54 citations · 182 across the 23 of their papers we have counts for
32 papers
Dimension reduction for elastoplastic rods in the bending regime
Stefan Neukamm, Kai Richter
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…
Linearization and Homogenization of nonlinear elasticity close to stress-free joints
Stefan Neukamm, Kai Richter
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 linear…
Efficient uncertainty quantification for mechanical properties of randomly perturbed elastic rods
Patrick Dondl, Yongming Luo, Stefan Neukamm +1
Motivated by an application involving additively manufactured bioresorbable polymer scaffolds supporting bone tissue regeneration, we investigate the impact of uncertain geometry p…
Representative volume element approximations in elastoplastic spring networks
Sabine Haberland, Patrick Jaap, Stefan Neukamm +2
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 evol…
Modeling and simulation of nematic LCE rods
Sören Bartels, Max Griehl, Jakob Keck +1
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 en…
A homogenized bending theory for prestrained plates
Klaus Böhnlein, Stefan Neukamm, David Padilla-Garza +1
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 pro…
A nonlinear bending theory for nematic LCE plates
Sören Bartels, Max Griehl, Stefan Neukamm +2
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 b…
Onset of fracture in random heterogeneous particle chains
Laura Lauerbach, Stefan Neukamm, Mathias Schäffner +1
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…
Quantitative stochastic homogenization of nonlinearly elastic, random laminates
Stefan Neukamm, Mathias Schäffner, Mario Varga
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 th…
Stochastic two-scale convergence and Young measures
Martin Heida, Stefan Neukamm, Mario Varga
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 th…
Quantitative estimates in stochastic homogenization for correlated coefficient fields
Antoine Gloria, Stefan Neukamm, Felix Otto
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 o…
Mechanical behaviour of heterogeneous nanochains in the -limit of stochastic particle systems
Laura Lauerbach, Stefan Neukamm, Mathias Schäffner +1
Nanochains of atoms, molecules and polymers have gained recent interest in the experimental sciences. This article contributes to an advanced mathematical modeling of the mechanica…
Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems
Julian Fischer, Stefan Neukamm
We derive optimal-order homogenization rates for random nonlinear elliptic PDEs with monotone nonlinearity in the uniformly elliptic case. More precisely, for a random monotone ope…
Two-scale homogenization of abstract linear time-dependent PDEs
Stefan Neukamm, Mario Varga, Marcus Waurick
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…
Stochastic homogenization of -convex gradient flows
Martin Heida, Stefan Neukamm, Mario Varga
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 -convex…
Derivation of a homogenized bending--torsion theory for rods with micro-heterogeneous prestrain
Robert Bauer, Stefan Neukamm, Mathias Schäffner
In this paper we investigate rods made of nonlinearly elastic, composite--materials that feature a micro-heterogeneous prestrain that oscillates (locally periodic) on a scale that…
Lipschitz estimates and existence of correctors for nonlinearly elastic, periodic composites subject to small strains
Stefan Neukamm, Mathias Schäffner
We consider periodic homogenization of nonlinearly elastic composite materials. Under suitable assumptions on the stored energy function (frame indifference; minimality, non-degene…
Stochastic unfolding and homogenization
Martin Heida, Stefan Neukamm, Mario Varga
The notion of periodic two-scale convergence and the method of periodic unfolding are prominent and useful tools in multiscale modeling and analysis of PDEs with rapidly oscillatin…
H-compactness of elliptic operators on weighted Riemannian Manifolds
Helmer Hoppe, Jun Masamune, Stefan Neukamm
In this paper we study the asymptotic behavior of second-order uniformly elliptic operators on weighted Riemannian manifolds. They naturally emerge when studying spectral propertie…
Stochastic unfolding and homogenization of spring network models
Stefan Neukamm, Mario Varga
The aim of our work is to provide a simple homogenization and discrete-to-continuum procedure for energy driven problems involving stochastic rapidly-oscillating coefficients. Our…
An introduction to the qualitative and quantitative theory of homogenization
Stefan Neukamm
We present an introduction to periodic and stochastic homogenization of ellip- tic partial differential equations. The first part is concerned with the qualitative theory, which we…
Berry-Esseen Theorem and Quantitative homogenization for the Random Conductance Model with degenerate Conductances
Sebastian Andres, Stefan Neukamm
We study the random conductance model on the lattice , i.e. we consider a linear, finite-difference, divergence-form operator with random coefficients and the associa…
Quantitative homogenization in nonlinear elasticity for small loads
Stefan Neukamm, Mathias Schäffner
We study quantitative periodic homogenization of integral functionals in the context of non-linear elasticity. Under suitable assumptions on the energy densities (in particular fra…
Stochastic homogenization of nonconvex discrete energies with degenerate growth
Stefan Neukamm, Mathias Schaffner, Anja Schlomerkemper
We study the continuum limit of discrete, nonconvex energy functionals defined on crystal lattices in dimensions . Since we are interested in energy functionals with rando…