By Khemais Saanouni
The objective of this booklet is to summarize the present premier equipment for modeling, simulating, and optimizing steel forming procedures, and to give the most beneficial properties of recent, cutting edge tools at present being constructed with a view to doubtless be the commercial instruments of the following day. It discusses harm (or illness) prediction in digital steel forming, utilizing complicated multiphysical and multiscale absolutely coupled constitutive equations. Theoretical formula, numerical facets in addition to software to varied sheet and bulk steel forming are awarded in detail.
Virtual steel forming is these days inescapable whilst seeking to optimize numerically a number of steel forming procedures so that it will layout complex mechanical elements. to do that, hugely predictive constitutive equations accounting for the total coupling among a variety of actual phenomena at a variety of scales below huge deformation together with the ductile harm prevalence are required. furthermore, totally 3D adaptive numerical equipment concerning time and house discretization are required which will resolve appropriately the linked preliminary and boundary price difficulties. This e-book makes a speciality of those major and complementary elements with software to a variety of steel forming and machining processes.
1. parts of Continuum Mechanics and Thermodynamics.
2. Thermomechanically-Consistent Modeling of the Metals habit with Ductile Damage.
3. Numerical tools for fixing steel Forming Problems.
4. program to digital steel Forming.
Chapter 1 components of Continuum Mechanics and Thermodynamics (pages 1–62): Khemais Saanouni and Pierre Devalan
Chapter 2 Thermomechanically?Consistent Modeling of the Metals habit with Ductile harm (pages 63–242): Khemais Saanouni and Pierre Devalan
Chapter three Numerical tools for fixing steel Forming difficulties (pages 243–354): Khemais Saanouni and Pierre Devalan
Chapter four program to digital steel Forming (pages 355–492): Khemais Saanouni and Pierre Devalan
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Extra info for Damage Mechanics in Metal Forming
161] apply. 151] is automatically fulfilled. 151] between associated force and flux variables ensures the existence of pseudo-potential dissipation according to Casimir–Onsager symmetry relationships [GER 83]. Let us finally note that the materially simple continua to which the hypothesis of the existence of the pseudo-potential of dissipations is applicable, and which, are characterized by normal dissipation evolutions, are often referred to as Standard Generalized Media or SGM [GER 83], [HAL 87].
DA0 The second-rank tensor S , which is symmetric due to the symmetry of purely Lagrangian, is called the Piola–Kirchhoff stress tensor, defined by: S JF 1 . F 1 T or S F 1. 0 where J 0 / t . 115]). 71] via inverse convective transport of the elementary resultant force vector dFt ( nt ) , does not exist in a physical sense, the Piola–Kirchhoff stress tensor, unfortunately, has no physical meaning either. Specifically, it cannot express the equilibrium of a solid, since it cannot be assigned force-related boundary conditions on the boundary of reference initial configuration C0 .
6. dAt This purely Eulerian tensor of “true” stress is symmetric and depends on the Eulerian coordinates of point Pt . Other definitions of stress tensors can be presented. dAt J . F The second-rank operator tensor, defined by: J . 70] Elements of Continuum Mechanics and Thermodynamics 21 This tensor is clearly non-symmetric and, like F , it is neither purely Eulerian nor purely Lagrangian. It can serve perfectly to express the equilibrium of a solid, since it can be associated with the appropriate boundary conditions on the current deformed configuration Ct .