Abstract
When a solid flattens, an eigenvalue of the stretch matrix becomes null. In this chapter, flattening is taken into account. Then the volume impenetrability condition is: the eigenvalues of the stretch matrix are non negative. If the rank of this matrix becomes equal to 2, the solid flattens in a 2D domain (a solid is flatten in a plate by a power hammer); if the rank is 1, the solid flattens in a 1D domain (an ingot is transformed into a wire in an extruder); if the rank is 0, the solid flattens into a point. Evolution with dimension change is investigated. The evolution may be smooth (the extruder case) or non smooth (the power hammer case).
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Frémond, M. (2017). Flattening. Smooth and Non Smooth Evolutions. In: Virtual Work and Shape Change in Solid Mechanics. Springer Series in Solid and Structural Mechanics, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-319-40682-4_34
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DOI: https://doi.org/10.1007/978-3-319-40682-4_34
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