On the correspondence principle in the plane creep problem of ageing homogeneous media with developing slits and cavities

Назаров, С. А.; Trapeznikov, L. P.; Shoikhet, B. A.

doi:10.1016/0021-8928(87)90119-5

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“…However, at the final stage, explicitly or implicitly, the main role is played by the correspondence principle (cf. [32,35] 2)-(1.4) with the matrices defined by (1.14), the Poisson ratio can be interpreted as the composition of Volterra integral operators, 15) which allows, in principle, to express the singular solution of the creep problem by means of the singular solutions to the elasticity system. However, it leads also to some difficulties connected with the fact that the operators defined by (1.15) do not commute.…”

Section: Main Results and Structure Of The Papermentioning

confidence: 99%

Analysis of crack singularities in an aging elastic material

Costabel¹,

Dauge²,

Назаров³

et al. 2006

ESAIM: M2AN

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Abstract. We consider a quasistatic system involving a Volterra kernel modelling an hereditarilyelastic aging body. We are concerned with the behavior of displacement and stress fields in the neighborhood of cracks. In this paper, we investigate the case of a straight crack in a two-dimensional domain with a possibly anisotropic material law. We study the asymptotics of the time dependent solution near the crack tips. We prove that, depending on the regularity of the material law and the Volterra kernel, these asymptotics contain singular functions which are simple homogeneous functions of degree 1 2 or have a more complicated dependence on the distance variable r to the crack tips. In the latter situation, we observe a novel behavior of the singular functions, incompatible with the usual fracture criteria, involving super polynomial functions of ln r growing in time.Mathematics Subject Classification. 35Q72, 74D05, 74G70.

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Section: Main Results and Structure Of The Papermentioning

confidence: 99%