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Advancements in multiresolution analysis. (English) Zbl 1352.74411
Summary: Materials have a hierarchical nature, deriving often their most useful properties from microscale or nanoscale constituents. Multiresolution analysis, a generalized continuum mechanics-based theory, uses extra degrees of freedom to account for an arbitrary number of these nested length scales. In the past, multiresolution analyses have focused mostly on metal alloys. While this article addresses recent advances in image-based multiresolution analysis of metal alloys, it also highlights extensions to multiresolution theory for modeling of bone mechanics and multiresolution analysis of polymers and polymer nanocomposites. A strong link between molecular dynamics simulations and macroscale multiresolution analyses is shown for both polymers and polymer nanocomposites. The forthcoming work is greatly indebted to the pioneering advances of Ted Belytschko in many areas of computational mechanics; his influence on our work and on the field of finite elements as a whole is substantial.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35Q74 PDEs in connection with mechanics of deformable solids
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