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  1. Zeitschrift für angewandte Mathematik und Physik
  2. Zeitschrift für angewandte Mathematik und Physik : Volume 66
  3. Zeitschrift für angewandte Mathematik und Physik : Volume 66, Issue 5, October 2015
  4. A nanosized circular inhomogeneity in finite plane elastostatics
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Zeitschrift für angewandte Mathematik und Physik : Volume 67
Zeitschrift für angewandte Mathematik und Physik : Volume 66
Zeitschrift für angewandte Mathematik und Physik : Volume 66, Issue 6, December 2015
Zeitschrift für angewandte Mathematik und Physik : Volume 66, Issue 5, October 2015
Periodic solutions to nonlinear wave equations with spatially dependent coefficients
Bifurcations for a coupled Schrödinger system with multiple components
Nonlinear Schrödinger operators with zero in the spectrum
The selection for dispersal: a diffusive competition model with a free boundary
Static semicoercive normal compliance contact problem with limited interpenetration
Spectrum of a diffusion operator with coefficient changing sign over a small inclusion
Existence and large time behavior for a stochastic model of modified magnetohydrodynamic equations
Hamiltonian elliptic systems involving nonlinear Schrödinger equations with critical growth
Extending the zero-derivative principle for slow–fast dynamical systems
Asymptotic limits of Navier–Stokes equations with quantum effects
Vanishing capillarity–viscosity limit for the incompressible inhomogeneous fluid models of Korteweg type
The Cauchy problem for compressible Navier–Stokes equations with shear viscosity and large data
Factorization technique for the fourth-order nonlinear Schrödinger equation
Nonlinear perturbations of a periodic Schrödinger equation with supercritical growth
On the well-posedness for a multi-dimensional compressible viscous liquid–gas two-phase flow model in critical spaces
A sharp upper bound for the first Dirichlet eigenvalue of a class of wedge-like domains
Existence of multiple positive solutions for Schrödinger–Poisson systems with critical growth
Boundedness in a quasilinear fully parabolic Keller–Segel system with logistic source
On uniqueness and stability of Sobolev’s solution in scattering by wedges
Decay of the compressible magnetohydrodynamic equations
Blow-up analysis for a semilinear parabolic equation with time-dependent coefficients under nonlinear boundary flux
N-soliton solutions and asymptotic analysis for a Kadomtsev–Petviashvili–Schrödinger system for water waves
Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis–fluid system
Approximate solutions to the initial value problem for some compressible flows
Multiple sign-changing radially symmetric solutions in a general class of quasilinear elliptic equations
Stationary flow of non-Newtonian fluid with nonmonotone frictional boundary conditions
Resonant radial oscillations of an inhomogeneous gas in the frustum of a cone
Characterization of rotatory hydrodynamic triply diffusive convection
Trapping of surface gravity waves by a vertical flexible porous plate near a wall
The effect of Thompson and Troian’s nonlinear slip condition on Couette flows between concentric rotating cylinders
Near-tip field for diffraction on square lattice by rigid constraint
Small amplitude waves in a pre-stressed compressible elastic layer with one fixed and one free face
One-dimensional quasistatic model of biodegradable elastic curved rods
Weak solvability via bipotential method for contact models with nonmonotone boundary conditions
A generalized nonlocal vector calculus
Influence of nonlinear effects on the efficiency of a thermoelectric generator
On the equivalence of local and global area-constraint formulations for lipid bilayer vesicles
Second-gradient continua as homogenized limit of pantographic microstructured plates: a rigorous proof
A nanosized circular inhomogeneity in finite plane elastostatics
Improved variational bounds for conductive periodic composites with 3D microstructures and nonuniform thermal resistance
A mixed problem of plane elasticity theory for a multiply connected domain with partially unknown boundary: the case of a rhombus
Stability of linear systems in second-order form based on structure preserving similarity transformations
Existence, uniqueness and construction of the solution of the energy transfer problem in a rigid and non-convex blackbody with temperature-dependent thermal conductivity
Blow-up phenomena for compressible Euler equations with non-vacuum initial data
Zeitschrift für angewandte Mathematik und Physik : Volume 66, Issue 4, August 2015
Zeitschrift für angewandte Mathematik und Physik : Volume 66, Issue 3, June 2015
Zeitschrift für angewandte Mathematik und Physik : Volume 66, Issue 2, April 2015
Zeitschrift für angewandte Mathematik und Physik : Volume 66, Issue 1, February 2015
Zeitschrift für angewandte Mathematik und Physik : Volume 65
Zeitschrift für angewandte Mathematik und Physik : Volume 64
Zeitschrift für angewandte Mathematik und Physik : Volume 63
Zeitschrift für angewandte Mathematik und Physik : Volume 62
Zeitschrift für angewandte Mathematik und Physik : Volume 61
Zeitschrift für angewandte Mathematik und Physik : Volume 60
Zeitschrift für angewandte Mathematik und Physik : Volume 59
Zeitschrift für angewandte Mathematik und Physik : Volume 58
Zeitschrift für angewandte Mathematik und Physik : Volume 57
Zeitschrift für angewandte Mathematik und Physik : Volume 56
Zeitschrift für angewandte Mathematik und Physik : Volume 55
Zeitschrift für angewandte Mathematik und Physik : Volume 54
Zeitschrift für angewandte Mathematik und Physik : Volume 53
Zeitschrift für angewandte Mathematik und Physik : Volume 52
Zeitschrift für angewandte Mathematik und Physik : Volume 51
Zeitschrift für angewandte Mathematik und Physik : Volume 50
Zeitschrift für angewandte Mathematik und Physik : Volume 49
Zeitschrift für angewandte Mathematik und Physik : Volume 48

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A nanosized circular inhomogeneity in finite plane elastostatics

Content Provider SpringerLink
Author Wang, Xu Schiavone, Peter
Copyright Year 2015
Abstract We consider the deformation of a nanocomposite by incorporating the effect of surface elasticity on the finite plane deformations of a circular inhomogeneity embedded in a particular class of compressible hyperelastic materials of harmonic type subjected to uniform remote Piola stresses. We incorporate the surface mechanics by using a version of the continuum-based surface/interface model of Gurtin and Murdoch. A complete solution is derived by reducing the original boundary value problem to two coupled first-order differential equations which can be solved analytically. The solution clearly demonstrates that the stress fields in the composite are size dependent and that the stress field inside a circular inhomogeneity is, in general, non-uniform. Two special cases which admit an internal uniform, yet size-dependent stress field, are discussed.
Ending Page 2879
Page Count 9
Starting Page 2871
File Format PDF
ISSN 00442275
e-ISSN 14209039
Journal Zeitschrift für angewandte Mathematik und Physik
Issue Number 5
Volume Number 66
Language English
Publisher Springer Basel
Publisher Date 2015-04-16
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Micromechanics PDEs in connection with mechanics of deformable solids Mathematical Methods in Physics Harmonic material Finite deformation Analytic continuation Size-dependent elastic field Inhomogeneity Surface elasticity Nonlinear elasticity Theoretical and Applied Mechanics Differential equations on complex manifolds
Content Type Text
Resource Type Article
Subject Applied Mathematics Physics and Astronomy
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