Publications (184)
Hyperelastic bodies under homogeneous Cauchy stress induced by three-dimensional non-homogeneous deformations
L. Angela Mihai, Patrizio Neff
In isotropic finite elasticity, unlike in the linear elastic theory, a homogeneous Cauchy stress may be induced by non-homogeneous strains. To illustrate this, we identify compatib…
A polyconvex extension of the logarithmic Hencky strain energy
Robert J. Martin, Ionel-Dumitrel Ghiba, Patrizio Neff
Adapting a method introduced by Ball, Muite, Schryvers and Tirry, we construct a polyconvex isotropic energy function which is equal to…
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…
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…
Wave propagation in relaxed micromorphic continua: modelling metamaterials with frequency band-gaps
Angela Madeo, Patrizio Neff, Ionel-Dumitrel Ghiba +2
In this paper the relaxed micromorphic model proposed in [Patrizio Neff, Ionel-Dumitrel Ghiba, Angela Madeo, Luca Placidi, Giuseppe Rosi. A unifying perspective: the relaxed linear…
Real wave propagation in the isotropic relaxed micromorphic model
Patrizio Neff, Angela Madeo, Gabriele Barbagallo +3
For the recently introduced isotropic relaxed micromorphic generalized continuum model, we show that under the assumption of positive definite energy, planar harmonic waves have re…
Rotational invariance conditions in elasticity, gradient elasticity and its connection to isotropy
Ingo Münch, Patrizio Neff
For homogeneous higher gradient elasticity models we discuss frame-indifference and isotropy requirements. To this end, we introduce the notions of local versus global SO(3)-invari…
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 Legendre-Hadamard condition in Cosserat elasticity theory
Milad Shirani, David J. Steigmann, Patrizio Neff
The Legendre-Hadamard necessary condition for energy minimizers is derived in the framework of Cosserat elasticity theory.
A unifying perspective: the relaxed linear micromorphic continuum
Patrizio Neff, Ionel-Dumitrel Ghiba, Angela Madeo +2
We formulate a relaxed linear elastic micromorphic continuum model with symmetric Cauchy force-stresses and curvature contribution depending only on the micro-dislocation tensor. O…
Existence of minimizers in the geometrically non-linear 6-parameter resultant shell theory with drilling rotations
Mircea Birsan, Patrizio Neff
The paper is concerned with the geometrically non-linear theory of 6-parametric elastic shells with drilling degrees of freedom. This theory establishes a general model for shells,…
A hybrid H1xH(curl) finite element formulation for a relaxed micromorphic continuum model of antiplane shear
Adam Sky, Michael Neunteufel, Ingo Münch +2
One approach for the simulation of metamaterials is to extend an associated continuum theory concerning its kinematic equations, and the relaxed micromorphic continuum represents s…
Low-and high-frequency Stoneley waves, reflection and transmission at a Cauchy/relaxed micromorphic interface
Alexios Aivaliotis, Ali Daouadji, Gabriele Barbagallo +3
In this paper we study the reflective properties of a 2D interface separating a homogeneous solid from a band-gap metamaterial by modeling it as an interface between a classical Ca…
Towards the conception of complex engineering meta-structures: relaxed-micromorphic modelling of low-frequency mechanical diodes/high-frequency screens
Gianluca Rizzi, Domenico Tallarico, Patrizio Neff +1
In this paper we show that an enriched continuum model of the micromorphic type (Relaxed Micromorphic Model) can be used to model metamaterials' response in view of their use for m…
On the dispersion of waves for the linear thermoelastic relaxed micromorphic model
Aarti Khurana, Suman Bala, Hassam Khan +2
We present the complete set of constitutive relations and field equations for the linear thermoelastic relaxed micromorphic continuum and investigate its variants for wave propagat…
Global regularity for a physically nonlinear version of the relaxed micromorphic model on Lipschitz domains
Dorothee Knees, Sebastian Owczarek, Patrizio Neff
In this paper, we investigate the global higher regularity properties of weak solutions for a linear elliptic system coupled with a nonlinear Maxwell-type system defined on Lipschi…
Polyconvexity does not imply true-stress-true-strain monotonicity in the incompressible three-dimensional case
Dominik K. Klein, Maximilian P. Wollner, Patrizio Neff
