This contribution proposes the first 3D beam-to-beam interaction model for molecular interactions between curved slender fibers undergoing large deformations. While the general model is not restricted to a specific beam formulation, in the present work it is combined with the geometrically exact beam theory and discretized via the finite element method. A direct evaluation of the total interaction potential for general 3D bodies requires the integration of contributions from molecule or charge distributions over the volumes of the interaction partners, leading to a 6D integral (two nested 3D integrals) that has to be solved numerically. Here, we propose a novel strategy to formulate reduced section-to-section interaction laws for the resultant interaction potential between a pair of cross-sections of two slender fibers such that only two 1D integrals along the fibers' length directions have to be solved numerically. This section-to-section interaction potential (SSIP) approach yields a significant gain in efficiency, which is essential to enable the simulation of relevant time and length scales for many practical applications. In a first step, the generic structure of SSIP laws, which is suitable for the most general interaction scenario (e.g. fibers with arbitrary cross-section shape and inhomogeneous atomic/charge density within the cross-section) is presented. Assuming circular, homogeneous cross-sections, in a next step, specific analytical expressions for SSIP laws describing short-range volume interactions (e.g. van der Waals or steric interactions) and long-range surface interactions (e.g. Coulomb interactions) are proposed. The validity of the SSIP laws as well as the accuracy and robustness of the general SSIP approach to beam-to-beam interactions is thoroughly verified by means of a set of numerical examples considering steric repulsion, electrostatic or van der Waals adhesion.

中文翻译：

---

经历大 3D 变形的弯曲细长纤维之间的分子相互作用的计算模型，重点是静电、范德华力和空间排斥力

这一贡献提出了第一个 3D 光束到光束相互作用模型，用于经历大变形的弯曲细长纤维之间的分子相互作用。虽然一般模型不限于特定的梁公式，但在目前的工作中，它与几何精确的梁理论相结合，并通过有限元方法进行离散化。对一般 3D 物体的总相互作用势的直接评估需要对相互作用伙伴体积上的分子或电荷分布的贡献进行积分，从而导致必须以数值方式求解的 6D 积分（两个嵌套的 3D 积分）。这里，我们提出了一种新策略，为两个细长纤维的一对横截面之间的合成相互作用势制定简化的截面到截面相互作用定律，以便仅需要对沿纤维长度方向的两个一维积分进行数值求解。这种部分到部分的相互作用势 (SSIP) 方法显着提高了效率，这对于在许多实际应用中模拟相关时间和长度尺度至关重要。在第一步中，介绍了 SSIP 定律的通用结构，它适用于最一般的相互作用场景（例如，具有任意横截面形状和横截面内不均匀的原子/电荷密度的纤维）。假设圆形、均匀的横截面，在下一步中，提出了描述短程体积相互作用（例如范德华或空间相互作用）和长程表面相互作用（例如库仑相互作用）的 SSIP 定律的特定分析表达式。通过考虑空间排斥、静电或范德华附着力的一组数值示例，彻底验证了 SSIP 定律的有效性以及一般 SSIP 方法对束对束相互作用的准确性和稳健性。