Un Kerem, Spilker Robert L
Department of Biomedical Engineering and Scientific Computation Research Center, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA.
J Biomech Eng. 2006 Dec;128(6):934-42. doi: 10.1115/1.2354203.
The penetration method allows for the efficient finite element simulation of contact between soft hydrated biphasic tissues in diarthrodial joints. Efficiency of the method is achieved by separating the intrinsically nonlinear contact problem into a pair of linked biphasic finite element analyses, in which an approximate, spatially and temporally varying contact traction is applied to each of the contacting tissues. In Part I of this study, we extended the penetration method to contact involving nonlinear biphasic tissue layers, and demonstrated how to derive the approximate contact traction boundary conditions. The traction derivation involves time and space dependent natural boundary conditions, and requires special numerical treatment. This paper (Part II) describes how we obtain an efficient nonlinear finite element procedure to solve for the biphasic response of the individual contacting layers. In particular, alternate linearization of the nonlinear weak form, as well as both velocity-pressure, v-p, and displacement-pressure, u-p, mixed formulations are considered. We conclude that the u-p approach, with linearization of both the material law and the deformation gradients, performs best for the problem at hand. The nonlinear biphasic contact solution will be demonstrated for the motion of the glenohumeral joint of the human shoulder joint.
穿透法能够对动关节中柔软的含水双相组织之间的接触进行高效的有限元模拟。该方法的效率是通过将本质上的非线性接触问题分解为一对相互关联的双相有限元分析来实现的，在这两个分析中，将一个近似的、随空间和时间变化的接触牵引力应用于每个接触组织。在本研究的第一部分，我们将穿透法扩展到涉及非线性双相组织层的接触，并展示了如何推导近似接触牵引力边界条件。牵引力的推导涉及与时间和空间相关的自然边界条件，并且需要特殊的数值处理。本文（第二部分）描述了我们如何获得一个高效的非线性有限元程序来求解各个接触层的双相响应。特别地，考虑了非线性弱形式的交替线性化，以及速度 - 压力（v - p）和位移 - 压力（u - p）混合公式。我们得出结论，对于手头的问题，在材料定律和变形梯度都进行线性化的情况下，u - p 方法表现最佳。将针对人体肩关节的盂肱关节运动展示非线性双相接触解。
