Haider Mansoor A, Guilak Farshid
Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695.
Comput Methods Appl Mech Eng. 2007 Jun 15;196(31-32):2999-3010. doi: 10.1016/j.cma.2006.08.020.
Articular cartilage exhibits viscoelasticity in response to mechanical loading that is well described using biphasic or poroelastic continuum models. To date, boundary element methods (BEMs) have not been employed in modeling biphasic tissue mechanics. A three dimensional direct poroelastic BEM, formulated in the Laplace transform domain, is applied to modeling stress relaxation in cartilage. Macroscopic stress relaxation of a poroelastic cylinder in uni-axial confined compression is simulated and validated against a theoretical solution. Microscopic cell deformation due to poroelastic stress relaxation is also modeled. An extended Laplace inversion method is employed to accurately represent mechanical responses in the time domain.
关节软骨在机械负荷作用下表现出粘弹性，用双相或多孔弹性连续体模型可以很好地描述这种特性。迄今为止，边界元法尚未用于双相组织力学建模。一种在拉普拉斯变换域中建立的三维直接多孔弹性边界元法被应用于软骨应力松弛建模。模拟了多孔弹性圆柱体在单轴受限压缩下的宏观应力松弛，并与理论解进行了验证。还对多孔弹性应力松弛引起的微观细胞变形进行了建模。采用扩展拉普拉斯反演方法在时域中准确表示力学响应。
