# Multiscale modeling of spider dragline silk

• Multiskalenmodellierung von Spinnenseide

Spider dragline silk features an unusual combination of high strength, extensibility and stiffness, which outperforms some of the best materials known in terms of its mechanical performance. It is as strong as high-carbon steel, has a higher extensibility than the best commercial nylon filaments, and is tougher than Kevlar. For these reasons, dragline silk serves as a benchmark of modern polymer fiber technology, and the mass-production of a biomimetic material is of high interest. Developing artificial silk, however, requires a better understanding of the underlying molecular structure of silk that leads to the mechanical properties and the mechanism by which nature assembles this structure.Therefore, the aim of this research work is to understand the unique mechanical properties of spider silk fibers using a bottom-up computational approach. The threads of the European garden spider ${\textit{Araneus diadematus}}$, the most studied spider species, was considered for this work, more specifically the dragline spider silk. The hierarchical structure of dragline silk is composed of two major constituents, the amorphous phase and crystalline units, and its mechanical response has been attributed to these prime constituents. First, the mechanical behavior of the stiff crystalline units were analyzed from previous all atom simulations, and incorporated into finite element simulations. It is found that the strength of a silk fiber is mainly due to the embedded crystalline units, which are acting as crosslinks of silk proteins in the fiber. In contrast to crystalline units, the large extensibility and viscous behavior as evidenced by the time-dependency of silk mechanics in tensile loading is originated from the amorphous phase due to sliding of peptide chains, i.e., internal molecular friction. Beside these two major constituents of spider dragline silk, silk mechanics might also be influenced by the resistance against sliding of these two phases relative to each other under load. It is found that a perfectly relative horizontal motion has no significant resistance against sliding, however, slightly inclined loading causes measurable resistance. On the basis of modeling and numerical analysis of constituents of dragline silk, a three dimensional finite element model of a silk fiber is proposed. It is based on the secondary structure of the ${\textit{Araneus diadematus}}$ silk fiber, taking into account the plasticity of the $\beta$-sheet crystals as well as the viscous behavior of the amorphous matrix. The mechanical properties such as strength, extensibility, initial stiffness, post-stiffness, and toughness obtained from the finite element simulations show excellent agreement with available experimental data. An initially random distribution of crystals in the fiber silk rearranges during deformation, and forms a lamellar-like arrangement of the phases, which results in a high toughness.This work provides a fundamental understanding of silk's exceptional performance by linking the molecular properties and mechanisms to its macroscale mechanical behavior. The proposed computational models that encompass structure and mechanics at different scales in a bottom-up fashion, can assist the design of new materials that mimic and exceed the properties of biological analogs.