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TECHNICAL PAPERS

Elastic Fields due to Eigenstrains in a Half-Space

[+] Author and Article Information
Shuangbiao Liu1

Department of Mechanical Engineering,  Northwestern University, Evanston, IL 60208

Qian Wang

Department of Mechanical Engineering,  Northwestern University, Evanston, IL 60208

1

Currently at Caterpillar Inc., Technical Center E∕854, P. O. Box 1875, Peoria, IL 61656. e-mail: Liu̱Jordan@cat.com.

J. Appl. Mech 72(6), 871-878 (Mar 24, 2005) (8 pages) doi:10.1115/1.2047598 History: Received May 23, 2003; Revised March 24, 2005

Engineering components inevitably encounter various eigenstrains, such as thermal expansion strains, residual strains, and plastic strains. In this paper, a set of formulas for the analytical solutions to cases of uniform eigenstrains in a cuboidal region-influence coefficients, is presented in terms of derivatives of four key integrals. The linear elastic field caused by arbitrarily distributed eigenstrains in a half-space is thus evaluated by the discrete correlation and fast Fourier transform algorithm, along with the discrete convolution and fast Fourier transform algorithm. By taking advantage of both the convolution and correlation characteristics of the problem, the formulas of influence coefficients and the numerical algorithms are expected to enable efficient and accurate numerical analyses for problems having nonuniform distribution of eigenstrains and for contact problems.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

A half-space subject to eigenstrains, eij, inside a domain Ω. x′ and x are source points and observation points, respectively

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Figure 2

Target domain, elements, grid points, and labels

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Figure 3

Variation of stresses (σ11,σ22=σ33) in an infinite space along the x1 axis due to a specified strain, e11, uniformly distributed over an origin-centered cuboid for three different a∕b values

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Figure 4

Variation of u3 at the origin of a half-space with the depth of the cubic center for three different strains

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Figure 5

Stresses (σ11, σ22, and σ33) at three different locations (o, A, and B) in a half-space due to a specified strain, e22, inside a cuboid vs the depth of the cubic center

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Figure 6

Stress (σ11=σ22 and σ33) of a half-space at three different locations (o, C, and B) due to a specified strain, e33, inside a cuboid vs the depth of the cubic center

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Figure 7

Stress σ33 of a half-space along the x3 axis due to a uniform thermoelastic strain inside a sphere (radius a) for two different depths of the center (a or 1.5a)

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Figure 8

Distribution of stress σ33 over the center section with x2=0 due to a thermoelastic strain

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Figure 9

Variation of stress σ33 of a half-space along the x3 axis due to a thermoelastic strain

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Figure 10

Distribution of stress σ33 over the center section with x2=0 due to a thermoelastic strain. (a) Z0=a; (b) Z0=1.5a

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