11 papers · 1 filter
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…
Global existence and uniqueness of weak solutions for a Willis-type model of elastodynamics
Thomas Blesgen, Patrizio Neff
The existence and uniqueness of weak solutions is shown for a system related to the Willis model of elastodynamics. Both the whole space case and the case of a bounded smooth domai…
Rate-form equilibrium for an isotropic Cauchy-elastic formulation: Part I: modeling
Patrizio Neff, Nina J. Husemann, Sebastian Holthausen +2
We derive the rate-form spatial equilibrium system for a nonlinear Cauchy elastic formulation in isotropic finite-strain elasticity. For a given explicit Cauchy stress-strain const…
Two types of compressible isotropic neo-Hookean material models
Sergey N. Korobeynikov, Alexey Yu. Larichkin, Patrizio Neff
In this contribution, we present a systematic study of the performance of two known types of compressible generalization of the incompressible neo-Hookean material model. The first…
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…
Major symmetry of the induced tangent stiffness tensor for the Zaremba-Jaumann rate and Kirchhoff stress in hyperelasticity: two different approaches
Salvatore Federico, Sebastian Holthausen, Nina J. Husemann +1
We recall in this note that the induced tangent stiffness tensor appearing in a hypoelastic formulation based on the Zaremba-Jaumann corotational de…