Phase-field modeling of brittle fracture in heterogeneous bars

TL;DR

This paper uses phase-field modeling to analyze how heterogeneity in elastic and fracture properties affects brittle fracture behavior in a one-dimensional bar, revealing the influence of non-local effects and addressing ill-posedness issues.

Contribution

It provides a quantitative assessment of heterogeneity effects on phase-field fracture modeling in a 1D bar, highlighting the role of non-local regularization.

Findings

Heterogeneity influences elastic limit, peak stress, and fracture toughness.

Non-local phase-field regularization links heterogeneity to fracture behavior.

Non-locality can resolve ill-posedness in heterogeneous fracture problems.

Abstract

We investigate phase-field modeling of brittle fracture in a one-dimensional bar featuring a continuous variation of elastic and/or fracture properties along its axis. Our main goal is to quantitatively assess how the heterogeneity in elastic and fracture material properties influences the observed behavior of the bar, as obtained from the phase-field modeling approach. The results clarify how the elastic limit stress, the peak stress and the fracture toughness of the heterogeneous bar relate to those of the reference homogeneous bar, and what are the parameters affecting these relationships. Overall, the effect of heterogeneity is shown to be strictly tied to the non-local nature of the phase-field regularization. Finally, we show that this non-locality may amend the ill-posedness of the sharp-crack problem in heterogeneous bars where multiple points compete as fracture locations.