Journal ArticleDOI
Mean field variations in a statistical sample of heterogeneous linearly elastic solids
M.J. Beran,J.J. McCoy +1 more
TLDR
In this paper, the problem of determining the mean (i.e., statistical average) field quantities in a statistical sample of heterogeneous linearly elastic solids is discussed, and a formulation is obtained that determines {ui(x)}, where ui denotes the displacement field and the braces indicate an ensemble average.About:
This article is published in International Journal of Solids and Structures.The article was published on 1970-08-01. It has received 123 citations till now. The article focuses on the topics: Isotropy & Displacement field.read more
Citations
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Journal ArticleDOI
Analysis of Composite Materials—A Survey
TL;DR: In this paper, the authors review the analysis of composite materials from the applied mechanics and engineering science point of view, including elasticity, thermal expansion, moisture swelling, viscoelasticity, conductivity, static strength, and fatigue failure.
Book ChapterDOI
Variational and Related Methods for the Overall Properties of Composites
TL;DR: In this paper, the authors focus on variational and related methods for the overall properties of composites, such as fiber-reinforced composites or polycrystals, whose properties vary in a complicated fashion from point to point over a small, microscopic length scale, while they appear on average to be uniform.
Journal ArticleDOI
The Elastic Properties of Composite Materials
TL;DR: In this paper, the problem of determining the elastic properties of composite materials (polycrystals, polycrystals and porous or cracked solids) is approached in several ways, via scattering theory, through variational principles, or by the assumption of specific geometries for the material under consideration.
Journal ArticleDOI
Continuum Theory for Strain‐Softening
TL;DR: In this article, it is shown that failure occurs by progressive distributed damage during which the material exhibits strain-softening, i.e., a gradual decline of stress at increasing strain.
References
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Book
The theory of homogeneous turbulence
TL;DR: In this article, the kinematics of the field of homogeneous turbulence and the universal equilibrium theory of decay of the energy-containing eddies are discussed. But the authors focus on the dynamics of decay and not on the probability distribution of u(x).
Journal ArticleDOI
Elastic materials with couple-stresses
TL;DR: HAL as discussed by the authors is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not, which may come from teaching and research institutions in France or abroad, or from public or private research centers.
Journal ArticleDOI
Second gradient of strain and surface-tension in linear elasticity
TL;DR: In this article, a linear theory of deformation of an elastic solid was formulated, in which the potential energy-density is a function of the strain and its first and second gradients.
Journal ArticleDOI
On first strain-gradient theories in linear elasticity
Raymond D. Mindlin,N.N. Eshel +1 more
TL;DR: In this paper, a study of the linear theory of elasticity in which the potential energy-density depends on the gradient of the strain in addition to the strain was performed, and the relations connecting the stresses in the three forms and the boundary conditions in three forms were derived.
Journal ArticleDOI
Force at a Point in the Interior of a Semi-Infinite Solid
TL;DR: In this paper, a solution of the three-dimensional elasticity equations for a homogeneous isotropic solid is given for the case of a concentrated force acting in the interior of a semi-infinite solid.
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