Multi-temporal decomposition for elastoplastic ratcheting solids

TL;DR

This paper introduces a multi-temporal PGD-based method for efficiently simulating elastoplastic solids under cyclic loading, significantly reducing computational effort while maintaining accuracy.

Contribution

It develops a novel multi-temporal formulation using PGD to separate intra- and inter-cyclic responses, enabling efficient simulation of complex cyclic behaviors.

Findings

PGD solutions require few modes to accurately capture responses.

The method effectively simulates 2D cyclic problems and monopile foundation responses.

Significant reduction in computational cost compared to standard approaches.

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.