基于全隐式嵌套牛顿求解器的生物力学问题求解算法

IF 0.7 Q4 MECHANICS Theoretical and Applied Mechanics Pub Date : 2022-01-01 DOI:10.2298/tam221115012k
Markus M. Knodel, Stefano Di, A. Nägel, A. Grillo
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引用次数: 0

摘要

软体生物组织动力学的数值模拟是非常重要的,因为组织通常对外部和内部的作用表现出复杂的生物反应,包括大的变形和重塑。结合全局隐式方法(GIA)的优点和半隐式广义塑性算法(GPA)的通用性,我们提出了一种新的、高效的塑性算法,我们称之为生物力学基础塑性算法(BMBPA)。这是完全隐式的,基于嵌套牛顿求解器,自然适合大规模并行计算。Bilby-Kr吗?采用变形梯度张量的ner-Lee (BKL)乘法分解引入模型的未知量。我们区分全局和局部未知数,与局部方程和全局方程相关联,它们通过解析函数连接。BMBPA要求的应用条件很少,因此可以很容易地用于解决几种类型的生物学和生物力学问题。我们通过对纤维增强组织的单相模型进行两个数值实验来证明BMBPA的有效性。在一种情况下,我们考虑剪切压缩试验的一个立方的组织标本,而在另一种情况下,我们集中在一个圆柱体的无侧限压缩试验。BMBPA计算各向异性生物组织的变形和重塑只需几个小时,而GPA计算相同问题所需的时间要长得多。所有计算都是并行进行的,在所有测试中,BMBPA的性能明显高于GPA的性能。我们的模拟结果允许研究所考虑组织的整体力学行为,并使组织生物力学领域的进一步研究成为可能。
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An efficient algorithm for biomechanical problems based on a fully implicit nested Newton solver
Numerical simulations of the dynamics of soft biological tissues are highly non-trivial because tissues generally exhibit complex biological response to external and internal actions, including large deformations and remodeling. Combining the advantages of globally implicit approach (GIA) solvers with the general applicability of the semi-implicit General Plasticity Algorithm (GPA), introduced by some of us some years ago, we present a new, efficient plasticity algorithm, which we call Bio Mechanics Basis Plasticity Algorithm (BMBPA). This is fully implicit, based on a nested Newton solver, and naturally suited for massively parallel computations. The Bilby-Kr?ner-Lee (BKL) multiplicative decomposition of the deformation gradient tensor is employed to introduce the unknowns of our model. We distinguish between global and local unknowns, associated with local and global equations, which are connected by means of a resolution function. The BMBPA asks for very few conditions to be applied and thus can be easily employed to solve several types of biological and biomechanical problems. We demonstrate the efficacy of BMBPA by performing two numerical experiments of a monophasic model of fiber-reinforced tissues. In one case, we consider the shear-compression test of a cubic specimen of tissue, while, in the other case, we focus on the unconfined compression test of a cylinder. The BMBPA is capable of solving the deformation and the remodeling of anisotropic biological tissues by employing a computation time of hours, while the GPA, applied to the same problems as the BMBPA, needs a substantially longer amount of time. All computations were performed in parallel and, within all tests, the performance of the BMBPA displayed substantially higher than the one of the GPA. The results of our simulations permit to study the overall mechanical behavior of the considered tissue and enable further investigations in the field of tissue biomechanics.
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来源期刊
CiteScore
0.90
自引率
0.00%
发文量
4
审稿时长
32 weeks
期刊介绍: Theoretical and Applied Mechanics (TAM) invites submission of original scholarly work in all fields of theoretical and applied mechanics. TAM features selected high quality research articles that represent the broad spectrum of interest in mechanics.
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