Modeling curvature-resisting material surfaces with isogeometric analysis
Modeling curvature-resisting material surfaces with isogeometric analysis
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DOI：
10.1016/j.cma.2022.115649
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发表时间：
2022-11
影响因子：
7.2
通讯作者：
Animesh Rastogi;B. Dortdivanlioglu
中科院分区：
文献类型：
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作者：
Animesh Rastogi;B. Dortdivanlioglu
由于纳米结构、涂层和合成/生物双层聚合物混合物的新兴制造技术，对固体表面能及其在整体机械性能中的作用的理解得到了极大的关注。表面应力的连续数值模拟有效地结合了零厚度膜结合到散装，本质上占表面张力和表面弹性。压缩表面应力是不可能在一个纯粹的膜配方，忽略了表面抗弯。材料表面的延伸以考虑抗弯性，即，Steigmann-Ogden模型需要二阶空间导数，这对标准离散化技术提出了重大挑战。因此，表面曲率阻力对复杂几何形状的整体力学行为的影响仍然难以捉摸。在这里，我们开发了一个三维计算公式的曲率依赖的表面能量在有限的应变，使用表面丰富的等几何分析。与超弹性体相结合，材料表面的抗弯曲性形成了一个新的物理长度尺度，即，弹性弯曲长度。我们量化的弹性弯曲变形的影响，涉及软材料与薄涂层和液体壳表面的几个数值例子，捕捉细胞膜上观察到的出芽样行为。我们的研究结果表明，当材料表面抵抗弯曲变形时，整体力学行为更刚性，并说明曲率效应如何导致非零初始曲率状态下的复杂萌芽变形。所提出的方法提供了一个强大的计算基础，以帮助提高我们的理解和机械特性的软固体，纳米结构和生物膜在小尺度上。
Improved understanding of solid surface energy and its role in the overall mechanical properties is of great interest due to the emerging manufacturing techniques of nanostructures, coatings, and synthetic/biological bilayer–polymer hybrids. Continuum numerical modeling of surface stresses efficiently incorporates a zero-thickness membrane bonded to a bulk, intrinsically accounting for surface tension and surface elasticity. Compressive surface stresses are not possible in a purely membrane formulation, ignoring the surface flexural resistance. The extension of material surfaces to account for flexural resistance, i.e., the Steigmann–Ogden model, requires spatial derivatives of second order, posing significant challenges to standard discretization techniques. Hence, the effect of surface curvature resistance on the overall mechanical behavior of complex geometries remains elusive. Here, we develop a three-dimensional computational formulation of curvature-dependent surface energetics at finite strains using surface-enriched isogeometric analysis. Coupled with a hyperelastic bulk, bending-resistance of material surfaces furnishes a new physical length scale, i.e., the elastobending length. We quantify the effect of elastobending deformations for several numerical examples involving soft materials with thin coatings and liquid-shell surfaces, capturing budding-like behavior observed at cell membranes. Our results demonstrate a stiffer overall mechanical behavior when material surfaces resist bending deformations and illustrate how curvature effects lead to complex budding deformations at non-zero initial curvature states. The proposed methodology provides a robust computational foundation to help improve our understanding and mechanical characterization of soft solids, nanostructures, and biological membranes at small scales.