16 citations · 39 across the 18 of their papers we have counts for
20 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…
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…
A structure-preserving discretisation of SO(3)-rotation fields for finite Cosserat micropolar elasticity
Lucca Schek, Peter Lewintan, Wolfgang Müller +5
We introduce a new method, dubbed Geometric Structure-Preserving Interpolation (-SPIN) to preserve physics-constraints inherent in the material parameter limits of the finite-st…
Cosserat micropolar and couple-stress elasticity models of flexomagnetism at finite deformations
Adam Sky, David Codony, Stephan Rudykh +3
We propose geometrically nonlinear (finite) continuum models of flexomagnetism based on the Cosserat micropolar and its descendent couple-stress theory. These models introduce the…
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…
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…
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…
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…
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}[σ] , D \rangle…
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 deri…
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…
Intrinsic mixed-dimensional beam-shell-solid couplings in linear Cosserat continua via tangential differential calculus
Adam Sky, Jack S. Hale, Andreas Zilian +2
We present an approach to the coupling of mixed-dimensional continua by employing the mathematically enriched linear Cosserat micropolar model. The kinematical reduction of the mod…
Yet another best approximation isotropic elasticity tensor in plane strain
Jendrik Voss, Panos Gourgiotis, Peter Lewintan +2
For plane strain linear elasticity, given any anisotropic elasticity tensor , we determine a best approximating isotropic counterpart …
Novel -conforming elements on regular triangulations and Clough--Tocher splits for the planar relaxed micromorphic model
Adam Sky, Michael Neunteufel, Peter Lewintan +3
In this work we present a consistent reduction of the relaxed micromorphic model to its corresponding two-dimensional planar model, such that its capacity to capture discontinuous…
A computational approach to identify the material parameters of the relaxed micromorphic model
Mohammad Sarhil, Lisa Scheunemann, Peter Lewintan +2
We determine the material parameters in the relaxed micromorphic generalized continuum model for a given periodic microstructure in this work. This is achieved through a least squa…
On the representation of fourth and higher order anisotropic elasticity tensors in generalized continuum models
Marco Valerio d'Agostino, Robert J. Martin, Peter Lewintan +3
The classification of all fourth-order anisotropic tensor classes for classical linear elasticity is well known. In this article, we review the related problem of explicitly comput…
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…
Green's functions for the isotropic planar relaxed micromorphic model -- concentrated force and concentrated couple
Panos Gourgiotis, Gianluca Rizzi, Peter Lewintan +4
We derive the Green's functions (concentrated force and couple in an infinite space) for the isotropic planar relaxed micromorphic model. Since the relaxed micromorphic model parti…