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Rate type constitutive equations for fiber reinforced nonlinearly vicoelastic solids using spectral invariants
Institution:1. Department of Applied Mathematics and Science, Khalifa University of Science and Technology, Abu Dhabi, United Arab Emirates;2. Departamento de Ingeniería Mecánica, Universidad de Chile, Beauchef 851, Santiago Centro, Santiago, Chile;3. Department of Continuum Mechanics and Structures, Escuela deIngenieros de Caminos, Universidad Politecnica de Madrid, 28040 Madrid, Spain;1. Institute of Technology, Nirma University, Ahmedabad 382481, Gujarat, India;2. Faculty of Technology and Engineering, MS University of Baroda, Vadodara 370001, Gujarat, India;1. Lutsk National Technical University, Lvivska Str. 75, 43018 Lutsk, Ukraine;2. Bialystok University of Technology, Wiejska Str. 45C, 15-351 Bialystok, Poland;1. Department of Mechanical Engineering, Nagaoka University of Technology, 1603-1 Kamitomioka, Nagaoka 940-2188, Japan;2. Faculty of Environment and Information Sciences, Yokohama National University, 79-7 Tokiwadai, Hodogaya, Yokohama 240-8501, Japan;1. Mechanical Engineering Department, United States Naval Academy, 590 Hollway Road, Annapolis, MD, 21402, United States;2. United States Navy, United States;3. Army Research Laboratory, 2800 Powder Mill Rd, Adelphi, MD 20783, United States
Abstract:In this paper we are interested in developing constitutive equations for fiber-reinforced nonlinearly viscoelastic solids. It has been shown that constitutive equations for such bodies can be expressed in terms of a complete minimal set of 18 classical invariants associated with deformation and fiber orientation. In this paper, we give an alternative formulation using a set of spectral invariants. It is shown via the use of spectral invariants that only 11 of the 18 classical invariants are independent. We analyze the spectral invariants for two illustrative deformation gradients: (i) simple tension, and (ii) simple shear.
Keywords:Nonlinear viscoelasticity  Fiber reinforcement  Spectral physical invariants  Deformation indicators  Rate of deformation indicators
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