6 papers
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…
Constitutive properties for isotropic energies in ideal nonlinear elasticity for solid materials: numerical evidences for invertibility and monotonicity in different stress-strain pairs
Ionel-Dumitrel Ghiba, Robert Martin, Marius Apetrii +1
As a service for the solid mechanics community we gather in this paper constitutive properties of a collective list of isotropic elastic energies for compressible materials. Of int…
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…
The corotational stability postulate: positive incremental Cauchy stress moduli for diagonal, homogeneous deformations in isotropic nonlinear elasticity
Patrizio Neff, Nina J. Husemann, Aurélien S. Nguetcho Tchakoutio +2
In isotropic nonlinear elasticity the corotational stability postulate (CSP) is the requirement that \begin{equation*} \langle\frac{\mathrm{D}^{\circ}}{\mathrm{D} t}[Ï] , D \rangl…
Hypo-elasticity, Cauchy-elasticity, corotational stability and monotonicity in the logarithmic strain
Patrizio Neff, Sebastian Holthausen, Marco Valerio d'Agostino +4
We combine the rate-formulation for the objective, corotational Zaremba-Jaumann rate \begin{align} \frac{{\rm D}^{\rm ZJ}}{{\rm D} t} [Ï] = \mathbb{H}^{\rm ZJ}(Ï).D, \qquad D = {…
A natural requirement for objective corotational rates -- on structure preserving corotational rates
Patrizio Neff, Sebastian Holthause, Sergey N. Korobeynikov +2
We investigate objective corotational rates satisfying an additional, physically plausible assumption. More precisely, we require for \begin{equation*} \frac{{\rm D}^{\circ}}{{\rm…