In this paper, we present a computational framework based on fully Eulerian models for fluid–structure interaction for the numerical simulation of biological capsules. The flexibility of such models, given by the Eulerian treatment of the interface and deformations, allows us to easily deal with the large deformations experienced by the capsule. The modeling of the membrane is based on a full membrane elasticity Eulerian model that is capable of capturing both area and shear variations thanks to the so-called backward characteristics. In the validation section several test cases are presented with the goal of comparing our results to others present in the literature. In this part, the comparisons are done with different well-known configurations (capsule in shear flow and square-section channel), and by deepening the effect of the elastic constitutive law and capillary number on the membrane dynamics. Finally, to show the potential of this framework we introduce a new test case that describes the relaxation of a capsule in an opening channel. In order to increase the challenges of this test we study the influence of an internal nucleus, modeled as a hyperelastic solid, on the membrane evolution. Several numerical simulations of a 3D relaxation phenomenon are presented to provide characteristic shapes and curves related to the capsule deformations, while also modifying size and stiffness parameter of the nucleus.

中文翻译：

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用于具有弹性体核的胶囊数值模拟的完全欧拉模型

在本文中，我们提出了一种基于完全欧拉模型的流固耦合计算框架，用于生物胶囊的数值模拟。通过对界面和变形进行欧拉处理，此类模型具有灵活性，使我们能够轻松处理胶囊所经历的大变形。膜的建模基于全膜弹性欧拉模型，由于所谓的后向特性，该模型能够捕获面积和剪切变化。在验证部分，提出了几个测试用例，目的是将我们的结果与文献中的其他结果进行比较。在这一部分中，通过深化弹性本构定律和毛细管数对膜动力学的影响，对不同的众所周知的构型（剪切流中的胶囊和方形截面通道）进行了比较。最后，为了展示该框架的潜力，我们引入了一个新的测试用例，该测试用例描述了开放通道中胶囊的松弛。为了增加该测试的挑战，我们研究了模拟为超弹性固体的内核对膜演化的影响。提出了几种 3D 弛豫现象的数值模拟，以提供与胶囊变形相关的特征形状和曲线，同时还修改核的尺寸和刚度参数。