By J. C. F. Telles M.Sc., Ph.D. (auth.)
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Additional info for The Boundary Element Method Applied to Inelastic Problems
Sample text
3) is valid in the interior of the body. 5). o where n. 4) stands for the direction cosines of the outward normal to the boundary of the body. 5) 44 . o .. J o'a.. ,R. n i = + G(~ . +~ . ,] J ,1. 8) is an extended form of the Navier equation presented in eqn. 9) represents its traction boundary conditions (see eqn. 33 ». The above expressions can alternatively . R. + _v_u l-2v h. J.. 11) where bj and Pi are pseudobody forces and pseudotractions given by h. - ~~ .. b. J J and p. 1. p. + 2G(~a n + _v_ 1.
And that the rate. 21) becomes 1. 27) = constant. 28) t ) C depends on the initial conditions. 5). 0= y~ y { 1 - ~p t [ 1- E; l] [ j. 30) Alternatively, one can assume that initially an instantaneous e: = t (f 1) + constant rate. tatlc curve £ Fig. 5 Uniaxial stress-strain curve for (t =0 + £ = Y/E) . £ constant a -------------(£)3 / - - - - - - - - - - - - ( £)2 1-------------(£)1 y £ =0 (E 13 >(£1 2 >(£) 1 £ Fig. 6 Uniaxial stress-strain curve for [t = 0+ £ = i (~ + 1 ) £ = constant. 6. It is instructive now to point out an important distinction between the inviscid theory of plasticity and the viscoplastic theory adopted here.
7 Typical uniaxial creep curve under constant load. 35) is given in [66]. primary creep predominates. 37) are temperature dependent material parameters. 41 Generalization of the above equations to include time varying stress is a questionable assumption commonly made. strain rate at any time which is of interest. 39) seems to be acceptable for materials which only exhibits secondary creep and has been widely applied in many practical problems. Note that this equation together with the elastic strain rate (a/E) can be simulated by the nonlinear Maxwell model mentioned before.