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Amongst the various fascinating types of material behavior featured by magnetic gels and elastomers are magnetostrictive effects. That is, deformations in shape or changes in volume are induced from outside by external magnetic fields.…

Soft Condensed Matter · Physics 2024-01-30 Lukas Fischer , Andreas M. Menzel

In this paper we extend the recent theory of shear-localization in 2-dimensional amorphous solids to 3-D. In 2-D the fundamental instability of shear-localization is related to the appearance of a line of displacement quadrupoles, that…

Soft Condensed Matter · Physics 2015-12-11 Ratul Dasgupta , Oleg Gendelman , Pankaj Mishra , Itamar Procaccia , Carmel A. B. Z. Shor

The S-matrix in the static limit of a dispersion relation is a matrix of a finite order N of meromorphic functions of energy $\omega$ in the plane with cuts $(-\infty,-1],[+1,+\infty)$. In the elastic case it reduces to N functions…

High Energy Physics - Theory · Physics 2011-04-15 Meshcheryakov V. A

The geometry of mesoscopic inhomogeneities plays an important role in determining the macroscopic propagation behaviors of elastic waves in a heterogeneous medium. Nonequiaxed inhomogeneities can lead to anisotropic wave velocity and…

Geophysics · Physics 2020-05-05 Huijing He

The existing theory of incompatible elastic sheets uses the deviation of the surface metric from a reference metric to define the strain tensor [Efrati et al., J. Mech. Phys. Solids {\bf 57}, 762 (2009)]. For a class of simple axisymmetric…

Soft Condensed Matter · Physics 2017-05-24 Oz Oshri , Haim Diamant

Strain gradient theory is an accurate model for capturing the size effect and localization phenomena. However, the challenge in identification of corresponding constitutive parameters limits the practical application of the theory. We…

Computational Engineering, Finance, and Science · Computer Science 2021-12-30 Hua Yang , Bilen Emek Abali , Wolfgang H. Müller , Salma Barboura , Jia Li

We review 3-d reducible representation of the Lorentz group and introduce a 6-d irreducible representation tailored for transforming 6-d electromagnetic vector, and we show that the mixture of the density matrices associated with the left-…

Classical Physics · Physics 2024-11-25 M. A. Kuntman

In recent years, the paradigm of `soft glassy matter' has been used to describe diverse nonergodic materials exhibiting strong local disorder and slow mesoscopic rearrangement. As so far formulated, however, the resulting `soft glassy…

Soft Condensed Matter · Physics 2007-05-23 M. E. Cates , P. Sollich

A precisely selected elastic strain can be introduced in submicron-thick single-crystal SrTiO3 sheets using a silicon nitride stressor layer. A conformal stressor layer deposited using plasma-enhanced chemical vapor deposition produces an…

Materials Science · Physics 2020-02-27 J. A. Tilka , J. Park , Y. Ahn , A. Pateras , Z. Cai , P. G. Evans

We consider an algebra of even-order square tensors and introduce a stretching map which allows us to represent tensors as matrices. The stretching map could be understood as a generalized matricization. It conserves algebraic properties of…

Representation Theory · Mathematics 2023-02-08 Vyacheslav Futorny , Mikhail Neklyudov , Kaiming Zhao

Rare-earth tritellurides ($R$Te$_3$) exhibit complex charge-density-wave (CDW) phases intertwined with lattice symmetry, offering a platform to explore unconventional symmetry breaking in correlated materials. Elasto-optical probing, which…

Materials Science · Physics 2025-12-03 Kuiqing Tang

We study the nonlinear elastic response of a two-dimensional material to a localized boundary force, with the particular goal of understanding the differences observed between isotropic granular materials and those with hexagonal…

Soft Condensed Matter · Physics 2009-11-13 B. P. Tighe , J. E. S. Socolar

The homogenization results obtained by Bacca et al. (Homogenization of heterogeneous Cauchy-elastic materials leads to Mindlin second-gradient elasticity. Part I: Closed form expression for the effective higher-order constitutive tensor.…

Mathematical Physics · Physics 2014-01-03 Mattia Bacca , Francesco Dal Corso , Daniele Veber , Davide Bigoni

The crack tip mechanics of strain gradient plasticity solids is investigated analytically and numerically. A first-order mechanism-based strain gradient (MSG) plasticity theory based on Taylor's dislocation model is adopted and implemented…

Applied Physics · Physics 2020-10-16 V. Shlyannikov , E. Martínez-Pañeda , A. Tumanov , A. Tartygasheva

A large variety of materials, widely encountered both in engineering applications and in the biological realm, are characterised by a non-vanishing internal stress distribution, even in the absence of external deformations or applied…

Soft Condensed Matter · Physics 2024-03-15 Artur L. Gower , Tom Shearer , Pasquale Ciarletta , Michel Destrade

We present a new type of triangular $C^1$ finite elements developed for the plane strain crack problems within the simplified strain gradient elasticity (SGE). The finite element space contains a conventional fifth-degree polynomial…

Numerical Analysis · Mathematics 2025-01-06 Yury Solyaev , Vasiliy Dobryanskiy

It is fairly well known that rotation in three dimensions can be expressed as a quadratic in a skew symmetric matrix via the Euler-Rodrigues formula. A generalized Euler-Rodrigues polynomial of degree 2n in a skew symmetric generating…

Materials Science · Physics 2008-07-25 Andrew N. Norris

Physical experiments can characterize the elastic response of granular materials in terms of macroscopic state-variables, namely volume (packing) fraction and stress, while the microstructure is not accessible and thus neglected. Here, by…

Soft Condensed Matter · Physics 2015-06-16 Nishant Kumar , Stefan Luding , Vanessa Magnanimo

The modeling of the elastic properties of disordered or nanoscale solids 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…

Materials Science · Physics 2007-05-23 I. Goldhirsch , C. Goldenberg

This work studies scattering-induced elastic wave attenuation and phase velocity variation in 3D untextured cubic polycrystals with statistically equiaxed grains using the theoretical second-order approximation (SOA) and Born approximation…

Classical Physics · Physics 2022-02-17 Ming Huang , Peter Huthwaite , Stanislav I. Rokhlin , Michael J. S. Lowe