Fatigue Modelling With A Two-Dimensional Spring Network

Abstract

A random periodic two-dimensional spring network us built using a Poisson disk distribution and computing the Delaunay triangulation of the centers of the disks. The edges of the network represent springs that obey Hooke’s law with an adjustment on the spring constant. The adjustment allows spring to soften and to break. The two-dimensional spring network can, in combination with the adjustment, be used to model fatigue. The network softens during a cyclic loading. During each cycle the normal strain is increased until the normal stress equals a specific cyclic stress σcycle. The loading is continued until the network is broken into two pieces, with a number of N completed cycles. For a range of cyclic stresses the number of cycles before failure N is calculated and fitted with an exponential relation. The fitting parameters for networks with #n = 32 are similar to those of a networks with #n = 64. Throughout the cyclic loading springs will break and as a result the coordination of ¨ the network decreases. The coordination of the network can drop below 4. These ¨ networks are hypostatic, while the initial network was hyperstatic. This claim is asserted by the stress-strain curve. The transition from hyperstatic to hypostatic leads to a conceptual question: ”Is the spring network broken if it has teared into two pieces or when it is hypostatic?”.