Elastic constants for granular materials modeled as first-order strain-gradient continua |
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| Institution: | 1. Department of Civil and Environmental Engineering, University of Massachusetts, 30 Marston Hall, Amherst, MA 01002, USA;2. Bureau of High Speed Rail, Taipei, 110 Taiwan, ROC;1. Materials innovation institute (M2i), The Netherlands;2. Department of Mechanical Engineering, Technische Universiteit Eindhoven, The Netherlands;3. Department of Mathematics and Computer Sciences, Technische Universiteit Eindhoven, The Netherlands;4. Institute for Complex Molecular Systems, Technische Universiteit Eindhoven, The Netherlands;1. Institute for Materials Simulation, Department of Materials Science, Friedrich-Alexander University Erlangen-Nürnberg (FAU), Dr.-Mack-Str. 77, 90762 Fürth, Germany;2. Institute for Applied and Numerical Mathematics, Karlsruhe Institute of Technology (KIT), Kaiserstr. 12, 76128 Karlsruhe, Germany;1. School of Mechanical and Electrical Engineering, Harbin Institute of Technology, Harbin 150001, PR China;2. School of Mechanical Engineering, Purdue University, West Lafayette 47907, USA |
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| Abstract: | Formulation of a stress–strain relationship is presented for a granular medium, which is modeled as a first-order strain-gradient continuum. The elastic constants used in the stress–strain relationship are derived as an explicit function of inter-particle stiffness, particle size, and packing density. It can be demonstrated that couple-stress continuum is a subclass of strain-gradient continua. The derived stress–strain relationship is simplified to obtain the expressions of elastic constants for a couple-stress continuum. The derived stress–strain relationship is compared with that of existing theories on strain- gradient models. The effects of inter-particle stiffness and particle size on material constants are discussed. |
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