On discontinuous strain fields in finite elastostatics |
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Affiliation: | Department of Mechanics, School of Mathematical Sciences (SEMFE), National Technical University of Athens, 5 Heroes of Polytechnion Avenue, Zografou Campus, Athens, GR 157 73, Greece |
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Abstract: | A general method for the study of piece-wise homogeneous strain fields in finite elasticity is proposed. Critical homogeneous deformations, supporting strain jumping, are defined for any anisotropic elastic material under constant Piola–Kirchhoff stress field in three-dimensional elasticity. Since Maxwell’s sets appear in the neighborhood of singularities higher than the fold, the existence of a cusp singularity is a sufficient condition for the emergence of piece-wise constant strain fields. General formulae are derived for the study of any problem without restrictions or fictitious stress–strain laws. The theory is implemented in a simple shearing plane strain problem. Nevertheless, the procedure is valid for any anisotropic material and three-dimensional problems. |
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