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The three-dimensional axisymmetric Boussinesq problem of an isotropic half-space subjected to a concentrated normal quasi-static load is studied within the framework of linear dipolar gradient elasticity. Our main concern is to determine…

Mathematical Physics · Physics 2015-06-19 H. G. Georgiadis , P. A. Gourgiotis , D. S. Anagnostou

We investigate the finite bending and the associated bending instability of an incompressible dielectric slab subject to a combination of applied voltage and axial compression, using nonlinear electro-elasticity theory and its incremental…

Soft Condensed Matter · Physics 2018-10-04 Yipin Su , Bin Wu , Weiqiu Chen , Michel Destrade

Intrinsic nonlinear elasticity deals with the deformations of elastic bodies as isometric immersions of Riemannian manifolds into the Euclidean spaces (see Ciarlet [9,10]). In this paper, we study the rigidity and continuity properties of…

Analysis of PDEs · Mathematics 2026-02-24 Gui-Qiang G. Chen , Siran Li , Marshall Slemrod

Recent equations of motion for the large deflections of a cantilevered elastic beam are analyzed. In the traditional theory of beam (and plate) large deflections, nonlinear restoring forces are due to the effect of stretching on bending;…

Analysis of PDEs · Mathematics 2021-04-06 Maria Deliyianni , Justin T. Webster

This paper presents a comprehensive computational framework for investigating thermo-elastic fracture in transversely isotropic materials, where classical linear elasticity fails to predict physically realistic behavior near stress…

Numerical Analysis · Mathematics 2025-10-08 Saugata Ghosh , Dambaru Bhatta , S. M. Mallikarjunaiah

To draw conclusions as regards the stability and modelling limits of the investigated continuum, we consider a family of infinitesimal isotropic generalized continuum models (Mindlin-Eringen micromorphic, relaxed micromorphic continuum,…

Classical Physics · Physics 2021-06-11 Gianluca Rizzi , Geralf Hütter , Angela Madeo , Patrizio Neff

We present a field formulation for defects that draws from the classical representation of the cores as force dipoles. We write these dipoles as singular distributions. Exploiting the key insight that the variational setting is the only…

Materials Science · Physics 2016-06-02 Zhenlin Wang , Shiva Rudraraju , Krishna Garikipati

Analytical method for the second-order homogenization of two-phase composites within Mindlin-Toupin strain gradient elasticity theory is proposed. Direct approach and self-consistent approximation are used to reduce the homogenization…

Materials Science · Physics 2021-12-24 Y. O. Solyaev

We investigate a specific finite element model to study the thermoelastic behavior of an elastic body within the context of nonlinear strain-limiting constitutive relation. As a special subclass of implicit relations, the thermoelastic…

Numerical Analysis · Mathematics 2022-03-02 Hyun C. Yoon , Karthik K. Vasudeva , S. M. Mallikarjunaiah

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

Budiansky's nonlinear shell theory is particularized to a 2D setting, and thereupon generalized to a fully nonlinear, statically and kinematically exact, theory of strain-gradient elasticity of beams. The governing equations are displayed…

Classical Physics · Physics 2022-09-27 Marcelo Epstein , Mohammadjavad Javad

The atomic theory of elasticity of amorphous solids, based on the nonaffine response formalism, is extended into the nonlinear stress-strain regime by coupling with the underlying irreversible many-body dynamics. The latter is implemented…

Soft Condensed Matter · Physics 2014-11-03 A. Zaccone , P. Schall , E. M. Terentjev

Compressible Mooney-Rivlin theory has been used to model hyperelastic solids, such as rubber and porous polymers, and more recently for the modeling of soft tissues for biomedical tissues, undergoing large elastic deformations. We propose a…

Numerical Analysis · Mathematics 2025-10-20 Suzanne M. Shontz , Stephen A. Vavasis

In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…

Analysis of PDEs · Mathematics 2019-09-04 Fabian Christowiak , Carolin Kreisbeck

Crack-tip fields within a transversely isotropic strain-limiting elastic body are investigated under the influence of piecewise linear slope boundary loads. The mechanical response is characterized via a nonlinear constitutive framework…

General Mathematics · Mathematics 2026-04-30 S. M. Mallikarjunaiah , Saugata Ghosh , Dambaru Bhatta

Recent works have shown that in contrast to classical linear elastic fracture mechanics, endowing crack fronts in a brittle Green-elastic solid with Steigmann-Ogden surface elasticity yields a model that predicts bounded stresses and…

Mathematical Physics · Physics 2024-06-11 Casey Rodriguez

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

We introduce and study a new inverse problem for antiplane shear in elastic bodies with strain-gradient interfaces. The setting is a homogeneous isotropic elastic body containing an inclusion separated by a thin interface endowed with…

Analysis of PDEs · Mathematics 2025-09-19 Govanni Granados , Jeremy L. Marzuola , Casey Rodriguez

We present, to the best of our knowledge, the first complete three-dimensional numerical solutions to a broad range of boundary value problems for a general theory of finite strain gradient elasticity. We have chosen for our work, Toupin's…

Mathematical Physics · Physics 2015-08-24 Shiva Rudraraju , Anton van der Ven , Krishna Garikipati

In this note we investigate the asymptotic behavior of plane shear thickening fluids around a bounded obstacle. Different from the Navier-Stokes case considered by Gilbarg-Weinberger in \cite{GW1978}, where the good structure of the…

Analysis of PDEs · Mathematics 2020-07-15 Shuai Li , Tao Wang , Wendong Wang
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