A fixed-stress splitting method for nonlinear poroelasticity

IF 8.7 2区 工程技术 Q1 Mathematics
Johannes Kraus, Kundan Kumar, Maria Lymbery, Florin A. Radu
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引用次数: 0

Abstract

In this paper we consider a nonlinear poroelasticity model that describes the quasi-static mechanical behaviour of a fluid-saturated porous medium whose permeability depends on the divergence of the displacement. Such nonlinear models are typically used to study biological structures like tissues, organs, cartilage and bones, which are known for a nonlinear dependence of their permeability/hydraulic conductivity on solid dilatation. We formulate (extend to the present situation) one of the most popular splitting schemes, namely the fixed-stress split method for the iterative solution of the coupled problem. The method is proven to converge linearly for sufficiently small time steps under standard assumptions. The error contraction factor then is strictly less than one, independent of the Lamé parameters, Biot and storage coefficients if the hydraulic conductivity is a strictly positive and Lipschitz-continuous function.

Abstract Image

非线性孔弹性的定应力分裂方法
在本文中,我们考虑了一种非线性孔弹性模型,该模型描述了渗透性取决于位移发散的流体饱和多孔介质的准静态力学行为。这种非线性模型通常用于研究组织、器官、软骨和骨骼等生物结构,这些结构的渗透率/液压传导性与固体扩张呈非线性关系。我们制定了(扩展到当前情况下的)一种最流行的分割方案,即用于迭代求解耦合问题的固定应力分割法。在标准假设条件下,该方法可在足够小的时间步长内线性收敛。如果水力传导性是严格的正函数和 Lipschitz 连续函数,则误差收缩因子严格小于 1,与 Lamé 参数、Biot 和存储系数无关。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Engineering with Computers
Engineering with Computers 工程技术-工程:机械
CiteScore
16.50
自引率
2.30%
发文量
203
审稿时长
9 months
期刊介绍: Engineering with Computers is an international journal dedicated to simulation-based engineering. It features original papers and comprehensive reviews on technologies supporting simulation-based engineering, along with demonstrations of operational simulation-based engineering systems. The journal covers various technical areas such as adaptive simulation techniques, engineering databases, CAD geometry integration, mesh generation, parallel simulation methods, simulation frameworks, user interface technologies, and visualization techniques. It also encompasses a wide range of application areas where engineering technologies are applied, spanning from automotive industry applications to medical device design.
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