TY - GEN

T1 - A multi-scale continuum theory for heterogeneous materials

AU - Vernerey, Franck

AU - McVeigh, Cahal

AU - Liu, Wing Kam

AU - Moran, Brian

N1 - Funding Information:
Acknowledgements The authors gratefully acknowledge the support of the ONR D3D Digital Structure Consortium (award N00014-05-C-0241) and the National Science Foundation.
Publisher Copyright:
© 2007 Springer. Printed in the Netherlands.

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

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U2 - 10.1007/978-1-4020-6577-4_1

DO - 10.1007/978-1-4020-6577-4_1

M3 - Conference contribution

AN - SCOPUS:84962916571

SN - 9781402065767

T3 - Computational Methods in Applied Sciences

SP - 1

EP - 11

BT - Computational Plasticity

A2 - Onate, Eugenio

A2 - Owen, Roger

PB - Springer

T2 - 8th International Conference on Computational Plasticity, 2005

Y2 - 5 September 2005 through 8 September 2005

ER -