Non‐stationary plane problem of the successive origination of stress concentrators in a loaded body. Finite deformations and their superposition

Abstract

SUMMARYThe first (for the given class of problems) results of solving non-stationary plane problems of nonsimultaneous origination of holes and inclusions in a preliminary loaded solid with initial finite strains are presented and discussed. It is taken into account that the origination of a hole or an inclusion produces additional finite deformations (at least, at the vicinity of the hole) superimposed 'physically' on the finite initial ones. The problem is solved using the theory of repeated superposition of large deformations. It is supposed that the shape of stress concentrators is given at the moment of their origination.Calculations were made with the use of the specialized computer package 'Superposition' based on finite-element method. Stress fields are presented at different times. The change of maximal stresses in time is also presented. Copyright q 2008 John Wiley & Sons, Ltd. The first (for the given class of problems) results of solving non-stationary plane problems of non-simultaneous origination of holes and inclusions in a preliminary loaded solid with initial finite strains are presented and discussed.The solid's material is described by the Murnaghan potential. It is taken into account that the origination of holes and inclusions produces additional finite deformations (at least, at the vicinity of the hole) superimposed 'physically' on the finite initial ones.The problem is solved using the theory of repeated superposition of large deformations developed by Levin [1]. The given theory allows one to formulate and to solve problems for the case of finite strains when boundaries and boundary conditions are changed repeatedly. Moreover, this theory allows one to take into account the change of connectedness of a solid's domain and also the change of material properties of a part of the solid under loading.

Software for estimation of second order effective material properties of porous samples with geometrical and physical nonlinearity accounted for

“…A uniqueness of CAE Fidesys package is related to a possibility of solving problems in which new boundary surfaces (cavities) are originated under loading or material properties are changed in some part of the solid that leads to the redistribution of finite strains in the computational domain [7,12]. The package allows direct modeling of the redistribution of finite strains.…”

Numerical Analysis of Propagation of Nonlinear Waves in Prestressed Solids

“…The theory of repeated superposition of large strains is used for the problem solution (Levin, 1998;Levin & Vershinin, 2008;Levin et al, 2013). Let us consider the basic equations, initial conditions, and boundary conditions of this theory.…”

“…It's taken into account that waves propagation leads to new strains which superimpose on existing strains (induced anisotropy) in the media. The details of numerical algorithms implemented in CAE FIDESYS for the analysis of the propagation of nonlinear waves in elastic and viscoelastic bodies are discussed (Levin & Vershinin, 2008;Levin, Zingerman, Vershinin, Freiman, & Yangirova, 2013). The implementation of the spectral element method for the nonlinear dynamic problems of elasticity under finite strains is considered.…”

Numerical modeling of carbon‐based material systems and related topics

“…Tsotsova [5] proposes a variational approach to the identification of cracks in linear elastic materials based on measurements performed on the surface of the solid (inverse crack identification problem). The approach is illustrated by a sample finite element simulation; good convergence of the proposed iterative procedure is shown.Finally, contributions [6,7] propose novel computational techniques to model non-simultaneous origination of holes and inclusions in a preliminary loaded material undergoing large strains. Both papers employ the theory of repeated superposition of large deformations developed by Levin.…”

“…Finally, contributions [6,7] propose novel computational techniques to model non-simultaneous origination of holes and inclusions in a preliminary loaded material undergoing large strains. Both papers employ the theory of repeated superposition of large deformations developed by Levin.…”