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We analyze the asymptotic behavior of a junction problem between a plate and a perpendicular rod made of a nonlinear elastic material. The two parts of this multi-structure have small thicknesses of the same order $\delta$. We use the…

Numerical Analysis · Mathematics 2012-10-23 Dominique Blanchard , Georges Griso

The so-called indentation stiffness tomography technique for detecting the interior mechanical properties of an elastic sample with an inhomogeneity is analyzed in the framework of the asymptotic modeling approach under the assumption of…

Analysis of PDEs · Mathematics 2013-11-22 Ivan Argatov

The Johnson--Kendall--Roberts model of frictionless adhesive contact is extended to the case of a thin transversely isotropic elastic layer bonded to a rigid base. The leading-order asymptotic models are obtained for both compressible and…

Analysis of PDEs · Mathematics 2015-12-10 I. I. Argatov , G. S. Mishuris , V. L. Popov

Using rigorous constitutive linearization of second variation introduced in [6] we study weak stability of homogeneous deformation of the axially compressed circular cylindrical shell, regarded as a 3-dimensional hyperelastic body. We show…

Analysis of PDEs · Mathematics 2013-01-28 Yury Grabovsky , Davit Harutyunyan

The aim of this work is to study the asymptotic behavior of a structure made of plates of thickness $2\delta$ when $\delta\to 0$. This study is carried on within the frame of linear elasticity by using the unfolding method. It is based on…

Numerical Analysis · Mathematics 2011-09-12 Georges Griso

We consider the problem of satisfaction of boundary conditions when the generalized stress vector is given on the surfaces for elastic plates and shells. This problem was open also both for refined theories in the wide sense and…

Mathematical Physics · Physics 2020-06-12 Tamaz S. Vashakmadze

We rigorously derive a Kirchhoff plate theory, via $\Gamma$-convergence, from a three-di\-men\-sio\-nal model that describes the finite elasticity of an elastically heterogeneous, thin sheet. The heterogeneity in the elastic properties of…

Analysis of PDEs · Mathematics 2018-07-17 Virginia Agostiniani , Alessandro Lucantonio , Danka Lučić

A quasistatic unilateral frictionless contact problem for a rigid axisymmetric indenter pressed into a homogeneous, linearly elastic and transversely isotropic elastic layer bonded to a homogeneous, linearly elastic and transversely…

Analysis of PDEs · Mathematics 2012-07-09 I. I. Argatov , F. J. Sabina

We study equilibrium configurations of non-Euclidean plates, in which the reference metric is uniaxially periodic. This work is motivated by recent experiments on thin sheets of composite thermally responsive gels [1]. Such sheets bend…

Pattern Formation and Solitons · Physics 2015-06-12 Michael Moshe , Eran Sharon , Raz Kupferman

We derive asymptotic expansions for the displacement at the boundary of a smooth, elastic body in the presence of small inhomogeneities. Both the body and the inclusions are allowed to be anisotropic. This work extends prior work of…

Analysis of PDEs · Mathematics 2011-05-23 Elena Beretta , Eric Bonnetier , Elisa Francini , And Anna L Mazzucato

We investigate the effective elastic properties of periodic dilute two-phase composites consisting of an homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply…

Analysis of PDEs · Mathematics 2024-03-26 Daehee Cho , Doosung Choi , Mikyoung Lim

We propose bending energies for isotropic elastic plates and shells. For a plate, we define and employ a surface tensor that symmetrically couples stretch and curvature such that any elastic energy density constructed from its invariants is…

Soft Condensed Matter · Physics 2022-06-22 E. Vitral , J. A. Hanna

We derive asymptotic formulas for the solutions of the mixed boundary value problem for the Poisson equation on the union of a thin cylindrical plate and several thin cylindrical rods. One of the ends of each rod is set into a hole in the…

Analysis of PDEs · Mathematics 2019-02-20 R. Bunoiu , G. Cardone , S. A. Nazarov

An asymptotically exact two-dimensional theory of elastic-piezoceramic sandwich shells is derived by the variational-asymptotic method. The error estimation of the constructed theory is given in the energetic norm. As an application,…

Classical Physics · Physics 2016-06-08 Khanh Chau Le , Jeong-Hun Yi

In this paper we consider the inverse problem of determining, within an elastic isotropic thick plate modelled by the Reissner-Mindlin theory, the possible presence of an inclusion made of a different elastic material. Under some a priori…

Analysis of PDEs · Mathematics 2018-01-17 Antonino Morassi , Edi Rosset , Sergio Vessella

In this third and final paper of a series, elastic properties of numerically simulated isotropic packings of spherical beads assembled by different procedures and subjected to a varying confining pressure P are investigated. In addition P,…

Disordered Systems and Neural Networks · Physics 2016-09-08 Ivana Agnolin , Jean-Noël Roux

A model for a MEMS device, consisting of a fixed bottom plate and an elastic plate, is studied. It was derived in a previous work as a reinforced limit when the thickness of the insulating layer covering the bottom plate tends to zero. This…

Analysis of PDEs · Mathematics 2020-04-01 Philippe Laurençot , Katerina Nik , Christoph Walker

A rectangular plate of dielectric elastomer exhibiting gradients of material properties through its thickness will deform inhomogeneously when a potential difference is applied to compliant electrodes on its major surfaces, because each…

Soft Condensed Matter · Physics 2020-12-08 Yipin Su , Ray W. Ogden , Michel Destrade

We rigorously derive a Blake-Zisserman-Kirchhoff theory for thin plates with material voids, starting from a three-dimensional model with elastic bulk and interfacial energy featuring a Willmore-type curvature penalization. The effective…

Analysis of PDEs · Mathematics 2025-04-09 Manuel Friedrich , Leonard Kreutz , Konstantinos Zemas

Shell structures are generally modeled based on kinematic hypotheses, where some of the parameters are preferentially evaluated in a phenomenological manner. In this article, asymptotic analysis against the underlying three-dimensional…

Materials Science · Physics 2025-07-02 Xiwei Pan , Yichao Zhu