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IUTAM Symposium on Discretization Methods for Evolving Discontinuities
Proceedings of the IUTAM Symposium Held Lyon, France, 4-7 September, 2006
Discontinuities are important in the mechanics of solids and fluids. Examples are cracks, shear bands, rock faults, delamination and debonding. With mechanics focusing on smaller and smaller length scales, e.g. on the description of phase boundaries and dislocations, the need to properly model discontinuities increases. While these examples pertain to solid mechanics, albeit at a wide range of scales, technically important interface problems also appear at fluid-solid boundaries, e.g. in welding and casting processes, and in aeroelasticity.Discretization methods have traditionally been developed for continuous media and are less well suited for treating discontinuities. Indeed, they are approximation methods for the solution of the partial differential equations, which are valid on a domain. Discontinuities divide this domain into two or more parts and at the interface special solution methods must be employed. This holds a fortiori for moving or evolving discontinuities like LÃ¼ders-Piobert bands, Portevin-le-Chatelier bands, solid-state phase boundaries and dislocations. Also, fluid-solid interfaces cannot be solved accurately except at the expense of complicated and time-consuming remeshing procedures.In recent years, discretization methods have been proposed, which are more flexible and which have the potential of capturing (moving) discontinuities in a robust and efficient manner. Examples are meshfree methods, discontinuous Galerkin methods and finite element methods that exploit the partition-of-unity property of shape functions. This monograph assembles contributions of leading experts with the most recent developments in this rapidly evolving field.
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