Multiscale Modeling of Complex Materials: Phenomenological, by Tomasz Sadowski, Patrizia Trovalusci PDF

By Tomasz Sadowski, Patrizia Trovalusci

ISBN-10: 3709118115

ISBN-13: 9783709118115

ISBN-10: 3709118123

ISBN-13: 9783709118122

The papers during this quantity take care of fabrics technological know-how, theoretical mechanics and experimental and computational recommendations at a number of scales, delivering a legitimate base and a framework for lots of purposes that are hitherto handled in a phenomenological feel. the elemental ideas are formulated of multiscale modeling suggestions in the direction of sleek advanced multiphase fabrics subjected to numerous forms of mechanical, thermal loadings and environmental results. the focal point is on difficulties the place mechanics is very coupled with different concurrent actual phenomena. awareness is additionally all in favour of the historic origins of multiscale modeling and foundations of continuum mechanics at present followed to version non-classical continua with substructure, for which inner size scales play a vital role.

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Extra resources for Multiscale Modeling of Complex Materials: Phenomenological, Theoretical and Computational Aspects

Example text

1c, Πε is the tetrahedron with vertex xo and height ε, whose basis Pε has exterior unit normal n, while the three faces Pεi have exterior unit normals −ei . Then, by (3) and the balance equation (1)1 , 3 Πε b(x) dV + Pε s(x, n) dA + i=1 Pεi s(x, −ei ) dA = 0 . (24) If A(Pε ) is the area of the basis, the areas of the faces and the volume of Πε are V (Πε ) = 13 εA(Pε ) , (25) A(Pεi ) = A(Pε ) ni , respectively. If 1 s(x, −ei ) dA = s(xo , −ei ) , ε→0 A(Pεi ) P i ε 1 s(x, n) dA = s(xo , n) , lim ε→0 A(Pε ) P ε lim (26) from (24) divided by A(Pε ), in the limit for ε → 0 one gets 3 s(xo , n) + s(xo , −ei ) ni = 0 .

Belytschko. Conservation properties of the bridging domain method fod coupled molecular/continuum dynamics. International Journal for Numerical Methods in Engineering, 76:278–294, 2008. X. P. Xu and A. Needleman. Numerical simulations of fast crack growth in brittle solids. Journal of the Mechanics and Physics of Solids, 42:1397–1434, 1994. M. Zhou. A new look at the atomic level virial stress: on continuum-molecular system equivalence. Proceedings of the Royal Society London, A459:2347– 2392, 2003.

J. of Elasticity 56: 33-58, 1999 L. Bardella. Size effects in phenomenological strain gradient plasticity constitutively involving the plastic spin. Int. J. Engng. Sciences 48: 550-568, 2010 G. Capriz. Continua with Microstructure, Springer, Berlin 1989 G. G. Virga. Interactions in general continua with microstructure. Arch. Rat. Mech. L. Cauchy. Recherches sur l’´equilibre et le mouvement int´erieur des corps solides ou fluides, ´elastiques ou non ´elastiques. Bull. Soc. Philomath. pp. 9-13. Q. Chen, M.

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Multiscale Modeling of Complex Materials: Phenomenological, Theoretical and Computational Aspects by Tomasz Sadowski, Patrizia Trovalusci

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