281 citations · 921 across the 53 of their papers we have counts for
64 papers
Vector and matrix monotonicity characterisation of the "load forces" in nonlinear elasticity: compressible versus incompressible response
Jendrik Voss, Ionel-Dumitrel Ghiba, Robert J. Martin +1
In this paper, we study the relation between different notions of monotonicity for isotropic hyperelastic compressible and incompressible materials. We study how to define the mono…
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, Maximilian P. Wollner, Patrizio Neff
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 existence of minimizers
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 mat…
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…
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 $φ\colon\mathbb{R}^2\to \m…
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} [σ] = \mathbb{H}^{\rm ZJ}(σ).D, \qquad D = {\r…
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…
A constitutive condition for idealized isotropic Cauchy elasticity involving the logarithmic strain
Marco Valerio d'Agostino, Sebastian Holthausen, Davide Bernardini +4
Following Hill and Leblond, the aim of our work is to show, for isotropic nonlinear elasticity, a relation between the corotational Zaremba-Jaumann objective derivative of the Cauc…
The Biot stress -- right stretch relation for the compressible Neo-Hooke-Ciarlet-Geymonat model and Rivlin's cube problem
Ionel-Dumitrel Ghiba, Franz Gmeineder, Sebastian Holthausen +2
The aim of the paper is to recall the importance of the study of invertibility and monotonicity of stress-strain relations for investigating the non-uniqueness and bifurcation of h…
An essay on deformation measures in isotropic thin shell theories. Bending versus curvature
Ionel-Dumitrel Ghiba, Peter Lewintan, Adam Sky +1
It has become commonplace for the stored energy function of any realistic shell model to align ``within first order" with the classical Koiter membrane-bending (flexural) shell mod…
Rayleigh waves in isotropic elastic materials with micro-voids
Emilian Bulgariu, Ionel-Dumitrel Ghiba, Hassam Khan +1
In this paper, we show that a general method introduced by Fu and Mielke allows to give a complete answer on the existence and uniqueness of a subsonic solution describing the prop…
Explicit formula for the Gamma-convergence homogenized quadratic curvature energy in isotropic Cosserat shell models
Maryam Mohammadi Saem, Emilian Bulgariu, Ionel-Dumitrel Ghiba +1
We show how to explicitly compute the homogenized curvature energy appearing in the isotropic -limit for flat and for curved initial configuration Cosserat shell models, when a…
Linear constrained Cosserat-shell models including terms up to . Conditional and unconditional existence and uniqueness
Ionel-Dumitrel Ghiba, Patrizio Neff
In this paper we linearise the recently introduced geometrically nonlinear constrained Cosserat-shell model. In the framework of the linear constrained Cosserat-shell model, we pro…
A linear isotropic Cosserat shell model including terms up to . Existence and uniqueness
Ionel-Dumitrel Ghiba, Mircea Birsan, Patrizio Neff
In this paper we derive the linear elastic Cosserat shell model incorporating effects up to order in the shell thickness as a particular case of the recently introduce…
A geometrically nonlinear Cosserat (micropolar) curvy shell model via Gamma convergence
Maryam Mohammadi Saem, Ionel-Dumitrel Ghiba, Patrizio Neff
Using -convergence arguments, we construct a nonlinear membrane-like Cosserat shell model on a curvy reference configuration starting from a geometrically nonlinear, physically…
Cosserat micropolar elasticity: classical Eringen vs. dislocation form
Ionel-Dumitrel Ghiba, Gianluca Rizzi, Angela Madeo +1
In this paper we do a comparative presentation of the linear isotropic Cosserat elastic model from two perspectives: the classical Mindlin-Eringen-Nowacki description in terms of a…
Analytical solution of the uniaxial extension problem for the relaxed micromorphic continuum and other generalized continua (including full derivations)
Gianluca Rizzi, Hassam Khan, Ionel-Dumitrel Ghiba +2
We derive analytical solutions for the uniaxial extension problem for the relaxed micromorphic continuum and other generalized continua. These solutions may help in the identificat…
Morrey's conjecture for the planar volumetric-isochoric split. Part I: least convex energy functions
Jendrik Voss, Robert J. Martin, Ionel-Dumitrel Ghiba +1
We consider Morrey's open question whether rank-one convexity already implies quasiconvexity in the planar case. For some specific families of energies, there are precise condition…
Analytical solution of the cylindrical torsion problem for the relaxed micromorphic continuum and other generalized continua (including full derivations)
Gianluca Rizzi, Geralf Hütter, Hassam Khan +3
We solve the St.Venant torsion problem for an infinite cylindrical rod whose behaviour is described by a family of isotropic generalized continua, including the relaxed micromorphi…
Existence and uniqueness of Rayleigh waves in isotropic elastic Cosserat materials and algorithmic aspects
Hassam Khan, Ionel-Dumitrel Ghiba, Angela Madeo +1
We discuss the propagation of surface waves in an isotropic half space modelled with the linear Cosserat theory of isotropic elastic materials. To this aim we use a method based on…
Analytical solutions of the cylindrical bending problem for the relaxed micromorphic continuum and other generalized continua (including full derivations)
Gianluca Rizzi, Geralf Hütter, Angela Madeo +1
We consider the cylindrical bending problem for an infinite plate as modelled with a family of generalized continuum models, including the micromorphic approach. The models allow t…