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Constitutive Modeling of Strain Rate Sensitive Polymeric Gels and Biological Tissues


Event details

Date and time 20.09.2019 14:0015:00  
Place and room
Speaker Prof. Ghatu Subhash, Newton C. Ebaugh Professor, Mechanical and Aerospace Engineering, University of Florida
Category Conferences - Seminars
A comprehensive experimental and analytical modeling effort is carried out to capture the visco-hyperelastic response of soft materials. The commonly used thermodynamic dissipation-based models utilize strain energy density and dynamic viscous dissipation potentials, and have been studied to describe short-time memory responses of soft materials for over two decades. In this study, it is demonstrated that the existing forms of viscous dissipation potential in the literature do not capture strain rate dependence of elastic moduli and Poisson’s ratio, a phenomenon which has been experimentally observed in many soft tissues and polymeric gels. To capture the overall response of these materials, the current work is carried out in two phases: First, a generalized thermodynamic stability criterion for isotropic finite elastic solids is derived using the fundamental balance laws and field equations of continuum mechanics, which is then used to formulate constitutive inequalities for the polynomial forms of hyperelastic constitutive equations. It is shown that the model constants of a hyperelastic constitutive model should fall within a domain called the Region of Stability (ROS) for all three primary deformation modes, i.e., uniaxial compression, uniaxial tension and shear. It is then shown that experimental data from only a particular deformation mode of deformation may not capture the complex behavior of a material under multiaxial state of stress for hyperelastic materials and hence data must be captured from all three deformation modes to obtain a realistic constitutive behavior. Second, a novel generalized viscous dissipation potential form is proposed, which not only captures strain rate sensitivity, but also consists of physically-based model parameters that relate to the material’s strain rate sensitivity behavior. The proposed viscous dissipation potential is combined with standard polynomial-based hyperelastic strain energy density function to define visco-hyperelastic constitutive equation, which is then used to model quasi-static to high strain rate response of soft materials such as hydrogel, ballistic gelatin, human patellar tendon, porcine brain tissue. Finally, challenges of conducting simple shear experiments on hyperelatic materials are highlighted. The robustness of constitutive model for capturing deformations under complex loads such as wedge-indentation and high velocity long-rod impact on a rigid surface are demonstrated.

Professor Subhash obtained his PhD from University of California San Diego (UCSD) in 1991 and conducted post-doctoral research at California Institute of Technology (Caltech) during 1992-93. He joined Michigan Technological University in 1993 and then moved to University of Florida in 2007.
His research expertise is in multiaxial dynamic constitutive behavior of materials, processing-microstructure-property-performance relationships in advanced structural ceramics, and experimental solid mechanics. His research efforts have focused on  understanding the deformation mechanisms in a range of materials including refractory metals, bearing steels, bulk metallic glasses, ultrahard ceramics, low-density foams, nuclear ceramics, brain tissue, and polymeric gels. In the context of ceramics, his research is focused on experimental and computational investigations on pressure-induced amorphization in icosahedral ceramics. In the field of nuclear engineering, he has developed rapid processing technology to fabricate nuclear fuel and control rod pellets in few minutes compared to the traditional methods which take several hours. For this effort, he has received ‘Significant Contribution Award’ from Materials Science and Technology Division, American Nuclear Society (2014). His contributions in experimental solid mechanics have been recognized by the 2018 ‘Frocht Award’ from Society for Experimental Mechanics(SEM).  His current research interests in biomedical engineering include determination of contractile stresses due to cell growth in tissue phantoms and shock-induced cellular degradation in brain tissue.  His work on rolling contact fatigue of ultrahard bearings received ‘Best Paper Award’ in the Journal of Engineering Materials and Technology (2017).
Prof. Subhash is a fellow of the ASME and SEM. He serves as an Editor-in-Chief of Mechanics of Materials (an international journal) and as an Associate Editor of the Journal of the American Ceramic Society.  He has received numerous recognitions for excellence in teaching, research and professional service, including ‘Technology Innovator Award’ from University of Florida (2016) and Teacher/Scholar of the year (2013), ASME Student Section Advisor Award, Society of Automotive Engineers (SAE) Ralph R. Teetor Educational Award, and American Society for Engineering Education (ASEE) Outstanding New Mechanics Educator. He has graduated 34 PhD students and co-authored 190 peer reviewed journal articles, 80 conference proceedings, and 5 patents. He has co-authored a book on “Mechanics of Materials Laboratory Course” and is finalizing another book on “Dynamic Response of Ceramics”. His inventions have received international attention from major TV networks (Fox, CBS and 40 other local TV channels), radio stations (including NPR) and articles by Reuters and ASEE Morning Bell. He has also appeared in a PBS documentary in 2017 (Secrets of Spanish Florida) while discussing the impact response of ‘Coquina’, a material with which the oldest fort in the United States, the ‘Castillo de San Marcos’ was built in St. Augustine, Florida.


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  • Profs Brice Lecampion & Alexandre Alahi    


  • Prof. Brice Lecampion