This article proposes a novel computational modeling approach for short-ranged molecular interactions between curved slender fibers undergoing large 3D deformations, and gives a detailed overview how it fits into the framework of existing fiber or beam interaction models, either considering microscale molecular or macroscale contact effects. The direct evaluation of a molecular interaction potential between two general bodies in 3D space would require to integrate molecule densities over two 3D volumes, leading to a sixfold integral to be solved numerically. By exploiting the short-range nature of the considered class of interaction potentials as well as the fundamental kinematic assumption of undeformable fiber cross-sections, as typically applied in mechanical beam theories, a recently derived, closed-form analytical solution is applied for the interaction potential between a given section of the first fiber (slave beam) and the entire second fiber (master beam). This novel approach based on a pre-defined section-beam interaction potential (SBIP) requires only one single integration step along the slave beam length to be performed numerically. In terms of accuracy, the total beam-beam interaction potential resulting from this approach is shown to exhibit an asymptotically consistent angular and distance scaling behavior. In addition to elementary two-fiber systems, carefully chosen to verify accuracy and asymptotic consistence of the proposed SBIP approach, a potential practical application in form of adhesive nanofiber-grafted surfaces is studied. Involving a large number of helicoidal fibers undergoing large 3D deformations, arbitrary mutual fiber orientations as well as frequent local fiber pull-off and snap-into-contact events, this example demonstrates the robustness and computational efficiency of the new approach.
翻译:文章提出一个新的计算模型方法, 用于正在发生大型 3D 变形的曲线细细纤维之间的短距离分子互动, 并详细概述它如何适应现有纤维互动模型或梁互动模型的框架, 考虑微尺度分子效应或宏观接触效应。 对3D 空间中两个普通身体之间的分子互动潜力进行直接评估, 需要将两个3D 卷中的分子密度整合在一起, 从而产生一个六倍的内在组成部分, 需要用数字解析。 通过利用所考虑的相互作用潜力类别的短距离性以及不可变的纤维交叉剖面的基本动态假设, 通常适用于机械光学理论, 最近产生的、 封闭式分析解决方案用于第一组纤维( lave beam) 特定部分与整个第二纤维( 方向) 之间的互动潜力。 这种基于预定义的节流本地互动潜力( SBIP) 的新方法只需要在奴隶长度上迈出一个单一的整合步骤。 从精确度、 直径直径直径直径直行的直径直径直径和直径直径直径直径直径直径直径直径直行, 直到直径直径直径直径直径直径直至直至直至直径直径直径直至直至直径直径直至直至直至直至直至直至直至直直直直至直至直至直向直至直至直至直至直至直直直向直行, 直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直