Filters

20182

More filters

20232
Reset filters

Settings

search.filters.applied.f.access: openAccess × Author: Heidemann, Knut M. × End date: 2023 × End date: 2018 × DDC: 530 × Type: Text × WGL Institute: IPF ×

Search Results

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Topology determines force distributions in one-dimensional random spring networks
    (Woodbury, NY : Inst., 2018) Heidemann, Knut M.; Sageman-Furnas, Andrew O.; Sharma, Abhinav; Rehfeldt, Florian; Schmidt, Christoph F.; Wardetzky, Max
    Networks of elastic fibers are ubiquitous in biological systems and often provide mechanical stability to cells and tissues. Fiber-reinforced materials are also common in technology. An important characteristic of such materials is their resistance to failure under load. Rupture occurs when fibers break under excessive force and when that failure propagates. Therefore, it is crucial to understand force distributions. Force distributions within such networks are typically highly inhomogeneous and are not well understood. Here we construct a simple one-dimensional model system with periodic boundary conditions by randomly placing linear springs on a circle. We consider ensembles of such networks that consist of N nodes and have an average degree of connectivity z but vary in topology. Using a graph-theoretical approach that accounts for the full topology of each network in the ensemble, we show that, surprisingly, the force distributions can be fully characterized in terms of the parameters (N,z). Despite the universal properties of such (N,z) ensembles, our analysis further reveals that a classical mean-field approach fails to capture force distributions correctly. We demonstrate that network topology is a crucial determinant of force distributions in elastic spring networks.
  • Thumbnail Image
    Item
    Topology Counts: Force Distributions in Circular Spring Networks
    (College Park, Md. : APS, 2018) Heidemann, Knut M.; Sageman-Furnas, Andrew O.; Sharma, Abhinav; Rehfeldt, Florian; Schmidt, Christoph F.; Wardetzky, Max
    Filamentous polymer networks govern the mechanical properties of many biological materials. Force distributions within these networks are typically highly inhomogeneous, and, although the importance of force distributions for structural properties is well recognized, they are far from being understood quantitatively. Using a combination of probabilistic and graph-theoretical techniques, we derive force distributions in a model system consisting of ensembles of random linear spring networks on a circle. We show that characteristic quantities, such as the mean and variance of the force supported by individual springs, can be derived explicitly in terms of only two parameters: (i) average connectivity and (ii) number of nodes. Our analysis shows that a classical mean-field approach fails to capture these characteristic quantities correctly. In contrast, we demonstrate that network topology is a crucial determinant of force distributions in an elastic spring network. Our results for 1D linear spring networks readily generalize to arbitrary dimensions.