Stefan Neukamm
YOU?
Author Swipe
View article: Linearization and homogenization of nonlinear elasticity close to stress-free joints
Linearization and homogenization of nonlinear elasticity close to stress-free joints Open
In this paper, we study a hyperelastic composite material with a periodic microstructure and a prestrain close to a stress-free joint. We consider two limits associated with linearization and homogenization. Unlike previous studies that fo…
View article: Commutativity and non-commutativity of limits in the nonlinear bending theory for prestrained microheterogeneous plates
Commutativity and non-commutativity of limits in the nonlinear bending theory for prestrained microheterogeneous plates Open
In this paper we study the derivation of nonlinear bending models for prestrained elastic plates from three-dimensional non-linear elasticity via homogenization and dimension reduction. We compare effective models obtained by either simult…
View article: Dimension reduction for elastoplastic rods in the bending regime
Dimension reduction for elastoplastic rods in the bending regime Open
We rigorously derive an effective bending model for elastoplastic rods starting from three-dimensional finite plasticity. For the derivation we lean on a framework of evolutionary $Γ$-convergence for rate-independent systems. The main cont…
View article: Dimension-reduced mathematical modeling of self-shaping wooden composite bilayers
Dimension-reduced mathematical modeling of self-shaping wooden composite bilayers Open
Swelling and shrinkage of wood provides challenges when used as construction material. On the positive side, it allows for manufacturing curved wood elements by self-shaping upon drying. We present a two-dimensional model for simulating th…
View article: Linearization and Homogenization of nonlinear elasticity close to stress-free joints
Linearization and Homogenization of nonlinear elasticity close to stress-free joints Open
In this paper, we study a hyperelastic composite material with a periodic microstructure and a prestrain close to a stress-free joint. We consider two limits associated with linearization and homogenization. Unlike previous studies that fo…
View article: Quantitative stochastic homogenization of nonlinearly elastic, random laminates
Quantitative stochastic homogenization of nonlinearly elastic, random laminates Open
In this paper we study quantitative stochastic homogenization of a nonlinearly elastic composite material with a laminate microstructure. We prove that for deformations close to the set of rotations, the homogenized stored energy function …
View article: Onset of fracture in random heterogeneous particle chains
Onset of fracture in random heterogeneous particle chains Open
In mechanical systems, it is of interest to know the onset of fracture in dependence of the boundary conditions. Here we study a one-dimensional model which allows for an underlying heterogeneous structure in the discrete setting. Such mod…
View article: Efficient uncertainty quantification for mechanical properties of randomly perturbed elastic rods
Efficient uncertainty quantification for mechanical properties of randomly perturbed elastic rods Open
Motivated by an application involving additively manufactured bioresorbable polymer scaffolds supporting bone tissue regeneration, we investigate the impact of uncertain geometry perturbations on the effective mechanical properties of elas…
View article: A Homogenized Bending Theory for Prestrained Plates
A Homogenized Bending Theory for Prestrained Plates Open
The presence of prestrain can have a tremendous effect on the mechanical behavior of slender structures. Prestrained elastic plates show spontaneous bending in equilibrium—a property that makes such objects relevant for the fabrication of …
View article: Representative volume element approximations in elastoplastic spring networks
Representative volume element approximations in elastoplastic spring networks Open
We study the large-scale behavior of a small-strain lattice model for a network composed of elastoplastic springs with random material properties. We formulate the model as an evolutionary rate independent system (ERIS). In an earlier work…
View article: Modeling and simulation of nematic LCE rods
Modeling and simulation of nematic LCE rods Open
We introduce a nonlinear, one-dimensional bending-twisting model for an inextensible bi-rod that is composed of a nematic liquid crystal elastomer. The model combines an elastic energy that is quadratic in curvature and torsion with a Fran…
View article: A homogenized bending theory for prestrained plates
A homogenized bending theory for prestrained plates Open
The presence of prestrain can have a tremendous effect on the mechanical behavior of slender structures. Prestrained elastic plates show spontaneous bending in equilibrium -- a property that makes such objects relevant for the fabrication …
