In order to verify and test the multi-time step subcycling and dynamic cohesive element insertion algorithms presented in the previous chapter, we first apply them to simple 1-D systems. Problems in 1-D are much simpler to understand and solve, yet they are still valid examples of dynamic fracture problems. The experience gained in 1-D is very important in giving us direction for applying the same algorithms and any newly developed ones to 2-D problems, while minimizing our computational effort and time.
In the beginning of this chapter, we first introduce the reference 1-D problem and its analytical solution. In the sections that follow, we take a parametric approach in applying the subcycling and dynamic cohesive element insertion algorithms to various 1-D problems. Finally, we discuss our observations and conclusions in the last section.