Abstract
In many engineering applications, the elastic bodies in contact may undergo large transformations. In this case, a setting such as presented in Chap. 3 and in Chap. 10 is no longer valid, since it was restricted to small displacements and small strain. Taking into account large displacements and large strain, for instance in the hyperelastic framework, introduces many additional difficulties. First, one starts with losing many of the nice mathematical properties associated to the Signorini problem, notably the minimization problem does not involve anymore a quadratic functional and a convex set of admissible displacements. Therefore, it is much more challenging to study the well-posedness of the continuous problem, or to prove the convergence of the numerical methods. Moreover, difficulties appear in the formulation and numerical resolution of the contact and friction problems in this case.
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Chouly, F., Hild, P., Renard, Y. (2023). Contact and Self-contact in Large Strain. In: Finite Element Approximation of Contact and Friction in Elasticity. Advances in Mechanics and Mathematics(), vol 48. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-31423-0_11
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