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

rbatra's picture

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 making the differential form of the constitutive relation invalid. 

Please see R.C. Batra, Misuse of Eringen’s nonlocal elasticity theory for functionally graded materials, International Journal of Engineering Science 159 (2021) 103425.

 

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