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Linear viscoelasticity with couple-stresses
In the paper the llinear isothermal quasi-static theory of homogeneous and isotropic viscoelastic bodies with couple-stresses is established. The general representations of the linear hereditary laws both in an integral and differential form are given. Uniqueness of the mixed boundary-value problems is proved. The generalization of Betti's reciprocal theorem and that of Galerkin and Papkovich stress functions are obtained.
Uniqueness of the solution of the boundary-initial value problem for a linear elastic Cosserat continuum
On the existence and uniqueness of solution and some variational principles in linear theories of elasticity with couple-stresses. I: Cosserat continuum
A weak (generalized) solution to the boundary-value problems in Cosserat continuum is defined. Its existence, uniqueness and continuous dependence upon the given data is proved for the statical loading of bounded, inhomogeneous and anisotropic bodies. Principles of minimum potential energy, of minimum complementary energy and some generalized variational principles are established.
On the existence and uniqueness of solution and some variational principles in linear theories of elasticity with couple-stresses. II. Mindlin's elasticity with microstructure and the first strain-gradient theory
A weak solution to the boundary-value problems both in the Mindlin's theory of elasticity with microstructure and in the first strain-gradient theory is defined for the statical loading of bounded, inhomogeneous and anisotropic bodies. Its existence, uniqueness and continuous dependence upon the given data is proved and the principles of minimum potential energy and minimum complementary energy are establshed.
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