Incompressibility and Large Deformations

We present a new point of view on the motion of an incompressible solid with large deformations. The escription of the shape changes of the solid involves the stretch matrix of the classical polar decomposition. The incompressibility condition is , 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 . 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.