Lifetime-Oriented Structural Design Concepts- P11: At the beginning of 1996, the Cooperative Research Center SFB 398 financially supported by the German Science Foundation (DFG) was started at Ruhr-University Bochum (RUB). A scientists group representing the fields of structural engineering, structural mechanics, soil mechanics, material science, and numerical mathematics introduced a research program on “lifetimeoriented design concepts on the basis of damage and deterioration aspects”. | 258 3 Deterioration of Materials and Structures 386 within the mean part of the yield condition is a scaling factor that leads to total material softening for f qA 1. Nonlinear isotropic hardening is considered by the following relation q JpJe pw 3 HiSo a I 3 ffy y0 1 exp so where a Y K Nb 1 f Qa q describes the evolution of the scalar isotropic hardening parameter a and the determinants Je and Jp transform from CAUCHy- to KlRCHHOFF-stresses. Cyclic loading is accounted for by an advanced kinematic hardening model 87 using a superposition of at most four kinematic hardening tensors K JpJe 1 f qA 24 1 Ki with the following assumption for the material time derivative of the back stress tensor Ll . . Ll CiDp - bi ç ôkin Y Ki 1 - Skin Ki N Dp k where 1 for 1 2 3 or 1 K for 4 Dp yF g Y N is the i- symmetric plastic strain rate Dp G 1DpG 1 N describes the symmetric gradient of the yield surface K 3 2tr KKb is the norm of the back stress tensor K and k GKG k 6kin are model parameters and 3 controls the decomposition of isotropic and kinematic hardening. The evolution of the void volume fraction f is described by f f growth fnucl qC 1 f tr DPG 1 fnucl which is related to f in according to . Note that an additional material coefficient qC is introduced in which is necessary to calibrate the Gurson model according to the results from unit cell analyses 387 . fnucl in represents a nucleation law according to 197 with fnucl fn sn TH exp ep sn 2 ep 1 2 n where fn sn and en are model parameters and ep is given by . . z A . . A v 3 2 ITG-1 2 I To describe the physical process of void nucleation adequately the evolution of ép is only defined for loading. In case of unloading no nucleation of micropores is considered. For the consideration of the coalescence of the micropores the phenomenological law according to 797 is used f for f fc fc K f fc for f fc with K f fc and f ff Jc qA Modelling 259 Fig. . Numerical and .
