A Manifold Learning Approach to Accelerate Phase Field Fracture Simulations in the Representative Volume Element

TL;DR

This paper introduces a manifold learning approach using locally linear embedding to accelerate phase field fracture simulations in heterogeneous materials by reducing computational costs while maintaining accuracy.

Contribution

It applies LLE manifold learning to microcrack pattern data, enabling efficient reconstruction of fracture simulations with adaptive error control.

Findings

Significant reduction in simulation time.

High accuracy in microcrack pattern reconstruction.

Adaptive error estimation for computational efficiency.

Abstract

The multiscale simulation of heterogeneous materials is a popular and important subject in solid mechanics and materials science due to the wide application of composite materials. However, the classical FE2 (finite element2) scheme can be costly, especially when the microproblem is nonlinear. In this paper, we consider the case when the microproblem is the phase field formulation for fracture. We adopt the locally linear embedding (LLE) manifold learning approach, a method for non-linear dimension reduction, to extract the manifold that contains a collection of phase-field-represented initial microcrack patterns in the representative volume element (RVE). Then the output data corresponding to any other microcrack pattern, e.g., the evolved phase field at a fixed load, can be accurately reconstructed using the learned manifold with minimum computation. The method has two features: a minimum number of parameters for the scheme, and an input-specific error bar. The latter feature enables an adaptive strategy for any new input on whether to use the proposed, less expensive reconstruction, or to use an accurate but costly high-fidelity computation instead.