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By E. Stein

Five major issues of computational plasticity are handled via specialists within the box with most up-to-date study effects, similar to constant linearizations and finite point concepts, the numerical research for strong volume-preserving time-integration on the plastic movement rule, the research and finite-element computation of shearband localizations and likewise of shake down load-factors for arbitrary non-linear kinematic hardening fabrics. the purpose used to be primarely an built-in illustration of the mathematical types, the research of numerical equipment and the latest algorithms for the constant and reliable computation of huge dimensional platforms. the importance might be visible within the choice of textbook-like remedies of significant new effects from popular scientists.

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We say that a set of the internal state variables (-y(cr),g(cr)), of course together with the evolution equations and the initial values for -y(cr) and g(cr), describes the prior history of inelastic deformation of the crystal. nd let consider purely elastic deformation temperature process. e. keeping 33 Constitutive Equations for Thennoplasticity the internal state variables -y(a) and g(a) constant. 21 h with the Lie derivative. 26) ab el (l;;-r) =Tab- Tac(d:lc + w:lc)gdb- Tcd(d:lc + wdc)gad. 28) Diference between these two rates is el ab (l;;-r) - (Lv-rtb = Tac(~c + W~c)gdb + Tcb(~c + w~c)gad.

P, r) ~A. 13) with cp, cp1 E Ad(JR+, llf). A solution cp E ~ ( JR+, \If) is unstable if and only if there exist Theorem 1. (JR+, llf) at cp for some~ = rc E T (cf. (IR+, llf) {cf. (t),cpl_,(t)). e. 17) (it means that temperature -a =-a# and strain e = e# are constant in B). 18) of the thermodynamic plastic flow process. For some r = Tc E T the solution cp is not unique. ( rc)} on the trajectory we can expect more than one solution {cf. 10). So we have at {rc, cp( rc)} branching of the solution.

21) gives pt9~ = -divq + pt9i. 31). P. 34) denotes the specific heat. ycr represents the internal heating generated by the rate of internal dissippation. This term describes the main contribution to the thermo-mechanical coupling phenomena. y

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