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Second-order structured deformations: relaxation, integral representation and applications. (English) Zbl 1370.74067

Summary: Second-order structured deformations of continua provide an extension of the multiscale geometry of first-order structured deformations by taking into account the effects of submacroscopic bending and curving. We derive here an integral representation for a relaxed energy functional in the setting of second-order structured deformations. Our derivation covers inhomogeneous initial energy densities (i.e., with explicit dependence on the position); finally, we provide explicit formulas for bulk relaxed energies as well as anticipated applications.

MSC:

74G65 Energy minimization in equilibrium problems in solid mechanics
74M25 Micromechanics of solids
74A60 Micromechanical theories
74P10 Optimization of other properties in solid mechanics
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