@inproceedings{24e3da0a032948439868ca8410063147,

title = "A multi-scale continuum theory for heterogeneous materials",

abstract = "For the design of materials, it is important to faithfully model the physics due to interactions at the microstructural scales [18, 17, 19]. While bruteforce modeling of all the details of the microstructure is too costly, current homogenized continuum models suffer from their inability to sufficiently capture the correct physics - especially where localization and failure are concerned. To overcome this limitation, a multi-scale continuum theory is proposed so that kinematic variables representing the deformation at various scales are incorporated. The method of virtual power is then used to derive a system of coupled governing equations, each equation representing a particular scale and its interactions with the macro-scale. A constitutive relation is then introduced to preserve the underlying physics associated with each scale. The inelastic behavior is represented by multiple yield functions, each representing a particular scale of microstructure, but collectively coupled through the same set of internal variables. The proposed theory is applied to model porous metals and high strength steel. For the high strength steel the microstructure of interest consists of two populations of inclusions at distinct scales, in an alloy matrix.",

author = "Franck Vernerey and Cahal McVeigh and Liu, {Wing Kam} and Brian Moran",

year = "2007",

month = jan,

day = "1",

language = "English (US)",

isbn = "9781402065767",

series = "Computational Methods in Applied Sciences",

publisher = "Springer Netherland",

pages = "1--11",

editor = "Eugenio Onate and Roger Owen",

booktitle = "Computational Plasticity",

note = "8th International Conference on Computational Plasticity, 2005 ; Conference date: 05-09-2005 Through 08-09-2005",

}