Vol. 11, No. 4, 2016

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A unified theory for constitutive modeling of composites

Wenbin Yu

Vol. 11 (2016), No. 4, 379–411
DOI: 10.2140/jomms.2016.11.379

A unified theory for multiscale constitutive modeling of composites is developed using the concept of structure genomes. Generalized from the concept of the representative volume element, a structure genome is defined as the smallest mathematical building block of a structure. Structure genome mechanics governs the necessary information to bridge the microstructure length scale of composites and the macroscopic length scale of structural analysis and provides a unified theory to construct constitutive models for structures including three-dimensional structures, beams, plates, and shells over multiple length scales. For illustration, this paper is restricted to construct the Euler–Bernoulli beam model, the Kirchhoff–Love plate/shell model, and the Cauchy continuum model for structures made of linear elastic materials. Geometrical nonlinearity is systematically captured for beams, plates/shells, and Cauchy continuum using a unified formulation. A general-purpose computer code called SwiftComp (accessible at https://cdmhub.org/resources/scstandard) implements this unified theory and is used in a few example cases to demonstrate its application.

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Mechanics of Structure Genome, Structural Mechanics, Micromechanics, Composites Mechanics, Homogenization
Received: 25 September 2015
Revised: 28 April 2016
Accepted: 11 May 2016
Published: 4 August 2016
Wenbin Yu
Purdue University
704 W Stadium Ave.
West Lafayette, IN 47907
United States