Sharp-interface limits for brittle fracture via the inverse-deformation formulation

Timothy J. Healey; Roberto Paroni; Phoebus Rosakis

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arXiv · 2403.00838

Sharp-interface limits for brittle fracture via the inverse-deformation formulation

Timothy J. Healey·Roberto Paroni·Phoebus Rosakis

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Abstract

We derive sharp-interface models for one-dimensional brittle fracture via the inverse-deformation approach. Methods of Gamma-convergence are employed to obtain the singular limits of previously proposed models. The latter feature a local, non-convex stored energy of inverse strain, augmented by small interfacial energy, formulated in terms of the inverse-strain gradient. They predict spontaneous fracture with exact crack-opening discontinuities, without the use of damage (phase) fields or pre-existing cracks; crack faces are endowed with a thin layer of surface energy. The models obtained herewith inherit the same properties, except that surface energy is now concentrated at the crack faces. Accordingly, we construct energy-minimizing configurations. For a composite bar with a breakable layer, our results predict a pattern of equally spaced cracks whose number is given as an increasing function of applied load.

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Timothy J. Healey, Roberto Paroni, Phoebus Rosakis. 2024-02-29. Sharp-interface limits for brittle fracture via the inverse-deformation formulation. https://arxiv.org/abs/2403.00838

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