Phase field modeling of crack propagation under combined shear and tensile loading with hybrid formulation

TL;DR

This paper compares anisotropic and hybrid phase field models for crack propagation under combined shear and tensile loading, demonstrating the hybrid formulation's superiority in accurately capturing damage in heterogeneous materials.

Contribution

The study introduces a comparative analysis of anisotropic and hybrid phase field formulations for crack modeling under combined loading, highlighting the hybrid approach's advantages.

Findings

Hybrid formulation better models residual stiffness effects.

Anisotropic formulation may cause spurious crack growth.

Hybrid approach provides more accurate load-displacement response.

Abstract

The crack phase field model has been well established and validated for a variety of complex crack propagation patterns within a homogeneous medium under either tensile or shear loading. However, relatively less attention has been paid to crack propagation under combined tensile and shear loading or crack propagation within composite materials made of two constituents with very different elastic moduli. In this work, we compare crack propagation under such circumstances modelled by two representative formulations, anisotropic and hybrid formulations, which have distinct stiffness degradation schemes upon crack propagation. We demonstrate that the hybrid formulation is more adequate for modeling crack propagation problems under combined loading because the residual stiffness of the damaged zone in the anisotropic formulation may lead to spurious crack growth and altered load-displacement response.