A residual stiffness-based model for the fatigue damage of biological soft tissues

Significance 

Collagen is found in a variety of connective tissues ranging from cartilage, bones, tendons, ligaments, and skin. Depending upon the degree of mineralization, collagen tissues may be rigid such as the case in bones, compliant as it is found in tendon, or have a gradient from rigid to compliant such as the case in cartilage. Biologically-derived and chemically-treated collagenous tissues are widely used in many medical applications such as bioprosthetic heart valves, cardiovascular grafting and patch, ligament, tendon, sclera, and hernia repair and replacement. Most biological tissues are comprised of networks of collagen fibers embedded in a ground substance and can be regarded as fiber reinforced composites. Presently, biologically-derived and chemically-treated collagenous tissues such as glutaraldehyde-treated bovine pericardium (GLBP) are widely used in many medical applications. The long-term cyclic loading-induced tissue fatigue damage has been identified as one of the primary factors limiting the durability of such medical devices and an in-depth understanding of the fatigue behaviors of biological tissues is critical to increase device durability. However, a limited number of fatigue damage experiments have been performed on biological tissues due to complexity and time-consuming nature of such fatigue experiments. Consequently, accurate constitutive models for fatigue damage are lacking.

Previously developed models assumed a linear dependence of the damage and permanent set on the fatigue cycle, which may not reflect the actual damage evolution process. Therefore, there is a need to further delve on this issue and ascertain the current inhibitions. In this regard, Georgia Institute of Technology and Emory University researchers: Dr. Hai Dong, Dr. Minliang Liu, Dr. Caitlin Martin and led by Professor Wei Sun performed a rigorous fatigue experiment on GLBP tissues, and developed a novel residual stiffness-based fatigue model. Their work is currently published in the Journal of the Mechanics and Physics of Solids.

In their approach, the stress, strain and permanent set at a maximum of 8 different fatigue cycles, up to 15 million cycles, were obtained, which demonstrated a nonlinear stress softening and a nonlinear permanent set accumulation. Based on the experimental data, the researchers developed a novel residual stiffness-based fatigue model. The fatigue model considered the fatigue-induced reduction of initial stiffness and stiffening effect, in contrast to the existing damage-based model that only considered the fatigue-induced reduction of the initial stiffness. Moreover, a new constitutive relation was proposed to describe how the fatigue life (the cycle number at failure) depends on the equivalent strain, analogous to the stress versus fatigue life (S-N) curve for traditional engineering material.

The authors reported that the novel fatigue model could characterize the stress softening and nonlinear permanent set effects when referring to the pre-fatigued configuration. In addition, the reported model could also describe the nonlinear stress stiffening effect when referring to the post-fatigued configuration. To be specific, the dependence of the residual stiffness on the fatigue cycle number was obtained. The residual stiffness exhibited a nonlinear degradation with the increasing cycle number, and reduced more rapidly in the initial cycles than the later ones.

In summary, the researchers here performed uniaxial fatigue testing on the glutaraldehyde-treated bovine pericardium tissues, and successfully developed a novel residual stiffness-based fatigue model, incorporating nonlinear stiffness degradation and nonlinear permanent set accumulation. A new constitutive relation was developed to describe how the fatigue life depends on the equivalent strain. Remarkably, the model predictions were seen to be in good agreement with the experiment. In a statement to Advances in Engineering, Professor Wei Sun mentioned that the experimental results and the novel model they developed could be applied to fatigue analyses of medical devices to improve durability.

A residual stiffness-based model for the fatigue damage of biological soft tissues - Advances in Engineering A residual stiffness-based model for the fatigue damage of biological soft tissues - Advances in Engineering

About the author

Dr. Hai Dong is currently working as a Postdoctoral Fellow in the Tissue Mechanics Lab at the Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University. He obtained the Ph.D. degree in Mechanics & Engineering Science from Peking University, in 2016. His research interests include: nonlinear constitutive models of cardiovascular tissues; engineering analysis of cardiovascular surgery; fatigue of biological tissues.

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About the author

Dr. Minliang Liu is currently working as a Postdoctoral Fellow in the Tissue Mechanics Lab at the Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University. He received a B.Eng. degree in Mechatronic Engineering from Zhejiang University, in 2015. He received a Ph.D. degree in Mechanical Engineering from Georgia Institute of Technology, in 2020.

His research interests include: identification of constitutive parameters by solving inverse problems; machine learning applications in biomechanics; computational patient-specific cardiovascular modeling; experimental characterization and constitutive modeling of cardiovascular tissues; uncertainty quantification in computational biomechanics.

About the author

Dr. Wei Sun is an Associate Professor of the Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University. Dr. Sun is an established investigator in the fields of cardiovascular biomechanics, computational mechanics, and bioprosthetic heart valves.

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Reference

Hai Dong, Minliang Liu, Caitlin Martin, Wei Sun. A residual stiffness-based model for the fatigue damage of biological soft tissues. Journal of the Mechanics and Physics of Solids; volume 143 (2020) 104074.

Go To Journal of the Mechanics and Physics of Solids

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