Abstract
We present a new point of view on the motion of an incompressible solid with large deformations. The description of the shape changes of the solid involves the stretch matrix \(\mathbf {W}\) of the classical polar decomposition. The incompressibility condition is \(\det \mathbf {W}\,\ge \,1\), accounting for possible cavitation or phase change. The reaction to the incompressibility condition is a pressure which is positive. There is cavitation or phase change when the pressure is null. The motion of a three-dimensional solid is investigated between time 0 and a final time \(T>0\). It is possible to prove that the model is coherent in terms of mechanics and mathematics. Let us note that the pressure is a measure allowing possible internal collisions due to cavitation.
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Bonetti, E., Frémond, M. (2017). Incompressibility and Large Deformations. In: Frémond, M., Maceri, F., Vairo, G. (eds) Models, Simulation, and Experimental Issues in Structural Mechanics. Springer Series in Solid and Structural Mechanics, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-48884-4_10
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DOI: https://doi.org/10.1007/978-3-319-48884-4_10
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