Stability and size-dependency of temperature-related Cauchy–Born hypothesis |
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| Authors: | AR Khoei P Ghahremani MJ Abdolhosseini Qomi P Banihashemi |
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| Affiliation: | 1. Department of Physics and Earth Sciences, University of Ferrara, Italy;2. Divisão de Metrologia de Materiais, Instituto Nacional de Metrologia, Qualidade e Tecnologia (INMETRO), Brazil;3. Department of Environmental Chemistry, College of Science, Islamic Azad University, Isfahan (Khorasgan) Branch, Iran;4. Department of Engineering, UST, MECAMAT, University of Vic - Central University of Catalonia, Spain;1. Department of Civil and Environmental Engineering, Michigan State University, USA;2. Department of Materials Science and Engineering, Massachusetts Institute of Technology, USA;1. Department of Neurology, Isfahan University of Medical Sciences, Iran;2. Isfahan Research Committee of Multiple Sclerosis (IRCOMS), Isfahan University of Medical Sciences, Iran;3. Medical Students’ Research Center, Isfahan University of Medical Sciences, Iran;4. Department of Biostatistics and Epidemiology, School of Public health, Isfahan University of Medical Sciences, Iran;5. Alzahra Research Institute, Isfahan University of Medical Sciences, Isfahan, Iran;1. Chelyabinsk State University, Chelyabinsk 454001, Russia;2. National University of Science and Technology “MIS&S”, Moscow 119049, Russia |
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| Abstract: | In continuum mechanics, the constitutive models are usually based on the Cauchy–Born (CB) hypothesis which seeks the intrinsic characteristics of the material via the atomistic information and it is valid in small deformation. The main purpose of this paper is to investigate the temperature effect on the stability and size-dependency of Cauchy–Born hypothesis. Three-dimensional temperature-related Cauchy–Born formulations are developed for crystalline structure and the stability and size-dependency of temperature-related Cauchy–Born hypothesis are investigated by means of direct comparison between atomistic and continuous mediums. In order to control the temperature effect, the Nose–Hoover thermostat is employed. Since the Helmholtz free energy is temperature dependent; the first Piola–Kirchhoff stresses are explicitly computed as the first derivative of the Helmholtz free energy density to the deformation gradient. It is numerically shown that the validity surfaces become smaller at higher temperature, which is significant in larger specimen. It is also presented that the material stability decreases with increasing the ambient temperature. |
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