By Miguel Vaz Junior, Eduardo A. de Souza Neto, Pablo A. Munoz-Rojas
Chapter 1 fabrics Modeling – demanding situations and views (pages 1–22): Prof. Miguel Vaz, Prof. Eduardo A. de Souza Neto and Prof. Dr. Pablo Andres Munoz?Rojas
Chapter 2 neighborhood and Nonlocal Modeling of Ductile harm (pages 23–72): Jose Manuel de Almeida Cesar de Sa, Francisco Manuel Andrade Pires and Filipe Xavier Costa Andrade
Chapter three fresh Advances within the Prediction of the Thermal houses of steel hole Sphere buildings (pages 73–110): Thomas Fiedler, Irina V. Belova, Graeme E. Murch and Andreas Ochsner
Chapter four Computational Homogenization for Localization and harm (pages 111–164): Thierry J. Massart, Varvara Kouznetsova, Ron H. J. Peerlings and Marc G. D. Geers
Chapter five A combined Optimization process for Parameter identity utilized to the Gurson harm version (pages 165–204): Prof. Dr. Pablo Andres Munoz?Rojas, Luiz Antonio B. da Cunda, Eduardo L. Cardoso, Prof. Miguel Vaz and Guillermo Juan Creus
Chapter 6 Semisolid steel Alloys Constitutive Modeling for the Simulation of Thixoforming tactics (pages 205–256): Roxane Koeune and Jean?Philippe Ponthot
Chapter 7 Modeling of Powder Forming strategies; program of a Three?Invariant Cap Plasticity and an Enriched Arbitrary Lagrangian–Eulerian FE approach (pages 257–299): Amir R. Khoei
Chapter eight Functionally Graded Piezoelectric fabric structures – A Multiphysics point of view (pages 301–339): Wilfredo Montealegre Rubio, Sandro Luis Vatanabe, Glaucio Hermogenes Paulino and Emilio Carlos Nelli Silva
Chapter nine Variational Foundations of enormous pressure Multiscale reliable Constitutive versions: Kinematical formula (pages 341–378): Prof. Eduardo A. de Souza Neto and Raul A. Feijoo
Chapter 10 A Homogenization?Based Prediction approach to Macroscopic Yield energy of Polycrystalline Metals Subjected to Cold?Working (pages 379–412): Kenjiro Terada, Ikumu Watanabe, Masayoshi Akiyama, Shigemitsu Kimura and Kouichi Kuroda
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Extra info for Advanced Computational Materials Modeling: From Classical to Multi-Scale Techniques
De Santi N. A. (2010) Numerical prediction of ductile failure onset under tensile and compressive stress states. International Journal of Damage Mechanics, 19, 175–195. Ladeve` ze, P. and Lemaitre, J. (1984) Damage effective stress in quasi unilateral conditions, 16th International Congress of Theoretical and Applied Mechanics, Lyngby, Denmark. Lemaitre, J. (1992) A Course on Damage Mechanics, Springer-Verlag, Berlin. , and Lee, H. (1987) A nonlocal damage theory. International Journal of Fracture, 34, 239–250.
2 Lemaitre’s simpliﬁed damage model. 41) where the backstress tensor, β, has been simply ignored from the original equation. 43b) for which the loading/unloading conditions γ˙ ≥ 0, Fp ≤ 0, and γ˙ Fp = 0 must hold. 2. 2 Numerical Implementation The numerical implementation of Lemaitre’s simpliﬁed damage model has been proposed by de Souza Neto  and is brieﬂy reviewed in this section. The efﬁciency is attained by numerically integrating the material model by means of a conventional fully implicit elastic predictor/return mapping scheme, typically adopted in a ﬁnite element framework (see Ref.
2010) Multi-scale parallel ﬁnite element analyses of LDH sheet formability tests based on crystallographic homogenization method. International Journal of Mechanical Sciences, 52, 183–197. , and Peri´c, D. (2009) A sub-stepping scheme for multi-scale analysis of solids. Computer Methods in Applied Mechanics and Engineering, 198, 1006–1016. 1 Introduction The gradual internal deterioration at the microscopic level which may eventually lead to the occurrence of macroscopic failure in ductile metals undergoing plastic deformations, has been subjected to a detail study over the last decades.