An orthotropic viscoelastic material model for passive myocardium: theory and algorithmic treatment
An orthotropic viscoelastic material model for passive myocardium: theory and algorithmic treatment
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DOI：
10.1080/10255842.2014.881475
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发表时间：
2015-08-18
影响因子：
1.6
通讯作者：
Kaliske, Michael
中科院分区：
文献类型：
--
作者：
Cansiz, F. Baris Can;Dal, Huesnue;Kaliske, Michael
这一贡献提出了一种新颖的本构模型，以模拟有限应变下被动心肌的正交各向异性速率依赖性行为。在本构水平上考虑正交各向异性粘性效应的动机在于理论预测与实验观察结果之间的不一致。根据实验观察，该材料被认为是几乎不可压缩、超弹性、正交各向异性和粘性的。粘弹性响应通过流变模型来表达，该模型由弹簧与并联的麦克斯韦元件组成。在这种情况下，等容自由能函数被分解为弹性平衡部分和粘性非平衡部分。基线弹性响应由 Holzapfel 和 Ogden 的正交各向异性模型建模 [Holzapfel GA，Ogden RW。 2009.被动心肌的本构模型：基于结构的材料表征框架。 Philos Trans Roy Soc A 数学物理工程科学。 367：3445-3475]。所提出的模型的本质方面是考虑每个方向的不同松弛机制。为此，自由能函数的非平衡响应在对数应变空间中构建，并附加地分解为三个各向异性部分，表示纤维、片材和法线方向，每个部分都伴随着不同的耗散势，控制与每个方向相关的粘性应变的演化。控制粘性流的演化方程具有能量激活的非线性形式。麦克斯韦分支中的能量存储具有二次形式，导致对数应变空间中的线性应力-应变响应。在数值方面，在拉格朗日设置中讨论了适合隐式有限元方法的算法方面。与从文献中获得的实验数据相比，该模型表现出极好的一致性。此外，使用所提出的模型进行的心脏周期的有限元模拟显示应变场相对于弹性解存在显着偏差。
This contribution presents a novel constitutive model in order to simulate an orthotropic rate-dependent behaviour of the passive myocardium at finite strains. The motivation for the consideration of orthotropic viscous effects in a constitutive level lies in the disagreement between theoretical predictions and experimentally observed results. In view of experimental observations, the material is deemed as nearly incompressible, hyperelastic, orthotropic and viscous. The viscoelastic response is formulated by means of a rheological model consisting of a spring coupled with a Maxwell element in parallel. In this context, the isochoric free energy function is decomposed into elastic equilibrium and viscous non-equilibrium parts. The baseline elastic response is modelled by the orthotropic model of Holzapfel and Ogden [Holzapfel GA, Ogden RW. 2009. Constitutive modelling of passive myocardium: a structurally based framework for material characterization. Philos Trans Roy Soc A Math Phys Eng Sci. 367:3445-3475]. The essential aspect of the proposed model is the account of distinct relaxation mechanisms for each orientation direction. To this end, the non-equilibrium response of the free energy function is constructed in the logarithmic strain space and additively decomposed into three anisotropic parts, denoting fibre, sheet and normal directions each accompanied by a distinct dissipation potential governing the evolution of viscous strains associated with each orientation direction. The evolution equations governing the viscous flow have an energy-activated nonlinear form. The energy storage in the Maxwell branches has a quadratic form leading to a linear stress-strain response in the logarithmic strain space. On the numerical side, the algorithmic aspects suitable for the implicit finite element method are discussed in a Lagrangian setting. The model shows excellent agreement compared to experimental data obtained from the literature. Furthermore, the finite element simulations of a heart cycle carried out with the proposed model show significant deviations in the strain field relative to the elastic solution.