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Fiber orientation effects in simple shearing of fibrous soft tissues
Affiliation:1. School of Engineering and Applied Science, University of Virginia, Charlottesville, VA 22904, USA;2. Department of Mechanical Engineering, Dublin City University, Glasnevin, Dublin 9, Ireland;1. Department of Mechanical & Industrial Engineering, Montana State University, United States;2. Department of Cell Biology & Neurosciences, Montana State University, United States;3. Department of Orthopaedics & Sports Medicine, University of Washington, United States;1. Institute of Environmental Engineering, ETH Zurich, Zurich, Switzerland;2. Institute for Biomedical Engineering, University and ETH Zurich, Zurich, Switzerland;1. Radboud University Medical Center, Radboud Institute for Health Sciences, Nijmegen, The Netherlands;2. Department of Orthopedic Surgery, State University of New York, Upstate Medical University, Syracuse, NY, USA;3. University of Twente, Laboratory for Biomechanical Engineering, Faculty of Engineering Technology, Enschede, The Netherlands;1. Division of Biomedical Engineering, The Chinese University of Hong Kong, Hong Kong;2. School of Biomedical Sciences, The Chinese University of Hong Kong, Hong Kong;1. Rehabilitation Sciences Institute, University of Toronto, 500 University Avenue, Toronto, ON, M5G 1V7, Canada;2. Toronto Rehabilitation Institute – University Health Network, Lyndhurst Centre, 520 Sutherland Drive, Toronto, ON, M4G 3V9, Canada;3. Institute of Biomaterials and Biomedical Engineering, University of Toronto, 164 College Street, Room 407, Toronto, ON, M5S 3G9, Canada;4. Department of Mechanical Engineering, University of Alberta, Donadeo Innovation Centre for Engineering, 9211-116 Street NW, Room 10-368, Edmonton, AB, T6G 1H9, Canada;5. Institute of Physical Activity and Sport Sciences, Cruzeiro do Sul University, Rua Galvão Bueno, 868, 13o. andar, Bloco B, Liberdade, Sao Paulo, SP, 01506-000, Brazil;6. Department of Mechanical Engineering, Federal University of Santa Catarina, Caixa Postal 476 – Campus Universitário – Trindade, 88040-900, Florianópolis, SC, Santa Catarina, Brazil;7. Department of Physical Therapy, University of Toronto, 500 University Avenue, Toronto, ON, M5G 1V7, Canada;1. Department of Biomedical Engineering, University of Southern California, Los Angeles, CA, USA;2. PERCRO Laboratory, TeCIP Institute, Scuola Superiore Sant’Anna, via Alamanni 13b, 56010 Ghezzano, San Giuliano Terme, Pisa, Italy;3. Division of Biokinesiology and Physical Therapy, University of Southern California, Los Angeles, CA, USA
Abstract:Fiber-reinforcement is a common feature of many soft biological tissues. Continuum mechanics modeling of the mechanical response of such tissues using transversely isotropic hyperelasticity is now well developed. The fundamental deformation of simple shear within this framework is examined here. It is well known that the normal stress effect characteristic of nonlinear elasticity plays a crucial role in maintaining a homogeneous deformation state in the bulk of the specimen. Here we consider the effect of anisotropy and fiber-orientation on the shear and normal stresses. It is shown that the confining traction that needs to be applied to the top and bottom faces of a block in order to maintain simple shear can be compressive or tensile depending on the degree of anisotropy and on the angle of orientation of the fibers. In the absence of such an applied traction, an unconfined sample tends to bulge outwards or contract inwards perpendicular to the direction of shear so that one has the possibility of both a positive or negative Poynting effect. The results are illustrated using experimental data obtained by other authors for porcine brain white matter. The general results obtained here are relevant to the development of accurate shear test protocols for the determination of constitutive properties of fibrous biological soft tissues.
Keywords:Simple shear  Fibrous biological soft tissues  Fiber-reinforced transversely isotropic materials  Fiber orientation  Poynting effect
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