1. Variational upscaling for modeling state of strain-dependent behavior and stress-induced crystallization in rubber-like materials
- Author
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Patrick Le Tallec, Julie Diani, Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
- Subjects
Physics ,Structural material ,General Physics and Astronomy ,02 engineering and technology ,[SPI.MECA.MSMECA]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Materials and structures in mechanics [physics.class-ph] ,01 natural sciences ,010305 fluids & plasmas ,law.invention ,020303 mechanical engineering & transports ,Distribution (mathematics) ,0203 mechanical engineering ,Natural rubber ,Mechanics of Materials ,Position (vector) ,law ,visual_art ,0103 physical sciences ,visual_art.visual_art_medium ,General Materials Science ,Affine transformation ,Boundary value problem ,Statistical physics ,Crystallization ,Energy (signal processing) - Abstract
International audience; The purpose of this paper is to present a general upscaling strategy for deriving macroscopic constitutive laws for rubber-like materials from the knowledge of the network distribution and a mechanical description of the individual chains and of their free energy. The microscopic configuration is described by the position of the cross-links and is not obtained by an affine assumption but by minimizing the corresponding free energy on stochastic large representative volume elements with adequate boundary conditions. This general framework is then approximated by using a microsphere (directional) description of the network. It is presented in a global setting and is extended in order to handle situations with tube-like constraints and stress-induced crystallization.
- Published
- 2020