Self-organizing fractal damage patterns in dynamically-loaded heterogeneous materials

Abstract

The present paper treats the problem of dynamic propagation of damage in porous or composite materials with hyperelastic constituents subjected to rapid surface loading using a mechanistically derived constitutive theory, the High-Fidelity-Generalized-Method-of-Cells (HFGMC), specifically developed for the micromechanics of composites, and an explicit time-integration scheme. The constitutive theory includes a material density (damage) variable representing the mass fraction of intact material, associated with a homogenized stress, a momentum balance equation associated with a conserved mass of degrading matter and an evolution equation for the damage variable, based on local mass balance and a sharp energy threshold. Representative examples are solved, showing the emergence of spatial damage patterns of fractal character and associated power-law temporal dissipation correlations, both found to comply with experimental observations. The model can be used for material damage simulation in civil-engineering, biomechanical and geophysical applications. The paper complements previous studies on the application of the HFGMC to stress analysis in hyperelastic composites with fixed damage, quasistatic evolution of damage in hyperelastic composites and slow evolution of damage in viscoelastic composites.