Innovative Numerical Approaches for Multi-Field and by Kerstin Weinberg, Anna Pandolfi

By Kerstin Weinberg, Anna Pandolfi

This e-book offers readers with an in depth perception into varied and intriguing contemporary advancements in computational sturdy mechanics, documenting new views and horizons. the subjects addressed hide a variety of present study, from computational fabrics modeling, together with crystal plasticity, micro-structured fabrics, and biomaterials, to multi-scale simulations of multi-physics phenomena. specific emphasis is put on pioneering discretization tools for the answer of coupled non-linear difficulties at varied size scales. The ebook, written by means of best specialists, displays the extraordinary advances which were made within the box during the last decade and extra, mostly a result of improvement of a valid mathematical heritage and effective computational thoughts. The contents construct upon the 2014 IUTAM symposium celebrating the 60th birthday of Professor Michael Ortiz, to whom this publication is devoted. His paintings has lengthy been well-known as pioneering and is a constant resource of concept for lots of researchers. it's was hoping that by means of delivering a "taste" of the sphere of computational mechanics, the publication will advertise its acceptance one of the mechanics and physics communities.

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Kikuchi, N. (1997). Macro and micro scale modeling of thermal residual stresses in metal matrix composite surface layers by the homogenization method. Computational Mechanics, 19, 188–201. 9. , & Cho, M. (2011). Numerically generated tangent stiffness matrices using the complex variable derivative method for nonlinear structural analysis. Computer Methods in Applied Mechanics and Engineering, 200, 403–413. 10. , & Khandelwal, K. (2015). Automatic implementation of finite strain anisotropic hyperelastic models using hyper-dual numbers.

Journal of Nonlinear Science, 10, 661. 23. , & Sternberg, P. (2001). Energy estimates for the von Kármán model of thin-film blistering. Journal of Mathematical Physics, 42, 192. 24. , & Sternberg, P. (2002). In-plane displacements in thin-film blistering. Proceedings of the Royal Society of Edinburgh Section A, 132, 911. 25. , Müller, S. (2002). Energy scaling of compressed elastic films. Archive for Rational Mechanics and Analysis, 164, 1. 26. , James, R. , & Müller, S. (2002). A theorem on geometric rigidity and the derivation of nonlinear plate theory from 3d elasticity.

Q=k ∂x (23) (24) Effective mechanical properties of granular beds are of heavy interest in many theoretical studies. Some of these include: calculation of the principal elastic modulus of vertical compression of spherical particles without any lateral extension [30]; derivation of the finite and incremental elasticity of random packing of identical particles using energy methods [32]; enhancement of the derived formulas based on the pressure dependence of the elastic moduli of granular packings [2, 3].

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