# An elasto-viscoplastic model to describe the ratcheting behavior of articular cartilage

## Abstract

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.

## Keywords

Articular cartilage Constitutive model Logarithmic stress rate Ratcheting## Notes

### Funding

This study was funded by the National Natural Science Foundation of China (11702036) and Chengdu University New Faculty Start-up Funding (2081915038).

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

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