The incompressible von K\'arm\'an theory for thin prestrained plates

Abstract

We derive a new version of the von K\'arm\'an energy and the corresponding Euler-Langrange equations, in the context of thin prestrained plates, under the condition of incompressibility relative to the given prestrain. Our derivation uses the theory of $\Gamma$-convergence in the calculus of variations, building on prior techniques in [Conti, Dolzmann (2009)] and [Lewicka, Mahadevan, Pakzad (2011)].