21 citations · 170 across the 35 of their papers we have counts for
47 papers
Discrete-to-continuum linearization in atomistic dynamics
Manuel Friedrich, Manuel Seitz, Ulisse Stefanelli
In the stationary case, atomistic interaction energies can be proved to -converge to classical elasticity models in the simultaneous atomistic-to-continuum and linearization lim…
Geometric rigidity on Sobolev spaces with variable exponent and applications
Stefano Almi, Maicol Caponi, Manuel Friedrich +1
We present extensions of rigidity estimates and of Korn's inequality to the setting of (mixed) variable exponents growth. The proof techniques, based on a classical covering argume…
Derivation of effective theories for thin 3D nonlinearly elastic rods with voids
Manuel Friedrich, Leonard Kreutz, Konstantinos Zemas
We derive a dimension-reduction limit for a three-dimensional rod with material voids by means of -convergence. Hereby, we generalize the results of the purely elastic setting […
A proof of finite crystallization via stratification
Leonard Kreutz, Manuel Friedrich
We devise a new technique to prove two-dimensional crystallization results in the square lattice for finite particle systems. We apply this strategy to energy minimizers of configu…
Existence of quasi-static crack evolution for atomistic systems
Rufat Badal, Manuel Friedrich, Joscha Seutter
We consider atomistic systems consisting of interacting particles arranged in atomic lattices whose quasi-static evolution is driven by time-dependent boundary conditions. The inte…
One-dimensional viscoelastic von Kármán theories derived from nonlinear thin-walled beams
Manuel Friedrich, Lennart Machill
We derive an effective one-dimensional limit from a three-dimensional Kelvin-Voigt model for viscoelastic thin-walled beams, in which the elastic and the viscous stress tensor comp…
Non-interpenetration conditions in the passage from nonlinear to linearized Griffith fracture
Stefano Almi, Elisa Davoli, Manuel Friedrich
We characterize the passage from nonlinear to linearized Griffith-fracture theories under non-interpenetration constraints. In particular, sequences of deformations satisfying a Ci…
Nonlinear and Linearized Models in Thermoviscoelasticity
Rufat Badal, Manuel Friedrich, Martin Kružík
We consider a quasistatic nonlinear model in thermoviscoelasticity at a finite-strain setting in the Kelvin-Voigt rheology where both the elastic and viscous stress tensors comply…
From atomistic systems to linearized continuum models for elastic materials with voids
Manuel Friedrich, Leonard Kreutz, Konstantinos Zemas
We study an atomistic model that describes the microscopic formation of material voids inside elastically stressed solids under an additional curvature regularization at the discre…
The double-bubble problem on the square lattice
Manuel Friedrich, Wojciech Górny, Ulisse Stefanelli
We investigate minimal-perimeter configurations of two finite sets of points on the square lattice. This corresponds to a lattice version of the classical double-bubble problem. We…
Derivation of a one-dimensional von Kármán theory for viscoelastic ribbons
Manuel Friedrich, Lennart Machill
We consider a two-dimensional model of viscoelastic von Kármán plates in the Kelvin's-Voigt's rheology derived from a three-dimensional model at a finite-strain setting. As the wid…
Tilings with nonflat squares: a characterization
Manuel Friedrich, Manuel Seitz, Ulisse Stefanelli
Inspired by the modelization of 2D materials systems, we characterize arrangements of identical nonflat squares in 3D. We prove that the fine geometry of such arrangements is compl…
Geometric rigidity in variable domains and derivation of linearized models for elastic materials with free surfaces
Manuel Friedrich, Leonard Kreutz, Konstantinos Zemas
We present a quantitative geometric rigidity estimate in dimensions generalizing the celebrated result by Friesecke, James, and Müller to the setting of variable domains. L…
Lattice ground states for Embedded-Atom Models in 2D and 3D
Laurent Bétermin, Manuel Friedrich, Ulisse Stefanelli
The Embedded-Atom Model (EAM) provides a phenomenological description of atomic arrangements in metallic systems. It consists of a configurational energy depending on atomic positi…
-convergence for free-discontinuity problems in linear elasticity: Homogenization and relaxation
Manuel Friedrich, Matteo Perugini, Francesco Solombrino
We analyze the -convergence of sequences of free-discontinuity functionals arising in the modeling of linear elastic solids with surface discontinuities, including phenomena as…
Stability of configurations in 3D
Laurent Bétermin, Manuel Friedrich, Ulisse Stefanelli
Inspired by the issue of stability of molecular structures, we investigate the strict minimality of point sets with respect to configurational energies featuring two- and three-bod…
Emergence of rigid Polycrystals from atomistic Systems with Heitmann-Radin sticky disk energy
Manuel Friedrich, Leonard Kreutz, Bernd Schmidt
We investigate the emergence of rigid polycrystalline structures from atomistic particle systems. The atomic interaction is governed by a suitably normalized pair interaction energ…
Two-well linearization for solid-solid phase transitions
Elisa Davoli, Manuel Friedrich
In this paper we consider nonlinearly elastic, frame-indifferent, and singularly perturbed two-well models for materials undergoing solid-solid phase transitions in any space dimen…
Integral representation for energies in linear elasticity with surface discontinuities
Vito Crismale, Manuel Friedrich, Francesco Solombrino
In this paper we prove an integral representation formula for a general class of energies defined on the space of generalized special functions of bounded deformation () in…
Equilibrium of immersed hyperelastic solids
Manuel Friedrich, Martin Kružík, Ulisse Stefanelli
We discuss different equilibrium problems for hyperelastic solids immersed in a fluid at rest. In particular, solids are subjected to gravity and hydrostatic pressure on their imme…
Lower semicontinuity for functionals defined on piecewise rigid functions and on
Manuel Friedrich, Matteo Perugini, Francesco Solombrino
In this work, we provide a characterization result for lower semicontinuity of surface energies defined on piecewise rigid functions, i.e., functions which are piecewise affine on…
Crystallization in a one-dimensional periodic landscape
Manuel Friedrich, Ulisse Stefanelli
We consider the crystallization problem for a finite one-dimensional collection of identical hard spheres in a periodic energy landscape. This issue arises in connection with the i…
Equilibrium configurations for epitaxially strained films and material voids in three-dimensional linear elasticity
Vito Crismale, Manuel Friedrich
We extend the results about existence of minimizers, relaxation, and approximation proven by Chambolle et al. in 2002 and 2007 for an energy related to epitaxially strained crystal…
Atomistic potentials and the Cauchy-Born rule for carbon nanotubes: a review
Manuel Friedrich, Edoardo Mainini, Paolo Piovano
Carbon nanotubes are modeled as point particle configurations in the framework of Molecular Mechanics, where interactions are described by means of short range attractive-repulsive…