We study constitutive conditions of hyperelastic potentials for incompressible material behavior in three dimensions. By means of a counterexample, we show that polyconvexity does…
From frequency-dependent models to frequency-independent enriched continua for mechanical metamaterials
Gianluca Rizzi, Marco Valerio d'Agostino, Jendrik Voss +3
Mechanical metamaterials have recently gathered increasing attention for their uncommon mechanical responses enabling unprecedented applications for elastic wave control. To model…
On the convexity of nonlinear elastic energies in the right Cauchy-Green tensor
David Yang Gao, Patrizio Neff, Ionel Roventa +1
We present a sufficient condition under which a weak solution of the Euler-Lagrange equations in nonlinear elasticity is already a global minimizer of the corresponding elastic ene…
On some fundamental misunderstandings in the indeterminate couple stress model. A comment on recent papers of A.R. Hadjesfandiari and G.F. Dargush
Patrizio Neff, Ingo Münch, Ionel-Dumitrel Ghiba +1
In a series of papers which are either published [A.R. Hadjesfandiari and G.F. Dargush, Couple stress theory for solids, Int. J. Solids Struct. 48, 2496-2510, 2011; A.R. Hadjesfand…
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…
Korn-Maxwell-Sobolev inequalities for general incompatibilities
Franz Gmeineder, Peter Lewintan, Patrizio Neff
We establish a family of coercive Korn-type inequalities for generalised incompatible fields in the superlinear growth regime under sharp criteria. This extends and unifies several…
Loss of ellipticity for non-coaxial plastic deformations in additive logarithmic finite strain plasticity
Patrizio Neff, Ionel-Dumitrel Ghiba
In this paper we consider the additive logarithmic finite strain plasticity formulation from the view point of loss of ellipticity in elastic unloading. We prove that even if an el…
A logarithmic minimization property of the unitary polar factor in the spectral norm and the Frobenius matrix norm
Patrizio Neff, Yuji Nakatsukasa, Andreas Fischle
The unitary polar factor in the polar decomposition of the matrix is the minimizer for both and its Hermitian part $\| \mathrm{sym Log}(Q^…
Maxwell meets Korn: A New Coercive Inequality for Tensor Fields with Square-Integrable Exterior Derivative
Patrizio Neff, Dirk Pauly, Karl-Josef Witsch
Maxwell meets Korn: A New Coercive Inequality for Tensor Fields with Square-Integrable Exterior Derivative
In search of constitutive conditions in isotropic hyperelasticity: polyconvexity versus true-stress-true-strain monotonicity
Maximilian P. Wollner, Gerhard A. Holzapfel, Patrizio Neff
The polyconvexity of a strain-energy function is nowadays increasingly presented as the ultimate material stability condition for an idealized elastic response. While the mathemati…
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…
A rank-one convex, non-polyconvex isotropic function on with compact connected sublevel sets
Jendrik Voss, Ionel-Dumitrel Ghiba, Robert J. Martin +1
According to a 2002 theorem by Cardaliaguet and Tahraoui, an isotropic, compact and connected subset of the group of invertible matrices is ra…
Sum of squared logarithms - An inequality relating positive definite matrices and their matrix logarithm
Mircea Birsan, Patrizio Neff, Johannes Lankeit
Let y1, y2, y3, a1, a2, a3 > 0 be such that y1 y2 y3 = a1 a2 a3 and y1 + y2 + y3 >= a1 + a2 + a3, y1 y2 + y2 y3 + y1 y3 >= a1 a2 + a2 a3 + a1 a3. Then the following inequality hold…
Inconsistency of uhyper and umat in Abaqus for compressible hyperelastic materials
Herbert Baaser, Robert J. Martin, Patrizio Neff
In this article, we revisited Bažant's comments on the implementation of hyperelastic material models in commercial finite element software. We would like to clarify that our asse…
On the dislocation density tensor in the Cosserat theory of elastic shells
Mircea Birsan, Patrizio Neff
We consider the Cosserat continuum in its finite strain setting and discuss the dislocation density tensor as a possible alternative curvature strain measure in three-dimensional C…
On Grioli's minimum property and its relation to Cauchy's polar decomposition
Patrizio Neff, Johannes Lankeit, Angela Madeo
The unitary polar factor of a matrix F is the unitary matrix Q realizing the minimum of the norm of F-Q over all unitary matrices Q. Tracing back the development on the optimality…
Transparent anisotropy for the relaxed micromorphic model: macroscopic consistency conditions and long wave length asymptotics
