Abstract
In this paper we analyse static properties of mass spring models (MSMs) with the focus of modelling non crystalline materials, and explore basic improvements, which can be made to MSMs with disordered point placement. Presented techniques address the problem of high variance of MSM properties which occur due to randomised nature of point distribution. The focus is placed on tuning spring parameters in a way which would compensate for local non-uniformity of point and spring density. We demonstrate that a simple force balancing algorithm can improve properties of the MSM on a global scale, while a more detailed stress distribution analysis is needed to achieve local scale improvements. Considered MSMs are three dimensional.
Highlights
That condition (a) does not apply to the nodes which lie on the border of the mass spring models (MSMs), where forces will sum to a value that counteracts the outside pressure
Since we have identified that in uniform compression the force exerted by a spring equals F = −kLe, our first attempt at improving accuracy of random MSMs could be by setting the stiffness coefficients of the springs in such way that kL = const
We have demonstrated possible accuracy problems one may face when using disordered MSMs
Summary
If the numerical model has a regular, lattice-like topology which determines the potential crack placement, it creates “easy propagation planes” for cracks (whether it is based on MSM or FEM, or some other modelling technique) In such models cracks tend to form and propagate along lattice dependent directions and resulting patterns may reflect lattice properties instead of material ones (Figure 2). Presented techniques allow to improve both global and local behaviour of disordered mass-spring networks It should be noted, that we investigate only the static properties of MSMs. We do not address here the question of how these systems evolve over time or what are the most efficient numerical schemes to track their dynamics. Efficient ways of simulating the dynamics can be found e.g., in [18,19]
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