## 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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