intra-cyclic dependence from the inter-cyclic variation. In contrast with the standard incremental approach, which solves the (non-linear and computationally intensive) mechanical balance equations at every time step, the proposed PGD approach allows the mechanical balance equations to be solved exclusively for the small-time intra-cyclic response, while the large-time inter-cyclic response is described by simple scalar algebraic equations. Numerical simulations exhibiting complex cyclic responses, including a 2D problem and an application to a monopile foundation, demonstrate that PGD solutions with a limited number of space-time degrees of freedom may be obtained numerically, only requiring a few modes to accurately capture the reference response.

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