Localization of Strain in a Softening Bar

In the preceding section we obtained some general results concerning a series coupling of discrete elements, for which the reasoning is somewhat easier than for a continuous bar. Now let us discuss the behavior of a uniaxially stressed bar of a homogeneous material.

It may appear that using a classical stress-strain formulation including softening is a natural way to introduce fracture (loss of strength down to zero). However, this is not straightforward. If no other precaution is taken, the resulting model is both physically incorrect and numerically ill-posed. I. et us see why.