By Franz Roters, Philip Eisenlohr, Thomas R. Bieler, Dierk Raabe
Written through the prime specialists in computational fabrics technology, this convenient reference concisely reports an important elements of plasticity modeling: constitutive legislation, section ameliorations, texture tools, continuum techniques and harm mechanisms. consequently, it offers the information had to stay away from disasters in serious structures udner mechanical load.With its a variety of program examples to micro- and macrostructure mechanics, this can be a useful source for mechanical engineers in addition to for researchers desirous to increase in this procedure and expand its outreach.
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Extra info for Crystal Plasticity Finite Element Methods: in Materials Science and Engineering
13) into the right Cauchy–Green deformation tensor (Eq. 8)) and neglecting terms of quadratic order: ÃÂ Ã Â @u T @u IC C D FT F D I C @x @x Â ÃT Â Ã Â ÃT @u @u @u @u D IC C C @x @x @x @x I C 2ε . 15) The corresponding relation for the right stretch tensor, using Eq. 11), thus reads U D C1/2 ICε . 16) From Eqs. 17) I) D I) . ~Bieler, and~Dierk~Raabe: Crystal Plasticity Finite Element Methods — ✐ Chap. roters9419c03 — 2010/7/23 — page 26 — le-tex ✐ ✐ 26 3 Continuum Mechanics The first measure (Eq.
Spatially invariant) deformations. The inverse of the deformation gradient, denoted by F 1 and defined as F 1 D grad x () F i j 1 D @x i /@y j , consequently maps from the current configuration back into the reference configuration. 4) AF . 6) and quantifies the ratio in volume (or inverse ratio in mass densities, and 0 ) between the current and reference configurations. The proof of Eq. 6) is skipped, but it can be easily demonstrated by considering the deformation of an arbitrary parallelepiped due to F.
Bieler, and~Dierk~Raabe: Crystal Plasticity Finite Element Methods — ✐ Chap. 8) termed right Cauchy–Green deformation tensor, characterizes the stretch λ that a material line along a experiences. Similarly, knowing the directions a1 and a2 and corresponding stretches (from Eq. 7)) of two infinitesimal line segments in the reference configuration, we can derive the angle θ between them in the current configuration from λ 1 λ 2 cos θ D a1 C a2 . 9) Since C is symmetric and positive-definite, all its eigenvalues μ 1 , μ 2 , and μ 3 are real and positive and the corresponding (unit-length) eigenvectors n1 , n2 , and n3 form an orthonormal basis.
Crystal Plasticity Finite Element Methods: in Materials Science and Engineering by Franz Roters, Philip Eisenlohr, Thomas R. Bieler, Dierk Raabe