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An exact transformation method is introduced that reduces the governing equations of a continuum structure coupled to strong nonlinearities to a low dimensional equation with memory. The method is general and well suited to problems with…

Dynamical Systems · Mathematics 2014-03-05 Robert Szalai

We consider a sequence of linear hyper-elastic, inhomogeneous and fully anisotropic bodies in a reference configuration occupying a cylindrical region of height epsilon. We then study, by means of Gamma-convergence, the asymptotic behavior…

Mathematical Physics · Physics 2017-04-03 Francois Murat , Roberto Paroni

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 with the principle of frame indifference under rotations.…

Analysis of PDEs · Mathematics 2023-01-25 Rufat Badal , Manuel Friedrich , Martin Kružík

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

Most cellular solids are random materials, while practically all theoretical results are for periodic models. To be able to generate theoretical results for random models, the finite element method (FEM) was used to study the elastic…

Materials Science · Physics 2007-05-23 Anthony Roberts , Ed Garboczi

Two equal and opposite distributed dead loads are applied orthogonally to the axis of an elastic rod in its rectilinear reference configuration, one at the extrados and the other at the intrados, such that the resultant applied force per…

Classical Physics · Physics 2026-04-21 Davide Bigoni , Diego Misseroni , Andrea Piccolroaz

Many materials of contemporary interest, such as gels, biological tissues and elastomers, are easily deformed but essentially incompressible. Traditional linear theory of elasticity implements incompressibility only to first order and thus…

Soft Condensed Matter · Physics 2015-06-22 J. S. Biggins , Z. Wei , L. Mahadevan

For solving the longstanding materials science problem of correlating elastic properties of a solid material to the formation of cracks we present a new general concept. This concept is applied to the technologically most important cracks…

Materials Science · Physics 2007-05-23 Petr Lazar , Raimund Podloucky , Walter Wolf

This paper is devoted to describe the deformations and the elastic energy for structures made of straight rods of thickness $2\delta$ when $\delta$ tends to 0. This analysis relies on the decomposition of the large deformation of a single…

Analysis of PDEs · Mathematics 2010-10-19 Dominique Blanchard , Georges Griso

The modeling of the elastic properties of granular or nanoscale systems requires the foundations of the theory of elasticity to be revisited, as one explores scales at which this theory may no longer hold. The only cases for which a…

Statistical Mechanics · Physics 2007-05-23 I. Goldhirsch , C. Goldenberg

Using the Jacobian matrix, we obtain theoretical expression of rigidity and the density of states of two-dimensional amorphous solids consisting of frictional grains in the linear response to an infinitesimal strain, in which we ignore the…

Soft Condensed Matter · Physics 2023-05-16 Daisuke Ishima , Kuniyasu Saitoh , Michio Otsuki , Hisao Hayakawa

The holographic duality has proven successful in linking seemingly unrelated problems in physics.Recently, intriguing correspondences between the physics of soft matter and gravity are emerging,including strong similarities between the…

Soft Condensed Matter · Physics 2022-06-07 Deng Pan , Teng Ji , Matteo Baggioli , Li Li , Yuliang Jin

We show existence of solutions for the equations of static atomistic nonlinear elasticity theory on a bounded domain with prescribed boundary values. We also show their convergence to the solutions of continuum nonlinear elasticity theory,…

Analysis of PDEs · Mathematics 2016-06-30 Julian Braun , Bernd Schmidt

Nonreciprocity has been introduced to various fields to realize asymmetric, nonlinear, and/or time non-revisal physical systems. By virtue of the Maxwell-Betti reciprocal theorem, breaking the time-reversal symmetry of dynamic mechanical…

Classical Physics · Physics 2021-01-05 Mohamed Shaat

The Young's modulus $E$ is the key mechanical property that determines the resistance of solids to tension/compression. In the present work, the correlation of the quantity $E$ with such characteristics as the total molar mass $M$ of alloy…

Materials Science · Physics 2023-06-16 B. N. Galimzyanov , M. A. Doronina , A. V. Mokshin

We consider the axial compression of a thin sheet wrapped around a rigid cylindrical substrate. In contrast to the wrinkling-to-fold transitions exhibited in similar systems, we find that the sheet always buckles into a single symmetric…

Soft Condensed Matter · Physics 2015-07-13 Norbert Stoop , Martin Michael Müller

We present a unified formulation of a rotationally invariant nonlinear elasticity for a variety of spontaneously anisotropic phases, and use it to study thermal fluctuations in nematic elastomers and spontaneously anisotropic gels. We find…

Soft Condensed Matter · Physics 2009-11-07 Xiangjun Xing , Leo Radzihovsky

Using confocal microscopy, we measure the packing geometry and interdroplet forces as a function of the osmotic pressure in a 3D emulsion system. We find that the nonlinear elastic response of the pressure with density is not a result of…

Soft Condensed Matter · Physics 2015-06-11 Ivane Jorjadze , Lea-Laetitia Pontani , Jasna Brujic

Granular elasticity, an elasticity theory useful for calculating static stress distribution in granular media, is generalized to the dynamic case by including the plastic contribution of the strain. A complete hydrodynamic theory is derived…

Soft Condensed Matter · Physics 2010-10-14 Yimin Jiang , Mario Liu

The Young\'s modulus of a nylon string has been determined experimentally by combining elasticity theory and wave optics. A diffraction experiment has been setup to determine the change in the string diameter for different tensile forces…