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Stability of Homogeneous States with Gradient Damage Models: Size Effects and Shape Effects in the Three-Dimensional Setting

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Abstract

Considering a family of gradient-enhanced damage models and taking advantage of its variational formulation, we study the stability of homogeneous states in a full three-dimensional context. We show that gradient terms have a stabilizing effect, but also how those terms induce structural effects. We emphasize the great importance of the type of boundary conditions, the size and the shape of the body on the stability properties of such states.

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Notes

  1. The response for which both strain and damage fields are constant in space.

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Authors and Affiliations

  1. Institut Jean Le Rond d’Alembert, Université Pierre et Marie Curie, 4 place Jussieu, 75252, Paris, France

    K. Pham

  2. Laboratoire de Mécanique des Solides, Ecole Polytechnique, 91128, Palaiseau Cedex, France

    J.-J. Marigo

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  1. K. Pham
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Pham, K., Marigo, JJ. Stability of Homogeneous States with Gradient Damage Models: Size Effects and Shape Effects in the Three-Dimensional Setting. J Elast 110, 63–93 (2013). https://doi.org/10.1007/s10659-012-9382-5

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