Numerical Calculations Models for Physical-Mechanical Systems

Some problems on the formation of concentrators in nonlinear viscoelastic material under finite deformations and their superposition and solution methods

V. A. Levin^a, K. M. Zingerman^b, G. E. Pekar<sup>a

a</sup> Lomonosov Moscow State University
^b Tver State University, Tver

Abstract: Quasistatic and nonstationary problems of successive origination of holes of different shape in 2D bodies made of viscoelastic material are considered. The shape of the holes is supposed to be given at the moment of their origination. Origination of the hole results in distribution of finite strains in the body. The theory of repeated superposition of large strains is used to state the problem. Mechanical properties of the material are described by Adamov's constitutive equations for incompressible viscoelastinc material. The expansion into the Proni's series is used in numerical modeling to integrate the viscoelastic constitutive equations. The program module has been realized and several such problems have been solved based on this approach. Results of the numerical experiment are given below.

Keywords: finite element analysis, theory of elasticity , viscoelasticity, Prony series, Large deformations, superposition of finite strains, incompressible material.

UDC: 539.3,539.4 519.6

Received: 15.03.2012
Revised: 21.05.2012

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