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A transformation strain changes the shape and size of the inclusion. In continuum mechanics, Eshelby's inclusion problem refers to a set of problems involving ellipsoidal elastic inclusions in an infinite elastic body. Analytical solutions to these problems were first devised by John D. Eshelby in 1957. [1] [2]
The problem of compatibility in continuum mechanics involves the determination of allowable single-valued continuous fields on simply connected bodies. More precisely, the problem may be stated in the following manner. [5] Figure 1. Motion of a continuum body. Consider the deformation of a body shown in Figure 1.
The J-integral represents a way to calculate the strain energy release rate, or work per unit fracture surface area, in a material. [1] The theoretical concept of J-integral was developed in 1967 by G. P. Cherepanov [2] and independently in 1968 by James R. Rice, [3] who showed that an energetic contour path integral (called J) was independent of the path around a crack.
Eigenstrain analysis usually relies on the assumption of linear elasticity, such that different contributions to the total strain are additive. In this case, the total strain of a material is divided into the elastic strain e and the inelastic eigenstrain :
When applied to plane stress and plane strain problems, this means that the approximate solution obtained for the stress and strain fields are constant throughout the element's domain. The element provides an approximation for the exact solution of a partial differential equation which is parametrized barycentric coordinate system (mathematics)
The half-space approach is an elegant solution strategy for so-called "smooth-edged" or "concentrated" contact problems. If a massive elastic body is loaded on a small section of its surface, then the elastic stresses attenuate proportional to 1 / d i s t a n c e 2 {\displaystyle 1/distance^{2}} and the elastic displacements by 1 / d i s t a n ...
In continuum mechanics, the infinitesimal strain theory is a mathematical approach to the description of the deformation of a solid body in which the displacements of the material particles are assumed to be much smaller (indeed, infinitesimally smaller) than any relevant dimension of the body; so that its geometry and the constitutive properties of the material (such as density and stiffness ...
In mechanics, strain is defined as relative deformation, compared to a reference position configuration. Different equivalent choices may be made for the expression of a strain field depending on whether it is defined with respect to the initial or the final configuration of the body and on whether the metric tensor or its dual is considered.
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