By Vaz M.Jr., de Souza Neto E.A., Munoz-Rojas P.A. (eds.)
With its dialogue of ideas for modeling advanced fabrics utilizing new numerical strategies, usually these in accordance with the finite aspect process, this monograph covers quite a number subject matters together with computational plasticity, multi-scale formulations, optimization and parameter id, harm mechanics and nonlinear finite components.
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Additional info for Advanced Computational Materials Modeling
It is important to remark that from a numerical implementation point of view, it is more useful to replace the evolution law of the back strain tensor, α, ˙ by the ˙ This may be done evolution law of its associated variable, the backstress tensor, β. 27) Thus, Eq. 1 Lemaitre’s ductile damage model. 1. 2 Principle of Maximum Inelastic Dissipation An alternative manner to obtain the evolution of the internal variables is by generalizing the principle of maximum plastic dissipation . In the present case, we apply such a principle for a constitutive model composed of both plastic and damage mechanisms, which is the case in Lemaitre’s model.
Pioneering work on the formulation of constitutive equations for ductile metals, which include internal deterioration, was carried out by Lemaitre . Using the method of local state and internal variables, Lemaitre has proposed a phenomenological model that includes the strong coupling between elastoplasticity and damage at the constitutive level. The original isotropic model was then further elaborated  and later extended by Lemaitre et al.  to account for the anisotropy of damage as well as for partial closure of microcracks under compressive stresses.
The ﬁrst nonlocal developments can be traced back to the 1960s with the pioneering works of Rogula  and Eringen . These authors were the ﬁrst ones trying to incorporate the inﬂuence of the microstructure into traditional (local) continuum theory by means of a nonlocal formulation. However, they limited their approach to the elastic domain and the ﬁrst nonlocal formulations within an elastoplastic framework only appeared in the beginning of the 1980s [13–15]. After these works, signiﬁcant developments have been made by several authors who addressed theoretical and computational issues on both integral-type and gradient-dependent nonlocal enrichments [16–25].