Two-Field Weak Solutions for a Class of Contact Models

Andaluzia Matei and Madalina Osiceanu
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Andaluzia Matei: Department of Mathematics, University of Craiova, A.I.Cuza 13, 200585 Craiova, Romania
Madalina Osiceanu: Doctoral School of Sciences, University of Craiova, A.I.Cuza 13, 200585 Craiova, Romania

Mathematics, 2022, vol. 10, issue 3, 1-17

Abstract: Two contact models are considered, with the behavior of the materials being described by a constitutive law governed by the subdifferential of a convex map. We deliver variational formulations based on the theory of bipotentials. In this approach, the unknowns are pairs consisting of the displacement field and the Cauchy stress tensor. The two-field weak solutions are sought into product spaces involving variable convex sets. Both models lead to variational systems which can be cast in an abstract setting. After delivering some abstract results, we apply them in order to study the weak solvability of the mechanical models as well as the data dependence of the weak solutions.

Keywords: nonlinear constitutive law; bipotential; two-field weak solution; well-posedness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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