Gabriele Barbagallo, Angela Madeo, Marco Valerio d'Agostino +3
In this paper, we study the anisotropy classes of the fourth order elastic tensors of the relaxed micromorphic model, also introducing their second order counterpart by using a Voi…
Rank-one convexity vs. ellipticity for isotropic functions
Robert J. Martin, Jendrik Voss, Ionel-Dumitrel Ghiba +1
It is well known that a twice-differentiable real-valued function on the group of invertible ma…
Polyconvex anisotropic hyperelasticity with neural networks
Dominik K. Klein, Mauricio Fernández, Robert J. Martin +2
In the present work, two machine learning based constitutive models for finite deformations are proposed. Using input convex neural networks, the models are hyperelastic, anisotrop…
Modeling real phononic crystals via the weighted relaxed micromorphic model with free and gradient micro-inertia
Angela Madeo, Manuel Collet, Marco Miniaci +3
In this paper the relaxed micromorphic continuum model with weighted free and gradient micro-inertia is used to describe the dynamical behavior of a real two-dimensional phononic c…
Regularity for a geometrically nonlinear flat Cosserat micropolar membrane shell with curvature
Andreas Gastel, Patrizio Neff
We consider the rigorously derived thin shell membrane -limit of a three-dimensional isotropic geometrically nonlinear Cosserat micropolar model and deduce full interior regula…
On the characterization of drilling rotation in the 6-parameter resultant shell theory
Mircea Birsan, Patrizio Neff
We analyze geometrically non-linear isotropic elastic shells and prove the existence of minimizers. In general, the model takes into account the effect of drilling rotations in she…
Complete band gaps including non-local effects occur only in the relaxed micromorphic model
Angela Madeo, Patrizio Neff, Marco Valerio d'Agostino +1
In this paper we substantiate the claim implicitly made in previous works that the relaxed micromorphic model is the only linear, isotropic, reversibly elastic, nonlocal generalize…
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…
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…
The isotropic relaxed micromorphic model in polar coordinates and its application to an elastostatic axisymmetric extension problem
Esmaeal Ghavanloo, Patrizio Neff
In this paper, we consider the isotropic relaxed micromorphic model in polar coordinates and use this representation to solve explicitly an elastostatic axisymmetric extension prob…
Optimality of the relaxed polar factors by a characterization of the set of real square roots of real symmetric matrices
Lev Borisov, Andreas Fischle, Patrizio Neff
We consider the problem to determine the optimal rotations which minimize for a…
The sum of squared logarithms inequality in arbitrary dimensions
Lev Borisov, Patrizio Neff, Suvrit Sra +1
We prove the \emph{sum of squared logarithms inequality} (SSLI) which states that for nonnegative vectors whose elementary symmetric polynomials satisfy $e_…
-trace-free generalized Korn inequalities for incompatible tensor fields in three space dimensions
Peter Lewintan, Patrizio Neff
For we prove an -version of the generalized trace-free Korn inequality for incompatible tensor fields in $ W^{1,\,p}_0(\operatorname{Curl}; Ω,\mathbb{R}^{3\t…
Korn inequalities for incompatible tensor fields in three space dimensions with conformally invariant dislocation energy
Peter Lewintan, Stefan Müller, Patrizio Neff
Let be an open and bounded set with Lipschitz boundary and outward unit normal . For we establish an improved version of the generalized $…
A variant of the linear isotropic indeterminate couple stress model with symmetric local force-stress, symmetric nonlocal force-stress, symmetric couple-stresses and complete traction boundary conditions
Ionel-Dumitrel Ghiba, Patrizio Neff, Angela Madeo +1
In this paper we venture a new look at the linear isotropic indeterminate couple stress model in the general framework of second gradient elasticity and we propose a new alternativ…
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…
Analytical solutions of the simple shear problem for certain types of micromorphic continuum models -- including full derivations
Gianluca Rizzi, Geralf Hütter, Angela Madeo +1
To draw conclusions as regards the stability and modelling limits of the investigated continuum, we consider a family of infinitesimal isotropic generalized continuum models (Mindl…
Lagrange and based Finite Element formulations for the relaxed micromorphic model
