An elasto-viscoplastic model to describe the ratcheting behavior of articular cartilage
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In the present work, a constitutive model for articular cartilage is proposed in finite elasto-viscoplasticity. For simplification, articular cartilage is supposed to be a typical composite composed of a soft basis and a fiber assembly. The stress tensor and free energy function are hence accordingly divided into two components. The high nonlinear stress-strain response is assumed to be mainly related to the fiber assembly and described by an exponential-type hypoelastic relation. Ratcheting is considered according to the viscoplasticity, the evolution rule of which is deduced from the dissipative inequality by the co-directionality hypotheses. Then, the capability of the proposed model is validated by comparing its predictions with related experimental observations. Results show that the ratcheting behavior and stress-strain hysteresis loops are reasonably captured by the proposed model.
KeywordsArticular cartilage Constitutive model Logarithmic stress rate Ratcheting
This study was funded by the National Natural Science Foundation of China (11702036) and Chengdu University New Faculty Start-up Funding (2081915038).
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Conflict of interest
The authors declare that they have no conflict of interest.
- Ateshian GA (2017) Mixture theory for modeling biological tissues: illustrations from articular cartilage. Springer, LondonGoogle Scholar
- Athanasiou K, Darling E, Hu J (2009) Articular cartilage tissue engineering. Synth Lect Tissue Eng 1(1):1–182Google Scholar
- Barker MK, Seedhom BB (2001) The relationship of the compressive modulus of articular cartilage with its deformation response to cyclic loading: does cartilage optimize its modulus so as to minimize the strains arising in it due to the prevalent loading regime? Rheumatology 40:274–284CrossRefGoogle Scholar
- Matzat SJ, Van TJ, Gold GE, Oei EH (2013) Quantitative MRI techniques of cartilage composition. Quant Imaging Med Surg 3:162–174Google Scholar
- Seifzadeh A, Oguamanam DC, Trutiak N, Hurtig M, Papini M (2012) Determination of nonlinear fibre-reinforced biphasic poroviscoelastic constitutive parameters of articular cartilage using stress relaxation indentation testing and an optimizing finite element analysis. Comput Methods Programs Biomed 107:315–326CrossRefGoogle Scholar
- Sophia Fox AJ, Bedi A, Rodeo SA (2009) The basic science of articular cartilage: structure, composition, and function Sports. Health 1:461–468Google Scholar
- Wilson W, van Donkelaar CC, Van RB, Huiskes R (2005) A fibril-reinforced poroviscoelastic swelling model for articular cartilage. R.G. Landes CoGoogle Scholar