Session: 06-01-01: Injury and Damage Biomechanics I - Organ and Tissue Injury Biomechanics 1

Paper Number: 145706

145706 - Rate-Dependent Damage Mechanics of Tendons: Experiments and Constitutive Modeling 

Biological soft tissues with load-bearing capabilities, such as ligaments and tendons, exhibit complex nonlinear and rate-dependent mechanical characteristics. An in-depth understanding of this behavior (comprising both bulk- and damage-mechanics aspects) is crucial for the development of computational models that are used to conduct surgical planning, devise rehabilitation strategies, and study conditions such as Anterior Cruciate Ligament (ACL) tear and tendonitis. Experimental characterization and modeling of such mechanical behavior with its underlying damage mechanisms that result in tissue fracture is non-trivial. For example, the classical approach of utilizing a failure stress value to capture material damage no longer applies because damage occurs gradually as collagen fibers break and slide over each other at the microscale.

To capture such gradual damage following a nonlinear and rate-dependent stress–strain response, we implement a multi-faceted modeling approach that integrates conventional hyperelastic stored energy function with an “energy limiter” that captures the asymptotic approach of the stored energy to a constant limiting value during failure. Uniaxial tensile tests are conducted on dog-bone specimens of fresh bovine tendons at four strain rate levels in the range of 0.001–1 /s. The standard dog-bone shape is modified to ensure that failure consistently occurs at the specimen gage section. 2D Digital Image Correlation is employed to validate strain uniformity and uniaxiality in the gage section prior to failure. To ensure a high-contrast speckle pattern, the specimen surface is dyed using Methylene blue. The experimental stress versus stretch data (the latter recorded using a virtual extensometer) at each strain rate is fit to an energy-limited Gent hyperelastic constitutive model. The proposed formulation captures bulk mechanical response via the two physically meaningful Gent model constants—initial tensile modulus and limiting chain extensibility parameter—and damage mechanics via two physically meaningful failure parameters—a failure sharpness parameter and an energy limiting parameter. Finally, we apply Bayesian statistics to capture the uncertainty in the model parameters at each strain rate and to formulate a rate-dependent function of model parameters. Our results show an increase in failure stress and initial modulus with strain rate. In addition, the sharpness of material softening (captured by the failure sharpness parameter) increases with strain rate. Unlike the failure stress, the strain at failure (captured by the energy limiting parameter) decreases with increasing strain rate.

Presenting Author: Kshitiz Upadhyay Louisiana State University

Presenting Author Biography: Dr. Kshitiz Upadhyay is an Assistant Professor in the Department of Mechanical and Industrial Engineering at LSU. His research interests lie in the broad area of mechanics of soft materials, with emphasis on constitutive modeling, injury biomechanics, experimental solid mechanics, and data-driven methods. His research is funded by the National Science Foundation (NSF), the Louisiana Board of Regents (LABoR), and LSU. Dr. Upadhyay currently serves as an Associate Guest Editor of Frontiers in Mechanical Engineering. He has received multiple awards for his research, including the Early Career Research Award from the World Council of Biomechanics in 2022, the Best Dissertation Award from the Department of Mechanical and Aerospace Engineering at the University of Florida (UF) in 2020, and the Gator Engineering Attribute Award of proffesional excellence from UF in 2020. Prior to joining LSU, Dr. Upadhyay worked as a Postdoctoral Fellow in the Hopkins Extreme Materials Institute at Johns Hopkins University (2020-2022). He received his Ph.D. and M.S in Mechanical Engineering from the University of Florida (2020 and 2019), and B.Tech. in Mechanical Engineering from the National Institute of Technology–Bhopal, India (2014).

Authors:

Yogesh Chandrashekar Louisiana State University
Kshitiz Upadhyay Louisiana State University