Jörg Schröder, Mohammad Sarhil, Lisa Scheunemann +1
Modeling the unusual mechanical properties of metamaterials is a challenging topic for the mechanics community and enriched continuum theories are promising computational tools for…
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 = {…
Poincare meets Korn via Maxwell: Extending Korn's First Inequality to Incompatible Tensor Fields
Patrizio Neff, Dirk Pauly, Karl-Josef Witsch
For a bounded three-dimensional domain with Lipschitz boundary we extend Korn's first inequality to incompatible tensor fields. For compatible tensor fields our estimate reduces to…
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…
Geometrically nonlinear Cosserat elasticity in the plane: applications to chirality
Sebastian Bahamonde, Christian G. Boehmer, Patrizio Neff
Modelling two-dimensional chiral materials is a challenging problem in continuum mechanics because three-dimensional theories reduced to isotropic two-dimensional problems become n…
Concurrent enforcement of polyconvexity and true-stress-true-strain monotonicity in incompressible isotropic hyperelasticity: application to neural network constitutive models
Maximilian P. Wollner, Dominik K. Klein, Herbert Baaser +2
The design of physics-augmented neural networks (PANNs) for the purposes of constitutive modeling has received considerable attention as of late for a variety of material behaviors…
Modeling a labyrinthine acoustic metamaterial through an inertia-augmented relaxed micromorphic approach
Jendrik Voss, Gianluca Rizzi, Patrizio Neff +1
We present an inertia-augmented relaxed micromorphic model that enriches the relaxed micromorphic model previously introduced by the authors via a term in 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…
Injectivity of the Cauchy-stress tensor along rank-one connected lines under strict rank-one convexity condition
Patrizio Neff, L. Angela Mihai
In this note, we show that the Cauchy stress tensor in nonlinear elasticity is injective along rank-one connected lines provided that the constitutive law is strictly rank-one…
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…
The exponentiated Hencky-logarithmic strain energy. Part III: Coupling with idealized isotropic finite strain plasticity
Patrizio Neff, Ionel-Dumitrel Ghiba
We investigate an immediate application in finite strain multiplicative plasticity of the family of isotropic volumetric-isochoric decoupled strain energies \begin{align*} F\mapsto…
Existence results for non-homogeneous boundary conditions in the relaxed micromorphic model
Ionel-Dumitrel Ghiba, Patrizio Neff, Sebastian Owczarek
In this paper we use a property of the extension operator from the space of tangential traces of in the context of the linear relaxed micromorphic model, a…
A commented translation of Hans Richter's early work "The isotropic law of elasticity"
Kai Graban, Eva Schweickert, Robert J. Martin +1
We provide a faithful translation of Hans Richter's important 1948 paper "Das isotrope Elastizitätsgesetz" from its original German version into English. Our introduction summariz…
A geometrically nonlinear Cosserat shell model for orientable and non-orientable surfaces: Discretization with geometric finite elements
Lisa Julia Nebel, Oliver Sander, Mircea Bîrsan +1
We investigate discretizations of a geometrically nonlinear elastic Cosserat shell with nonplanar reference configuration originally introduced by Bîrsan, Ghiba, Martin, and Neff…
Rank-one convexity implies polyconvexity for isotropic, objective and isochoric elastic energies in the two-dimensional case
Robert J. Martin, Ionel-Dumitrel Ghiba, Patrizio Neff
We show that in the two-dimensional case, every objective, isotropic and isochoric energy function which is rank-one convex on is already polyconvex on $\mathrm{…
On the convexity of the function C --> f(det C) on positive definite matrices
Stephan Lehmich, Patrizio Neff, Johannes Lankeit
We prove a condition on f \in C^2(\R+,\R) for the convexity of (f o det) on PSym(n), namely that f o det is convex on PSym(n) if and only if f"(s)+(n-1)/(ns) f'(s) >= 0 and f'(s)<=…
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…
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…
A Canonical Extension of Korn's First Inequality to H(Curl) motivated by Gradient Plasticity with Plastic Spin
Patrizio Neff, Dirk Pauly, Karl-Josef Witsch
We prove a Korn-type inequality in H(Curl) for tensor fields.
