Modeling Progressive Damage Accumulation in Bone Remodeling Explains the Thermodynamic Basis of Bone Resorption by Overl
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Modeling Progressive Damage Accumulation in Bone Remodeling Explains the Thermodynamic Basis of Bone Resorption by Overloading T. J. Sego1
· Yung-Ting Hsu2 · Tien-Min Chu3 · Andres Tovar4
Received: 4 May 2020 / Accepted: 18 September 2020 © Society for Mathematical Biology 2020
Abstract Computational modeling of skeletal tissue seeks to predict the structural adaptation of bone in response to mechanical loading. The theory of continuum damage–repair, a mathematical description of structural adaptation based on principles of damage mechanics, continues to be developed and utilized for the prediction of long-term peri-implant outcomes. Despite its technical soundness, CDR does not account for the accumulation of mechanical damage and irreversible deformation. In this work, a nonlinear mathematical model of independent damage accumulation and plastic deformation is developed in terms of the CDR formulation. The proposed model incorporates empirical correlations from uniaxial experiments. Supporting elements of the model are derived, including damage and yielding criteria, corresponding consistency conditions, and the basic, necessary forms for integration during loading. Positivity of mechanical dissipation due to damage is proved, while strain-based, associative plastic flow and linear hardening describe post-yield behavior. Calibration of model parameters to the empirical correlations from which the model was derived is then accomplished. Results of numerical experiments on a point-wise specimen show that damage and plasticity inhibit bone formation by dissipation of energy available to biological processes, leading to material failure that would otherwise be predicted to experience a net gain of bone. Keywords Bone remodeling · Bone overload · Damage · Elastoplasticity · Nonlinear structural mechanics
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T. J. Sego [email protected]
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Department of Intelligent Systems Engineering, Indiana University, Bloomington, IN, USA
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Department of Periodontics, University of Washington, Seattle, WA, USA
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Department of Restorative Dentistry, Indiana University, Indianapolis, IN, USA
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Department of Mechanical and Energy Engineering, Indiana University-Purdue University Indianapolis, Indianapolis, IN, USA 0123456789().: V,-vol
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1 Introduction Bone adapts to biomechanical conditions (Frost 1994). This is evidenced by that the trajectory of trabecular systems tends to align with principal stress directions (Koch 1917), by that osteotomies in bovine caused overloading strains and bone growth (Goodship et al. 1979), and by that prolonged disuse in canines resulted in bone loss (Uhthoff and Jaworski 1978). These mechanophysiological phenomena, combined with the consequences of evolutionary pressures associated with body weight and skeletal strength, are collectively referred to as Wolff’s law: bone restructures to better serve the functions required for a repeatedly experienced mechanical state, while using the least amount of material possible. Considering mechanical quantities l
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