View article: A nonlinear bending theory for nematic LCE plates
A nonlinear bending theory for nematic LCE plates Open
In this paper, we study an elastic bilayer plate composed of a nematic liquid crystal elastomer in the top layer and a nonlinearly elastic material in the bottom layer. While the bottom layer is assumed to be stress-free in the flat refere…
View article: Stochastic two-scale convergence and Young measures
Stochastic two-scale convergence and Young measures Open
In this paper we compare the notion of stochastic two-scale convergence in the mean (by Bourgeat, Mikelić and Wright), the notion of stochastic unfolding (recently introduced by the authors), and the quenched notion of stochastic two-scale…
View article: Quantitative estimates in stochastic homogenization for correlated coefficient fields
Quantitative estimates in stochastic homogenization for correlated coefficient fields Open
This paper is about the homogenization of linear elliptic operators in divergence form with stationary random coefficients that have only slowly decaying correlations. It deduces optimal estimates of the homogenization error from optimal g…
View article: Onset of fracture in random heterogeneous particle chains
Onset of fracture in random heterogeneous particle chains Open
In mechanical systems it is of interest to know the onset of fracture in dependence of the boundary conditions. Here we study a one-dimensional model which allows for an underlying heterogeneous structure in the discrete setting. Such mode…
View article: Quantitative stochastic homogenization of nonlinearly elastic, random laminates
Quantitative stochastic homogenization of nonlinearly elastic, random laminates Open
In this paper we study quantitative stochastic homogenization of a nonlinearly elastic composite material with a laminate microstructure. We prove that for deformations close to the set of rotations the homogenized stored energy function $…
View article: Two-scale homogenization of abstract linear time-dependent PDEs
Two-scale homogenization of abstract linear time-dependent PDEs Open
Many time-dependent linear partial differential equations of mathematical physics and continuum mechanics can be phrased in the form of an abstract evolutionary system defined on a Hilbert space. In this paper we discuss a general framewor…
View article: Stochastic homogenization of \Lambda -convex gradient flows
Stochastic homogenization of \Lambda -convex gradient flows Open
In this paper we present a stochastic homogenization result for a class of Hilbert space evolutionary gradient systems driven by a quadratic dissipation potential and a Λ-convex energy functional featuring random and rapidly oscillating co…
View article: Continuum Limit and Homogenization of Stochastic and Periodic Discrete Systems – Fracture in Composite Materials
Continuum Limit and Homogenization of Stochastic and Periodic Discrete Systems – Fracture in Composite Materials Open
The limiting behaviour of a one‐dimensional discrete system is studied by means of Γ‐convergence. We consider a toy model of a chain of atoms. The interaction potentials are of Lennard‐Jones type and periodically or stochastically distribu…
View article: Mechanical behaviour of heterogeneous nanochains in the $\Gamma$-limit of stochastic particle systems
Mechanical behaviour of heterogeneous nanochains in the $\Gamma$-limit of stochastic particle systems Open
Nanochains of atoms, molecules and polymers have gained recent interest in the experimental sciences. This article contributes to an advanced mathematical modeling of the mechanical properties of nanochains that allow for heterogenities, w…
View article: Mechanical behaviour of heterogeneous nanochains in the $Γ$-limit of stochastic particle systems
Mechanical behaviour of heterogeneous nanochains in the $Γ$-limit of stochastic particle systems Open
Nanochains of atoms, molecules and polymers have gained recent interest in the experimental sciences. This article contributes to an advanced mathematical modeling of the mechanical properties of nanochains that allow for heterogenities, w…
View article: Stochastic homogenization of $Λ$-convex gradient flows
Stochastic homogenization of $Λ$-convex gradient flows Open
In this paper we present a stochastic homogenization result for a class of Hilbert space evolutionary gradient systems driven by a quadratic dissipation potential and a $Λ$-convex energy functional featuring random and rapidly oscillating …
View article: <i>H</i>-Compactness of Elliptic Operators on Weighted Riemannian Manifolds
<i>H</i>-Compactness of Elliptic Operators on Weighted Riemannian Manifolds Open
In this paper we study the asymptotic behavior of second-order uniformly elliptic operators on weighted Riemannian manifolds. They naturally emerge when studying spectral properties of the Laplace–Beltrami operator on families of manifolds…