A length scale insensitive anisotropic phase field fracture model for hyperelastic composites

Tushar Kanti Mandal, Vinh Phu Nguyen, Jian Ying Wu

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49 Citations (Scopus)


Fracture of composites consisting of isotropic matrix and anisotropic fibers is an essential problem in many engineering applications. The computational simulation of such a fracture is complicated, but the use of phase field models (PFMs) is promising. Indeed, in PFMs, sharp cracks are not treated as discontinuities; instead, they are approximated as thin damage bands. Thus, PFMs can seamlessly model complex crack patterns like branching, merging, and fragmentation. However, previous PFMs for anisotropic fracture, which are mostly based on a PFM using a simple quadratic degradation function without any user-defined parameters, provide solutions that are sensitive to a length scale (that controls the width of the damage band). Moreover, those PFMs have considered a same softening behavior for isotropic and anisotropic part of composite – which is not correct. This paper presents a length scale insensitive PFM for brittle fracture of anisotropic hyperelastic solids considering distinct softening behavior of isotropic matrix and anisotropic fibers. This model is an extension of the model of Wu [JMPS, 103 (2017)] with a rational degradation function dependent on elasticity and fracture related material parameters. Fracture of fiber-reinforced composites and biological tissues, simulated using the proposed model within the framework of the finite element method, is presented with predictions in good agreement with previous findings and experiments. Most importantly, the results are independent of the incorporated length scale parameter. Moreover, preliminary results show that the proposed model is as efficient as the previous models.

Original languageEnglish
Article number105941
Number of pages21
JournalInternational Journal of Mechanical Sciences
Publication statusPublished - 15 Dec 2020


  • Anisotropy
  • Hyperelasticity
  • Length scale
  • PF-CZM
  • Quasi-brittle fracture
  • Variational approach to fracture

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