Abstract
We give several examples of modeling in nonlinear elasticity where a quasiconvexification procedure is needed. We first recall that the three-dimensional Saint Venant-Kirchhoff energy fails to be quasiconvex and that its quasiconvex envelope can be obtained by means of careful computations. Second, we turn to the mathematical derivation of slender structure models: an asymptotic procedure using T-convergence tools leads to models whose energy is quasiconvex by construction. Third, we construct an homogenized quasiconvex energy for square lattices.
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Raoult, A. (2010). Quasiconvex envelopes in nonlinear elasticity. In: Schröder, J., Neff, P. (eds) Poly-, Quasi- and Rank-One Convexity in Applied Mechanics. CISM International Centre for Mechanical Sciences, vol 516. Springer, Vienna. https://doi.org/10.1007/978-3-7091-0174-2_2
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DOI: https://doi.org/10.1007/978-3-7091-0174-2_2
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