ECCOMAS 2024

A combined volumetric-deviatoric and spectral decomposition-based phase-field model for brittle fracture

  • Rahaman, Mohammad Masiur (Indian Institute of Technology Bhubaneswar)
  • Behera, Akash Kumar (Indian Institute of Technology Bhubaneswar)
  • Pillai, Ayyappan Unnikrishna (Indian Institute of Technology Bhubaneswar)

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Being continuum approaches for modeling fracture, phase-field models (PFMs) have gained popularity over the years because of several advantages over the discrete approaches for predicting complex crack paths; viz. skirting the need for re-meshing, enrichment of finite element shape functions, and an explicit tracking of the crack surfaces. Recently, it has been realized that two of the widely used PFMs namely volumetric-deviatoric \cite{Amor} and spectral decomposition-based \cite{Miehe} PFMs do not work uniformly for different applied loading conditions. The PFMs based on volumetric-deviatoric components show nonphysical stresses under transverse compression. The spectral decomposition-based PFMs show nonphysical stresses under simple shear. Since these two types of PFMs are extensively used, a combined scheme of these two schemes that can work uniformly across all types of loading may be considered of significance. In this work, we have considered a combined volumetric-deviatoric and spectral decomposition scheme for the strain tensor to investigate tension-compression asymmetry within the phase field formulation. To demonstrate the efficacy of the proposed combined scheme, we have carried out a comparison study of the phase-field models with the volumetric-deviatoric, the spectral decomposition, and the proposed combined scheme of these two schemes through a few representative numerical examples under different loading conditions.