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We compute effective energies of thin bilayer structures composed by soft nematic elastic-liquid crystals in various geometrical regimes and functional configurations. Our focus is on order-strain interaction in elastic foundations composed…

Analysis of PDEs · Mathematics 2021-03-12 Pierluigi Cesana , Andres A Leon Baldelli

We study the onset of friction for rough contacting blocks whose interface is coated with a thin lubrication layer. High speed measurements of the real contact area and stress fields near the interface reveal that propagating shear cracks…

Soft Condensed Matter · Physics 2016-05-25 Elsa Bayart , Ilya Svetlizky , Jay Fineberg

The interaction of crack fronts with asperities is central to the criteria of fracture in heterogeneous materials and for predicting fracture surface formation. It is known how dynamic crack fronts respond to small, 1st-order,…

Soft Condensed Matter · Physics 2025-09-17 Itamar Kolvin , Mokhtar Adda-Bedia

We consider a nonlinear, frame indifferent Griffith model for nonsimple brittle materials where the elastic energy also depends on the second gradient of the deformations. In the framework of free discontinuity and gradient discontinuity…

Analysis of PDEs · Mathematics 2019-09-25 Manuel Friedrich

In this paper we study the asymptotic behaviour via Gamma-convergence of some integral functionals which model some multi-dimensional structures and depend explicitly on the linearized strain tensor. The functionals are defined in…

Functional Analysis · Mathematics 2007-05-23 Nadia Ansini , Francois Bille Ebobisse

This work is devoted to the analysis of the interplay between internal variables and high-contrast microstructure in inelastic solids. As a concrete case-study, by means of variational techniques, we derive a macroscopic description for an…

Analysis of PDEs · Mathematics 2024-10-14 Elisa Davoli , Chiara Gavioli , Valerio Pagliari

Second order systems whose drift is defined by the gradient of a given potential are considered, and minimization of the $L^1$-norm of the control is addressed. An analysis of the extremal flow emphasizes the role of singular trajectories…

Optimization and Control · Mathematics 2015-12-18 Zheng Chen , Jean-Baptiste Caillau , Yacine Chitour

We study stochastic homogenisation of free-discontinuity surface functionals defined on piecewise rigid functions which arise in the study of fracture in brittle materials. In particular, under standard assumptions on the density, we show…

Analysis of PDEs · Mathematics 2023-12-20 Antonio Flavio Donnarumma , Manuel Friedrich

We prove that certain nonlocal functionals defined on partitions made of measurable sets Gamma-converge to a local functional modeled on the perimeter in the sense of De Giorgi. Those nonlocal functionals involve generalized surface tension…

Analysis of PDEs · Mathematics 2025-06-26 Thomas Gabard , Vincent Millot

We resort to variational methods to evaluate the asymptotic behavior of fine metamaterials as a function of cell size. To zeroth order, the metamaterial behaves as a micropolar continuum with both displacement and rotation degrees of…

Classical Physics · Physics 2024-12-02 J. Ulloa , M. P. Ariza , J. E. Andrade , M. Ortiz

We have developed a simulation technique that uses non-linear finite element analysis and elastic fracture mechanics to compute physically plausible motion for three-dimensional, solid objects as they break, crack, or tear. When these…

Graphics · Computer Science 2023-03-21 James F. O'Brien , Jessica K. Hodgins

We investigate the problem of dimension reduction for plates in nonlinear magnetoelasticity. The model features a mixed Eulerian-Lagrangian formulation, as magnetizations are defined on the deformed set in the actual space. We consider…

Analysis of PDEs · Mathematics 2025-07-22 Marco Bresciani , Martin Kružík

The dynamics of a crack propagating in an elastic inhomogeneous material is investigated. The variations of the average crack velocity with the external loading are measured for a brittle rock and are shown to display two distinct regimes:…

Statistical Mechanics · Physics 2008-12-18 Laurent Ponson

Dynamic fracture in a wide class of materials reveals "fracture energy" $\Gamma$ much larger than the expected nominal surface energy due to the formation of two fresh surfaces. Moreover, the fracture energy depends on the crack velocity,…

Materials Science · Physics 2009-11-11 Eran Bouchbinder , Anna Pomyalov , Itamar Procaccia

We derive a dimension-reduction limit for a three-dimensional rod with material voids by means of $\Gamma$-convergence. Hereby, we generalize the results of the purely elastic setting [57] to a framework of free discontinuity problems. The…

Analysis of PDEs · Mathematics 2023-11-30 Manuel Friedrich , Leonard Kreutz , Konstantinos Zemas

Cracks are created by massive breakage of molecular or atomic bonds. The latter, in its turn, leads to the highly localized loss of material, which is the reason why even closed cracks are visible by a naked eye. Thus, fracture can be…

Materials Science · Physics 2016-10-28 Konstantin Volokh

This paper is intended to study impact forces of breaking waves on a rigid wall based on a nonlinear potential-flow theory. This is a model problem for some technologically important design issues such as the impact of breaking waves on…

Fluid Dynamics · Physics 2014-03-13 Jian-Jun Shu

$3d-2d$ dimensional reduction for hyperelastic thin films modeled through energies with point dependent growth, assuming that the sample is clamped on the lateral boundary, is performed in the framework of $\Gamma$-convergence. Integral…

Analysis of PDEs · Mathematics 2023-06-02 Michela Eleuteri , Francesca Prinari , Elvira Zappale

We carry out a variational study for integral functionals that model the stored energy of a heterogeneous material governed by finite-strain elastoplasticity with hardening. Assuming that the composite has a periodic microscopic structure,…

Analysis of PDEs · Mathematics 2024-03-08 Elisa Davoli , Chiara Gavioli , Valerio Pagliari

We introduce a lattice model able to describe damage and yielding in heterogeneous materials ranging from brittle to ductile ones. Ductile fracture surfaces, obtained when the system breaks once the strain is completely localized, are shown…

Materials Science · Physics 2010-10-18 Clara B. Picallo , Juan M. López , Stefano Zapperi , Mikko J. Alava