A constitutive model is developed to characterize a general class of polymer and polymer-like materials that displays hyperelastic orthotropic mechanical behavior. The strain energy function is derived from the entropy change associated with the deformation of constituent macromolecules and the strain energy change associated with the deformation of a representative orthotropic unit cell. The ability of this model to predict nonlinear, orthotropic elastic behavior is examined by comparing the theory to experimental results in the literature. Simulations of more complicated boundary value problems are performed using the finite element method.
A Microstructurally Based Orthotropic Hyperelastic Constitutive Law
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, January 15, 2001; final revision, September 11, 2001. Associate Editor: K. R. Rajagopal. Discussion on the paper should be addressed to the Editor, Professor Robert M. McMeeking, Department of Mechanical and Environmental Engineering University of California–Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
Bischoff, J. E., Arruda, E. A., and Grosh, K. (August 16, 2002). "A Microstructurally Based Orthotropic Hyperelastic Constitutive Law ." ASME. J. Appl. Mech. September 2002; 69(5): 570–579. https://doi.org/10.1115/1.1485754
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