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non-local elasticity theory

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Misuse of Eringen's non-local elasticity theory for functionally graded materials

Nearly 50 years ago, Eringen developed a nonlocal theory of elasic solids according to which the Causchy stress tensor "sigma" at a point x depends upon the strain tensor "epsilon" not only at the point x but also at all other points in the body.  For homogeneous solids, and a few additional assumptions, he showed that the constitutive relation can be reduced to a differential form that has become popular among people studying deformations of functionally graded materials (FGMs).  However, an FGM is inhomogeneous

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