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首页> 外文期刊>Journal of Biomechanics >A fast quadrature-based numerical method for the continuous spectrum biphasic poroviscoelastic model of articular cartilage.
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A fast quadrature-based numerical method for the continuous spectrum biphasic poroviscoelastic model of articular cartilage.

机译：基于快速正交的关节软骨双相波黏弹性模型的数值方法。

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摘要

A new and efficient method for numerical solution of the continuous spectrum biphasic poroviscoelastic (BPVE) model of articular cartilage is presented. Development of the method is based on a composite Gauss-Legendre quadrature approximation of the continuous spectrum relaxation function that leads to an exponential series representation. The separability property of the exponential terms in the series is exploited to develop a numerical scheme that can be reduced to an update rule requiring retention of the strain history at only the previous time step. The cost of the resulting temporal discretization scheme is O(N) for N time steps. Application and calibration of the method is illustrated in the context of a finite difference solution of the one-dimensional confined compression BPVE stress-relaxation problem. Accuracy of the numerical method is demonstrated by comparison to a theoretical Laplace transform solution for a range of viscoelastic relaxation times that are representative of articular cartilage.
机译：提出了一种新的数值方法，用于数值模拟关节软骨连续谱双相粘弹性（BPVE）模型。该方法的开发基于连续谱弛豫函数的复合高斯-勒格德勒正交逼近，可得出指数级数表示。利用系列中指数项的可分离性来开发一种数值方案，该方案可以简化为仅在前一个时间步就需要保留应变历史的更新规则。对于N个时间步长，所得的时间离散方案的成本为O（N）。在一维受限压缩BPVE应力松弛问题的有限差分解决方案的背景下，说明了该方法的应用和校准。通过与代表关节软骨的一系列粘弹性弛豫时间的理论Laplace变换解决方案进行比较，证明了数值方法的准确性。

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