A model of isotropic damage with strain-gradient effects: existence and uniqueness of weak solutions for progressive damage processes

Bisconti, Luca; Mariano, Paolo Maria; Markenscoff, Xanthippi

doi:10.1177/1081286518785423

Cited by 6 publications

(1 citation statement)

References 31 publications

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“…Despite this, our choice of considering the gradient of cofF among the entries of W is intended as an indicator of relative surface variation effects. Also, as already mentioned, the dependence of W on ∇detF is a way of accounting for confinement effects due to non-homogeneous volume variations (see [8] for a pertinent analysis in small strain regime). Explanations a part are necessary for justifying the representation of cracks in terms of varifold, which are special vector-valued measures.…”

Section: Physical Insightmentioning

confidence: 99%

Crack occurrence in bodies with gradient polyconvex energies

Kružík,

Mariano,

Mucci

2021

Preprint

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Energy minimality selects among possible configurations of a continuous body with and without cracks those compatible with assigned boundary conditions of Dirichlettype. Crack paths are described in terms of curvature varifolds so that we consider both "phase" (cracked or non-cracked) and crack orientation. The energy considered is gradient polyconvex: it accounts for relative variations of second-neighbor surfaces and pressure-confinement effects. We prove existence of minimizers for such an energy. They are pairs of deformations and varifolds. The former ones are taken to be SBV maps satisfying an impenetrability condition. Their jump set is constrained to be in the varifold support.

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Section: Physical Insightmentioning

confidence: 99%