Efficient Simulation of Soft Tissue for Human, Robotics, and Exoskeleton Applications 133 0.000 0.001 0.002 0.003 0.004 0.005 0.006 t in s 0 10 20 30 40 50 60 F in kN RB (Hip) RWM (Hip) FWM (Hip) 0.000 0.001 0.002 0.003 0.004 0.005 t in s 0 10 20 30 40 50 60 F in kN RB (Knee) RWM (Knee) FWM (Knee) Fig. 2 Joint forces in the knee and hip joint during landing on one leg required 14.3 seconds of CPU-time for simulation and the floating frame model with 10 modes required approximately 1307 seconds. Conclusion Wobbling masses significantly affect joint forces and rigid body motions, potentially reducing joint forces. While being computationally more demanding than the rigid body models, using the floating frame of reference formulation with modal reduction yields a substantial boost in computational efficiency as compared to nonlinear transient finite element simulations. For computing joint forces, a rigid wobbling mass approach may serve as an alternative to the floating frame of reference approach. However, using the floating frame of reference formulation for modeling wobbling masses in multibody dynamics offers substantial advantages, such as eliminating the need to compute inertia tensors from CAD models and enabling direct coupling with bones through finite element methods (FE) without the need for estimating spring stiffness and damping parameters for compliant joints. Additionally, the FFRF approach provides access to stresses and strains, which are not accessible in rigid body models. References 1. Maffulli, N., Longo, U.G., Gougoulias, N., Caine, D., and Denaro, V. “Sport injuries: A review of outcomes”. British Medical Bulletin, 97:47–80 (2011) 2. Gruber, K., Ruder, H., Denoth, J., and Schneider, K. “A comparative study of impact dynamics: wobbling mass model versus rigid body models”. Journal of Biomechanics, 31:439–444 (1998) 3. Inkol, K.A., Brown, C., McNally, W., Jansen, C., and McPhee, J. “Muscle torque generators in multibody dynamic simulations of optimal sports performance”. Multibody System Dynamics, 50:435–452 (2020) 4. Mazess, R.B., Barden, H.S., Bisek, J.P., and Hanson, J. “Dual-energy x-ray absorptiometry for total-body and regional bone-mineral and soft-tissue composition”. The American Journal of Clinical Nutrition, 56:1106–1112 (1990) 5. Stelletta, J., Dumas, R., and Lafon, Y. Chapter 23 - Modeling of the Thigh: A 3D Deformable Approach Considering Muscle Interactions, pages 497–521. Academic Press, 1 edition (2017) 6. Zwo¨lfer, A. and Gerstmayr, J. “A concise nodal-based derivation of the floating frame of reference formulation for displacement-based solid finite elements: Avoiding inertia shape integrals”. Multibody System Dynamics, 49:291–313 (2020) 7. Pechstein, A., Reischl, D., and Gerstmayr, J. “The applicability of the floating-frame based component mode synthesis to high-speed rotors”. In: Proceedings of the ASME 2011 International Design Engineering Technical Conferences {&}Computers and Information in Engineering Conference IDETC/CIE 2011, August 28-31, 2011, Washington, DC, USA(2011) 8. Zwo¨lfer, A. and Gerstmayr, J. “The nodal-based floating frame of reference formulation with modal reduction”. Acta Mechanica, 232:835– 851 (2021) 9. Janssen, I., Heymsfield, S.B., Wang, Z., and Ross, R. “Skeletal muscle mass and distribution in 468 men and women aged 18–88 yr”. JAppl Physiol, 89:81–88 (2000) 10. Arnold, N., Scott, J., and Bush, T.R. “A review of the characterizations of soft tissues used in human body modeling: Scope, limitations, and the path forward”. Journal of Tissue Viability, 32:286–304 (2023)
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