Analytical and numerical solutions for static and dynamic problems of the asymmetric theory of elasticity

The paper offers a number of new analytical solutions of static and dynamic wave problems for a linear elastic Cosserat continuum. We compare them to corresponding analytical solutions within the classical theory of elasticity and illustrate the manifestations of couple-stress effects using model materials. Concurrently with the derivation of the analytical solutions, the finite-element method is used to develop numerical solution algorithms for problems of the asymmetric theory of elasticity on static deformation. The algorithms give rise to nu-merical results that significantly expand the considered class of analytical solutions. The obtained results provide the basis for the performance of physical experiments that investigate the moment behavior of materials under elastic deformation.