-versions of generalized Korn inequalities for incompatible tensor fields in arbitrary dimensions with -integrable exterior derivative
Peter Lewintan, Patrizio Neff
For and we prove an -version of the generalized Korn-type inequality for incompatible, -integrable tensor fields havin…
Sharp rank-one convexity conditions in planar isotropic elasticity for the additive volumetric-isochoric split
Jendrik Voss, Ionel-Dumitrel Ghiba, Robert J. Martin +1
We consider the volumetric-isochoric split in planar isotropic hyperelasticity and give a precise analysis of rank-one convexity criteria for this case, showing that the Legendre-H…
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…
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…
Chirality in the plane
Christian G. Boehmer, Yongjo Lee, Patrizio Neff
It is well-known that many three-dimensional chiral material models become non-chiral when reduced to two dimensions. Chiral properties of the two-dimensional model can then be res…
Rediscovering G.F. Becker's early axiomatic deduction of a multiaxial nonlinear stress-strain relation based on logarithmic strain
Patrizio Neff, Ingo Münch, Robert Martin
We discuss a completely forgotten work of the geologist G.F. Becker on the ideal isotropic nonlinear stress-strain function. In doing this we provide the original paper from 1893 n…
The modified indeterminate couple stress model: Why Yang et al.'s arguments motivating a symmetric couple stress tensor contain a gap and why the couple stress tensor may be chosen symmetric nevertheless
Ingo Münch, Patrizio Neff, Angela Madeo +1
We show that the reasoning in favor of a symmetric couple stress tensor in Yang et al.'s introduction of the modified couple stress theory contains a gap, but we present a reasonab…
The Armstrong-Frederick cyclic hardening plasticity model with Cosserat effects
Krzysztof Chelminski, Patrizio Neff, Sebastian Owczarek
We propose an extension of the cyclic hardening plasticity model formulated by Armstrong and Frederick which includes micropolar effects. Our micropolar extension establishes coerc…
Shear, pure and simple
Christian Thiel, Jendrik Voss, Robert J. Martin +1
In a 2012 article in the International Journal of Non-Linear Mechanics, Destrade et al. showed that for nonlinear elastic materials satisfying Truesdell's so-called empirical inequ…
Defects in unidimensional structures
Mewen Crespo, Guy Casale, Loïc Le Marrec +1
In a previous work of the first authors, a non-holonomic model, generalising the micromorphic models and allowing for curvature (disclinations) to arise from the kinematic values,…
The geometrically nonlinear Cosserat micropolar shear-stretch energy. Part II: Non-classical energy-minimizing microrotations in 3D and their computational validation
Andreas Fischle, Patrizio Neff
In any geometrically nonlinear, isotropic and quadratic Cosserat micropolar extended continuum model formulated in the deformation gradient field and…
Higher order Bernstein-Bézier and Nédélec finite elements for the relaxed micromorphic model
Adam Sky, Ingo Muench, Gianluca Rizzi +1
The relaxed micromorphic model is a generalized continuum model that is well-posed in the space . Consequently, finite element formulations…
Do we need Truesdell's empirical inequalities? On the coaxiality of stress and stretch
Christian Thiel, Jendrik Voss, Robert J. Martin +1
Truesdell's empirical inequalities are considered essential in various fields of nonlinear elasticity. However, they are often used merely as a sufficient criterion for semi-invert…
Well-posedness for dislocation based gradient visco-plasticity with isotropic hardening
Nataliya Kraynyukova, Patrizio Neff, Sergiy Nesenenko +1
In this work we establish the well-posedness for infinitesimal dislocation based gradient viscoplasticity with isotropic hardening for general gradient monotone plastic flows. We a…
On in-plane drill rotations for Cosserat surfaces
Maryam Mohammadi Saem, Peter Lewintan, Patrizio Neff
We show under some natural smoothness assumptions that pure in-plane drill rotations as deformation mappings of a -smooth regular shell surface to another one parametrized ove…
Quasiconvex relaxation of isotropic functions in incompressible planar hyperelasticity
