Physics-Augmented Neural Network for Constitutive Modeling of Articular Cartilage with Regularized Meshfree Knee Joint Contact Simulation

  • CHOU, YU-CHUN (National Tsing Hua University)
  • Readioff, Rosti (University of Liverpool)
  • Huang, Tsung-Hui Huang (National Taiwan University)

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The knee joint is one of the most complex and heavily loaded joints in the human body, in which articular cartilage plays a critical role in load transmission and shock absorption. Articular cartilage provides a smooth, lubricated surface that facilitates load distribution and reduces contact pressure [1]. Damage or degeneration of this tissue alters joint mechanics and accelerates the onset of osteoarthritis, highlighting the need for accurate biomechanical modeling [2]. Constitutive modeling forms the foundation of knee joint analysis; however, conventional hyperelastic models combined with empirical damage formulations oversimplify the heterogeneous, nonlinear, and progressive mechanical response of soft tissues. Although deep neural networks offer increased flexibility in fitting experimental data, purely data-driven approaches lack physical interpretability and exhibit poor extrapolation under physiological loading conditions. To overcome these challenges, a physics-augmented neural network (PANN) framework is proposed. Within this framework, a constitutive artificial neural network (CANN [3]) is employed to learn the region-dependent hyperelastic behavior of articular cartilage while enforcing fundamental physical constraints. Progressive damage evolution is modeled using a stage-dependent formulation, in which a model-based neural network (MBNN) adaptively selects the most appropriate damage law at each stage of damage progression while enforcing damage irreversibility. The learned constitutive model is embedded within a regularized meshfree simulation framework [4] to investigate knee joint contact mechanics. This framework enables the simulation of large deformations and complex contact interactions without mesh distortion, while regularization is introduced to mitigate damage localization and enhance numerical stability. The proposed method is benchmarked by comparing contact pressure distributions and peak contact pressures on the meniscus surface with reference results, demonstrating its reliability for biomechanical applications. REFERENCES [1] Carballo, C. B., Nakagawa, Y., Sekiya, I., & Rodeo, S. A. Clin. Sports Med., 36, 413–425 (2017). [2] Seitz, A. M., Osthaus, F., Schwer, J., Warnecke, D., Faschingbauer, M., Sgroi, M., Ignatius, A., & Dürselen, L. Front. Bioeng. Biotechnol., 9, 659989 (2021). [3] Linka, K., & Kuhl, E. Comput. Methods Appl. Mech. Eng., 403, 115731 (2023). [4] Rodriguez, C., & Huang, T. H. Comput. Mech., 73, 599–618 (2024)