Finite strain HFGMC analysis of damage evolution in nonlinear periodic composite materials

Nathan Perchikov*, Jacob Aboudi, Konstantin Y. Volokh

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This work studies the evolution of damage in periodic composites with hyperelastic constituents prone to mechanical degradation under sufficient loading. The micromechanical problem is solved for quasistatic far-field loading for plane-strain conditions, using the finite strain high-fidelity general method of cells (FSHFGMC) approach to discretize the conservation equations. Damage is treated as degradation of material cohesion, modeled by a material conservation law with a stress-dependent damage-source (sink) term. The two-way coupled formulation with the internal variable representing damage is reminiscent of the phase-field approach to gradual cracks growth, albeit with a mechanistically derived governing equation, and with important theoretical differences in consequences. The HFGMC approach consists in enforcing equilibrium in each phase (in the cell-average sense) by stress linearization, using instantaneous tangent moduli, and subsequent iterative enforcement of continuity conditions, a formulation arguably natural for composite materials. The inherent stiffness of the underlying differential equations is treated by use of a predictor–corrector scheme. Various examples are solved, including those of porous material developing cracks close to the cavity, for various sizes and shapes of the cavity, damage in a two-phase composite of both periodic and random structure, etc. The proposed methodology is physically tractable and numerically robust and allows various generalizations.

Original languageEnglish
Pages (from-to)4361-4386
Number of pages26
JournalArchive of Applied Mechanics
Issue number12
StatePublished - Dec 2023


  • Composite
  • Damage
  • Hyperelastic
  • Micromechanics
  • Phase-field


Dive into the research topics of 'Finite strain HFGMC analysis of damage evolution in nonlinear periodic composite materials'. Together they form a unique fingerprint.

Cite this