Robert J. Martin, Jendrik Voss, Ionel-Dumitrel Ghiba +1
In this note, we provide an explicit formula for computing the quasiconvex envelope of any real-valued function with f…
Dev-Div- and DevSym-DevCurl-inequalities for incompatible square tensor fields with mixed boundary conditions
Sebastian Bauer, Patrizio Neff, Dirk Pauly +1
For an n-dimensional bounded domain we derive some inequalities bounding the norm of a square tensor field. Concerning the Div-Dev-inequality the bound is given by the trace-free p…
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…
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…
On the sum of squared logarithms inequality and related inequalities
Fozi M. Dannan, Patrizio Neff, Christian Thiel
We consider the sum of squared logarithms inequality and investigate possible connections with the theory of majorization. We also discuss alternative sufficient conditions on two…
A global higher regularity result for the static relaxed micromorphic model on smooth domains
Dorothee Knees, Sebastian Owczarek, Patrizio Neff
We derive a global higher regularity result for weak solutions of the linear relaxed micromorphic model on smooth domains. The governing equations consist of a linear elliptic syst…
Identification of scale-independent material parameters in the relaxed micromorphic model through model-adapted first order homogenization
Patrizio Neff, Bernhard Eidel, Marco Valerio d'Agostino +1
We rigorously determine the scale-independent short range elastic parameters in the relaxed micromorphic generalized continuum model for a given periodic microstructure. This is do…
Rank-one convexity implies polyconvexity in isotropic planar incompressible elasticity
Ionel-Dumitrel Ghiba, Robert J. Martin, Patrizio Neff
We study convexity properties of energy functions in plane nonlinear elasticity of incompressible materials and show that rank-one convexity of an objective and isotropic elastic e…
A first regularity result for the Armstrong-Frederick cyclic hardening plasticity model with Cosserat effects
Krzysztof CheÅmiÅski, Patrizio Neff, Sebastian Owczarek
The purpose of this article is to prove the Hölder continuity up to the boundary of the displacement vector and the microrotation matrix for the quasistatic, rate-independent Arms…
The isotropic Cosserat shell model including terms up to . Part II: Existence of minimizers
Ionel-Dumitrel Ghiba, Mircea Bîrsan, Peter Lewintan +1
We show the existence of global minimizers for a geometrically nonlinear isotropic elastic Cosserat 6-parameter shell model. The proof of the main theorem is based on the direct me…
Relaxed micromorphic modeling of the interface between a homogeneous solid and a band-gap metamaterial: new perspectives towards meta-structural design
Angela Madeo, Gabriele Barbagallo, Manuel Collet +3
In the present paper, the material parameters of the isotropic relaxed micromorphic model derived for a specific metamaterial in a previous contribution are used to model its trans…
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…
Primal and mixed finite element formulations for the relaxed micromorphic model
Adam Sky, Michael Neunteufel, Ingo Muench +2
The classical Cauchy continuum theory is suitable to model highly homogeneous materials. However, many materials, such as porous media or metamaterials, exhibit a pronounced micros…
Optimal incompatible Korn-Maxwell-Sobolev inequalities in all dimensions
Franz Gmeineder, Peter Lewintan, Patrizio Neff
We characterise all linear maps such that, for , \begin{align*} \|P\|_{L^{p^{*}}(\mathbb{R}^{n})}\leq…
NeÄas-Lions lemma revisited: An -version of the generalized Korn inequality for incompatible tensor fields
Peter Lewintan, Patrizio Neff
For we prove an -version of the generalized Korn inequality for incompatible tensor fields in . M…
Existence result for a dislocation based model of single crystal gradient plasticity with isotropic or linear kinematic hardening
Francois Ebobisse, Patrizio Neff, Elias C. Aifantis
We consider a dislocation-based rate-independent model of single crystal gradient plasticity with isotropic or linear kinematic hardening. The model is weakly formulated through th…
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-s…