The construction of constitutive relations for isotropic strain-hardening elastoplastic materials of the differential type of complexity <Emphasis Type="Italic">n</Emphasis>. Part 1. Finite strains

Using approaches in rational continuum mechanics, we have developed a mathematical theory of strict construction and specialization of constitutive equations for simple (in Noll’s sense) isotropic strain-hardening elastoplastic materials of the differential type of complexity n (analogs of the Rivlin–Ericksen solids of complexity n) as the most important representatives of the materials with infinitesimal fading path shape memory (a fading path shape memory on an arbitrarily small interval of the “past”). The strains are assumed to be arbitrary. The hierarchy of the constitutive relations is constructed according to the level of complexity of the material response to deformation. Translated from Problemy Prochnosti, No. 2, pp. 27–42, March–April, 2009.     

Study of Postdetonation Waves after the Counter Collision of Detonation Waves in a Bubble Liquid

High Temperature - The counter interaction of detonation waves in a liquid with bubbles of a combustible gas is considered based on numerical simulation. The effect of the initial volumetric gas...     

Phase diagram of the Co–Al–W system. structure and phase transformations near the Co<Subscript>3</Subscript>(Al,W) intermetallic composition range

Low-temperature portion of the polythermal section for the Co–Al–W system in the vicinity of the Co₃(Al, W) intermetallic composition has been studied experimentally using electron microscopy and hightemperature X-ray diffraction analysis. Low-temperature structural phase transformations and temperature ranges of the existence of phases have been determined. The morphology of Co₃(Al, W) intermetallic particles was studied as a function of the tungsten content in alloys.     

Modification of the Wilkins Method to Study the Dynamics of Axisymmetric Thick-Wall Shells with a Spiral Orthotropy

Modification of the Wilkins method has been performed for numerical investigation into dynamics of thick-wall cylindrical shells with a spiral orthotropy. Test calculations are shown to agree well with the known solutions. New physical effects have been found, which are absent from isotropic and cylindrically orthotropic bodies.     

Simulation of fading path shape memory in the theory of simple materials with elastoplastic behavior and initial loading surface

A mathematical theory is proposed rigorous construction and specialization of constitutive relations for simple (in the Noll’s sense) strain-hardening elastoplastic materials with an initial loading surface and a fading path shape memory at the active deformation segment. Strains and symmetry type of the material are taken to be arbitrary. Physical equations are derived for materials with no path shape memory, with a weak fading memory, and with a fading memory of the nth order. Based on the proposed constitutive relations, physical equations are constructed for isotropic materials. In the context of the fading path shape memory, a definition of an elastic-perfectly plastic material is given. Assuming the condition of smallness of measures of strains throughout the entire “past” history, a theory has been developed for rigorous construction and specialization of constitutive relations for materials with a first-order fading path shape memory for infinitesimal strains. Special emphasis is placed on isotropic materials. __________ Translated from Problemy Prochnosti, No. 4, pp. 5–18, July–August, 2007.     

Simulation in fracture of welded structures with developing damages

The main features of durability design of weld structures containinginitial technological defects are considered. Among these features are:(1)~structural analysis of welded structures; (2)~simulation of limit statesand evaluation of reliability of welds and, (3) optimisation and ensuring agiven reliability of structures. The main results of simulation are givenfor: fatigue curves, reliability functions, complete probabilistic lifediagrams, diagrams of defect standardisation and probabilistic durabilitysurfaces.     

Numerical investigation of the dynamic strength of thick-walled cylindrical shells with cracklike technological defects

A numerical method is proposed for the evaluation of the stress intensity factors in elastic thick-walled cylindrical shells with cracks subjected to dynamic loading. The method is based on the two-dimensional axially symmetric Wilkins algorithm and the equations of mechanics of brittle fracture. The strength of thick-walled cylinders loaded by pulses of internal pressure and containing technological defects (similar to mathematical cuts) formed at the sites of fixing of their ends by welding is investigated.Translated from Problemy Prochnosti, No. 1, pp. 76–87, January–February, 2005.