Analysis and Computation of Microstructure in Finite by Sergio Conti, Klaus Hackl

By Sergio Conti, Klaus Hackl

This booklet addresses the necessity for a basic realizing of the actual foundation, the mathematical habit and the numerical therapy of versions which come with microstructure. best scientists current their efforts related to mathematical research, numerical research, computational mechanics, fabric modelling and test. The mathematical analyses are in keeping with equipment from the calculus of adaptations, whereas within the numerical implementation worldwide optimization algorithms play a critical position. The modeling covers all size scales, from the atomic constitution as much as macroscopic samples. the improvement of the types ware guided via experiments on unmarried and polycrystals and effects should be checked opposed to experimental data.

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A strong local refinement towards the reentrant corner is observed. This leads to an improved convergence rate for the energy error because of the same reason mentioned for domain Ω2 . In total, the numerical results show clearly that the AFEMalgorithm converges for the domain Ω . The microstructures show the expected structure, namely an interior region, a boundary layer and small transition layer between the two regions. 6 Conclusions and Outlook The application of discontinuous Galerkin methods was motivated by stabilization techniques in [BC10, BC14] with penalty terms which imitate the surface energy in microstructures.

Mech. Appl. Math. : The uniqueness of solutions of some variational problems of the theory of phase equilibrium in solid bodies. J. Math. Sci. : A variational problem on the phase equilibrium of an elastic body. St. Petersbg. Math. J. 10, 477–506 (1998) Chapter 2 Variational Modeling of Slip: From Crystal Plasticity to Geological Strata Sergio Conti, Georg Dolzmann, and Carolin Kreisbeck Abstract. Slip processes are soft modes of deformation, characteristic of a variety of layered materials. The layers can be at the atomic scale, as in the plastic deformation of crystalline lattices, or on a macroscopic scale, as in stacks of cards or sheets of paper and geological strata.

Dolzmann within this DFG research project. The second author furthermore acknowledges the support by the DFG research center MATHEON and the Berlin Mathematical School. The third author acknowledges the support of the WCU program through KOSEF (R31-2008-000-10049-0) and the kind hospitality of the department for Computational Science and Engeneering of Yonsei University. 1 Numerical Simulation of Microstructure 27 Appendix A. 3. The quadratic form T : M → R reads 1 1 T (F) := |symF|2C − symF : C(A1 − A2 ) 2 2g 2 − γ det F for any F ∈ M.

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