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Plane-strain problems for a class of gradient elasticity models – a stress function approach. (English) Zbl 1308.74024

Summary: The plane strain problem is analyzed in detail for a class of isotropic, compressible, linearly elastic materials with a strain energy density function that depends on both the strain tensor \(\boldsymbol{\varepsilon} \) and its spatial gradient \(\nabla \boldsymbol{\varepsilon} \). The appropriate Airy stress-functions and double-stress-functions are identified and the corresponding boundary value problem is formulated. The problem of an annulus loaded by an internal and an external pressure is solved.

MSC:

74B05 Classical linear elasticity
74A10 Stress
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