Related papers: A derivation of linearized Griffith energies from …
Phase field models have emerged as a powerful and flexible framework for simulating complex interface-driven phenomena across a wide range of scientific and engineering applications. In fracture mechanics, the phase field…
We consider the nonlocal formulation of continuum mechanics described by peridynamics. We provide a link between peridynamic evolution and brittle fracture evolution for a broad class of peridynamic potentials associated with unstable…
The Hamiltonian formulation of lattice gauge theories plays a central role in quantum simulations of gauge theories, and understanding their spectrum and other properties is expected to become crucial in the upcoming years. The relevant…
The exact reduced density-matrix functional is derived from the Luttinger-Ward functional of the single-particle Green's function. Thereby, a formal link is provided between diagrammatic many-body approaches using Green's functions on the…
We summarize recent results regarding the equilibrium and non-equilibrium behavior of cold dilute atomic gases in the limit in which the two body scattering length a goes to infinity. In this limit the system is described by a Galilean…
In this work, we study the effective behavior of a two-dimensional variational model within finite crystal plasticity for high-contrast bilayered composites. Precisely, we consider materials arranged into periodically alternating thin…
Using a generalized cut vertex expansion we introduce the concept of an extended fracture function for the description of semi-inclusive deep inelastic processes in the target fragmentation region. Extended fracture functions are shown to…
We prove compactness with respect to $\Gamma$-convergence for a general class of non-local energies modelled after the ones considered in [Gobbino, CPAM (1998)]. We give an integral representation result for the limits, which are free…
Griffith's energetic criterion, or `energy balance', has for a century formed the basis for fracture mechanics; the energy flowing into a crack front is precisely balanced by the dissipation (fracture energy) at the front. If the crack…
Starting from a general classical model of many interacting particles we present a well defined step by step procedure to derive the continuum-mechanics equations of nonlinear elasticity theory with fluctuations which describe the…
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…
The dynamics of rapid brittle cracks is commonly studied in the framework of linear elastic fracture mechanics where nonlinearities are neglected. However, recent experimental and theoretical work demonstrated explicitly the importance of…
We address in this review unified analysis of phase-field models for cohesive fracture. Aiming to regularize the Barenblatt (1959) cohesive zone model, all the discussed models are distinguished by three characteristic functions, i.e., the…
We consider a model of energy minimization arising in the study of the mechanical behavior caused by cell contraction within a fibrous biological medium. The macroscopic model is based on the theory of non rank-one convex nonlinear…
During brittle crack propagation, a smooth crack front curve frequently becomes disjoint, generating a stepped crack and a material ligament that unites the newly formed crack fronts. These universal features fundamentally alter the…
If gradient systems depend on a microstructure, we want to derive a macroscopic gradient structure describing the effective behavior of the microscopic effects. We introduce a notion of evolutionary Gamma-convergence that relates the…
The modeling of cracks is an important topic - both in engineering as well as in mathematics. Since crack propagation is characterized by a free boundary value problem (the geometry of the crack is not known beforehand, but part of the…
We prove the uniform rectifiability of brittle fractures in arbitrary dimension. The existing approach for the Mumford-Shah functional, which relies on separation-type properties of the singular set, faces serious obstacles in the Griffith…
We have designed a new experimental setup able to investigate fracture of soft materials at small scales. At high crack velocity, where energy is mostly dissipated through viscoelastic processes, we observe an increasingly large high strain…
We study the non-Euclidean (incompatible) elastic energy functionals in the description of prestressed thin films, at their singular limits ($\Gamma$-limits) as $h\to 0$ in the film's thickness $h$. Firstly, we extend the prior results…