On the quasiconvex hull for a three-well problem in two dimensional linear elasticity
Por:
Capella A., Morales L.
Publicada:
1 ene 2022
Resumen:
We provide quantitative inner and outer bounds for the symmetric quasiconvex hull Qe(U) on linear strains generated by three-well sets U in Rsym2×2. In our study, we consider all possible compatible configurations for three wells and prove that if there exist two matrices in U that are rank-one compatible then Qe(U) coincides with its symmetric lamination convex hull Le(U). We complete this result by providing an explicit characterization of Le(U) in terms of the wells in U. Finally, we discuss the optimality of our outer bound and its relationship with quadratic polyconvex functions. © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
Filiaciones:
Capella A.:
Instituto de Matemáticas-UNAM, Mexico City, Mexico
Morales L.:
Instituto de Matemáticas-UNAM, Mexico City, Mexico
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