Theory of plasticity, creep and viscoelasticity

A.Nazarov is considered to be the first scientist in this area, who in 1937-39 fulfilled the works dedicated to analysis of load-carrying capacity of statically indeterminate systems. In 1959 the method of reduction of plane contact problem of plasticity theory for material which is strengthened with a power low to first kind Fredholm integral equation was suggested by Nagush Kh.Arutyunyan. The closure solution of this problem was obtained.Since 1956 several classes of solutions of plasticity theory equations, which allow investigating elasticoplastic stressed and limiting state of thick-walled cylindrical and conic bodies has been examined by Mesrop A.Zadoyan. Stressed states of bars made from strengthening materials in the process of combined torsion and bending were investigated. A number of interesting problems of plasticity theory for conic and torus-like bodies, anisotropic thick-walled tubes, as well as cylindrical and conic tubes in external temperature field were considered.

On the basis of C.Maslov's model of elastically creeping body in 1947 the mathematical theory for ageing materials which at the same time taking into account the factors of materials ageing and heredity as well as partial reversibility of creep deformation was suggested by N.Arutunyan. This theory is known as "Maslov-Arutunyan's creep theory". Hereinafter this theory was substantially generalized and developed by N.Arutunyan and was formulated as a creep theory of inhomogeneous heredity ageing bodies. It became the foundation for the theory of increasing deformable body.

On the base of suggested theories of creep a numerous plane and spatial, contact and mixed boundary value problems, important for application, were formulated and solved (N.Arutunyan, M.Manukyan and others). It is shown that the problems of shells creep in the frame of non-linear theory of heredity bring to the equivalent instantaneous problem in regard of displacements identity.

Investigations of mechanical properties of modern machines constructive elements working in high-frequency conditions were fulfilled. For the vibrating and impact processes, when disturbance function is satisfying Dirichlet conditions, shown that in machins elements appearing the phenomenon's of creep and relaxation. The bases of vibro-creep theory were developed (G.Shekyan).

The phenomenon's of creep in steel and aluminum monocrystals in the various programs of temperature variations have been investigated. The investigations of elasticorheology properties of fibrous composites were realized.