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Mathematical characterization and identification of remodeling,growth, aging and morphogenesis
Institution:1. Department of Civil, Environmental and Mechanical Engineering, University of Trento, via Mesiano 77, 38123 Trento, Italy;2. Accademia dei Lincei and Department of Mathematics, University of Rome TorVergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy;1. LMD – École normale supérieure de Paris – CNRS, 75005 Paris, France;2. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada;1. Faculty of Aerospace Engineering, Technion, Haifa, 32000, Israel;2. Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA;3. Department of Civil and Environmental Engineering, University of California, Davis, CA 95616, U.S.A.;4. Department of Mechanics, National Technical University of Athens, Greece;1. LMD/IPSL, CNRS, École normale supérieure, PSL Research University, École polytechnique, Université Paris-Saclay, Sorbonne Universités, UPMC Université Paris-6, 24, rue Lhomond, 75005 Paris, France;2. Department of Mathematical and Statistical Sciences, Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB T6G 2G1 Canada
Abstract:A clear demarcation between various processes of material evolution is established and the implications of the symmetry type on our ability to distinguish between them are investigated. The general features of the various types of material evolution are emphasized by establishing a spatio-temporal analogy between material uniformity and processes of material evolution.
Keywords:Material evolution  Symmetry groups  Normalizer  Natural states  Mandel stress  Functionally graded materials
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