Macro-architectured cellular materials: Properties, characteristic modes, and prediction methods

Abstract

Macro-architectured cellular (MAC) material is defined as a class of engineered materials having configurable cells of relatively large (i.e., visible) size that can be architecturally designed to achieve various desired material properties. Two types of novel MAC materials, negative Poisson’s ratio material and biomimetic tendon reinforced material, were introduced in this study. To estimate the effective material properties for structural analyses and to optimally design such materials, a set of suitable homogenization methods was developed that provided an effective means for the multiscale modeling of MAC materials. First, a strain-based homogenization method was developed using an approach that separated the strain field into a homogenized strain field and a strain variation field in the local cellular domain superposed on the homogenized strain field. The principle of virtual displacements for the relationship between the strain variation field and the homogenized strain field was then used to condense the strain variation field onto the homogenized strain field. The new method was then extended to a stress-based homogenization process based on the principle of virtual forces and further applied to address the discrete systems represented by the beam or frame structures of the aforementioned MAC materials. The characteristic modes and the stress recovery process used to predict the stress distribution inside the cellular domain and thus determine the material strengths and failures at the local level are also discussed.

Keywords

architectured material / cellular materials / multi-scale modeling / homogenization method / effective material properties / computational method

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Acknowledgements

This work was supported by MKP Structural Design Associates, Inc., a corporation in Ann Arbor, Michigan, USA.

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2018 Higher Education Press and Springer-Verlag GmbH Germany