On the mechanics of continua with boundary energies and growing surfaces.
On the mechanics of continua with boundary energies and growing surfaces.
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DOI：
10.1016/j.jmps.2013.01.007
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发表时间：
2013-06-01
影响因子：
5.3
通讯作者：
Kuhl E
中科院分区：
文献类型：
--
作者：
Papastavrou A;Steinmann P;Kuhl E
许多生物系统都被薄膜覆盖，用于保护、选择性吸收或跨膜转运。典型的例子是覆盖气道、食道和肠的粘膜。生物表面通常显示出与本体不同的机械行为;特别是，它们可以以不同的速率生长。生物表面的生长、形态不稳定性和屈曲已经通过将表面近似为有限厚度的层而得到了深入的研究;然而，生长从来没有归因于表面本身。在这里，我们建立了一个理论的连续与边界能量和生长表面的零厚度，在该表面配备有自己的势能，并允许增长独立的散装。在完全类比的运动方程，平衡方程，和本构方程的增长固体，我们推导出的控制方程的增长表面。我们说明了他们的空间离散使用有限元方法，并讨论了他们一致的算法线性化。为了证明体积和表面生长之间的概念差异，我们模拟了圆柱形管的内层的约束生长。我们的新方法对连续不断增长的表面是能够预测极端增长的内圆柱形表面，其初始面积的两倍以上。底层的算法框架是强大的和稳定的，它允许预测的形态变化，由于表面生长过程中的屈曲和超越。表面生长的建模在哮喘、胃炎、阻塞性睡眠呼吸暂停和肿瘤侵袭的诊断和治疗中具有直接的生物医学应用。除了生物医学应用之外，对生长诱导的形态不稳定性和表面扭曲的科学理解在材料科学、制造和微制造中具有重要意义，并在软光刻、计量和柔性电子学中应用。
Many biological systems are coated by thin films for protection, selective absorption, or transmembrane transport. A typical example is the mucous membrane covering the airways, the esophagus, and the intestine. Biological surfaces typically display a distinct mechanical behavior from the bulk; in particular, they may grow at different rates. Growth, morphological instabilities, and buckling of biological surfaces have been studied intensely by approximating the surface as a layer of finite thickness; however, growth has never been attributed to the surface itself. Here, we establish a theory of continua with boundary energies and growing surfaces of zero thickness in which the surface is equipped with its own potential energy and is allowed to grow independently of the bulk. In complete analogy to the kinematic equations, the balance equations, and the constitutive equations of a growing solid body, we derive the governing equations for a growing surface. We illustrate their spatial discretization using the finite element method, and discuss their consistent algorithmic linearization. To demonstrate the conceptual differences between volume and surface growth, we simulate the constrained growth of the inner layer of a cylindrical tube. Our novel approach towards continua with growing surfaces is capable of predicting extreme growth of the inner cylindrical surface, which more than doubles its initial area. The underlying algorithmic framework is robust and stable; it allows to predict morphological changes due to surface growth during the onset of buckling and beyond. The modeling of surface growth has immediate biomedical applications in the diagnosis and treatment of asthma, gastritis, obstructive sleep apnoea, and tumor invasion. Beyond biomedical applications, the scientific understanding of growth-induced morphological instabilities and surface wrinkling has important implications in material sciences, manufacturing, and microfabrication, with applications in soft lithography, metrology, and flexible electronics.
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影响因子：
5.3
作者：
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通讯作者：
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作者：
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通讯作者：
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DOI：
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发表时间：
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