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Polyconvexity for Cosserat nonlinear elasticity and nonlinear couple-stress theory
Diana Ciotir, Ionel-Dumitrel Ghiba, Patrizio Neff
We study a class of nonlinear elastic energies whose constitutive structure is naturally expressed in terms of a stretch variable but is not directly covered by the standard polyco…
Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem
Jendrik Voss, Robert J. Martin, Ionel-Dumitrel Ghiba +2
Motivated by classical constitutive inequalities in isotropic nonlinear elasticity theory, we investigate the monotonicity of isotropic tensor functions of the form \[ Σ_f\colon\ma…
Polyconvexity implies Hill's inequality in
Ionel-Dumitrel Ghiba, Patrizio Neff, Maximilian P. Wollner
For compressible nonlinear isotropic elasticity it is well known that rank-one convexity, polyconvexity and the monotonicity of the Cauchy stress tensor with respect to the logarit…
Nonlinear Kirchhoff-Love shell models derived from the Ciarlet-Geymonat energy: modelling and well-posedness
Ionel-Dumitrel Ghiba, Trung Hieu Giang, Catalina Ureche
Starting from a three-dimensional model based on the Ciarlet-Geymonat energy, we derive nonlinear shell models within the classical elasticity theory of compressible isotropic mate…
Propagation of Love waves in linear elastic isotropic Cosserat materials
Marius Apetrii, Emilian Bulgariu, Ionel-Dumitrel Ghiba +2
We investigate the propagation of Love waves in an isotropic half-space modelled as a linear {elastic isotropic} Cosserat material. To this aim, we show that a method commonly used…
Quasiconvex relaxation of planar Biot-type energies and the role of determinant constraints
Robert J. Martin, Ionel-Dumitrel Ghiba, Maximilian Köhler +3
We derive the quasiconvex relaxation of the Biot-type energy density for planar mappings $Ï\colon\mathbb{R}^2\to…