Edited by
Jacques Besson, CNRS, France.
Frédéric Lebon, Aix-Marseille University and Mechanics and Acoustics Laboratory (LMA), France.
Eric Lorentz, EDF R&D, France.
ISBN : 9781789450811
Publication Date : December 2024
Hardcover 382 pp
165.00 USD
Co-publisher
Numerical Methods for Strong Nonlinearities in Mechanics deals with recent advances in the numerical treatment of contact/friction and damage phenomena. Although physically distinct, these phenomena both lead to a strong nonlinearity in the mechanical problem, therefore limiting the regularity of the problem, which is now non-differentiable.
This has two direct consequences: on the one hand, the mathematical characteristics of the problem deviate from well-established forms, requiring innovative discretization schemes; on the other hand, the low regularity makes it particularly difficult to solve the corresponding large-scale algebraic systems robustly and efficiently. In addition, neither the uniqueness, nor the existence of solutions, remain assured, resulting in bifurcation points, limit loads and structural instabilities, which are always tricky to overcome numerically.
Part 1. Contact and Friction.
1. Lagrangian and Nitsche Methods for Frictional Contact, Franz Chouly, Patrick Hild and Yves Renard.
2. High-performance Computing in Multicontact Mechanics: From Elastostatics to Granular Dynamics, Pierre Alart.
3. Numerical Methods in Micromechanical Contact, Vladislav A. Yastrebov.
Part 2. Damage and Cracking.
4. Numerical Methods for Ductile Fracture, Jacques Besson.
5. Quasi-brittle Fracture Modeling, Éric Lorentz.
6. Extended Finite Element (XFEM) and Thick Level Set (TLS) Methods, Nicolas Moës.
7. Damage-to-Crack Transition, Sylvia Feld-Payet.
Jacques Besson is Research Director at the CNRS, France, where he conducts research into damage and fracture modeling of metallic materials.
Frédéric Lebon is Professor of Solid Mechanics at Aix-Marseille University and the Mechanics and Acoustics Laboratory (LMA), France.
Eric Lorentz is a senior expert at EDF R&D, France, where he conducts studies on damage modeling, applied to the performance of power generation structures.
