Theoretical and Experimental Analysis of Longitudinal Vibratory Systems

The simple harmonic motion of a spring mass system generally exhibits a behavior strongly influenced by the geometric parameters of the spring. The application of spring mass systems to the animation of brittle facture is revisited. The motivation arises from the recent popularity of peridynamics in the computational physics community. Peridynamic systems can be regarded as spring mass systems with two specific properties. First spring forces are based on a simple strain metric, thereby decoupling spring stiffness from spring length. Second masses are connected using a distance based criterion. The relatively large radius of influence typically leads to a few hundred springs for every mass point. Spring mass systems with these properties are shown to be simple to implement, trivially parallelized and well suited to animating brittle fracture. This experiments provides the possibility of understanding the differences between theoretical models that include well known corrections to determine the technical terms of a spring mass systems.