Titlebook: Variational Views in Mechanics; Paolo Maria Mariano Book 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to

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Numerical Study of Microstructures in Multiwell Problems in Linear Elasticity,ven by the minimum of two quadratic potentials whose minima are attained in distinct stress-free states. Such an energy typically fails to be quasiconvex in the sense of Morrey, so that minimizers may fail to exist and minimizing sequences converge to minimizers of the corresponding relaxed problem.

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Modeling of Microstructures in a Cosserat Continuum Using Relaxed Energies: Analytical and Numericang to model this phenomenon on a continuum level by employing the calculus of variations, specifically the concept of energy relaxation. In the framework of Cosserat continuum theory the free energy of the material is enriched with an interaction energy potential taking into account the counter rota

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Quasi-Monotonicity Formulas for Classical Obstacle Problems with Sobolev Coefficients and Applicatibility exponent larger than the space dimension. We provide applications to the free boundary analysis for the corresponding classical obstacle problems first, and then for nonlinear classical obstacle problems thanks to a linearization argument

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