Damage model with delay effect: Analytical and numerical studies of the evolution of the characteristic damage length

This paper studies the delayed damage model in a one-dimensional transient analysis. It is well-known that kind of model prevents the mesh dependency when it is used in a finite element code. The model problem concerns a clamped uniaxial damage elastic bar submitted to a step load at its extremity. In order to guarantee the correct behaviour of the model and to be able to choose the appropriate mesh size before performing a finite element calculation, an analytical evaluation of the size of the damaged zone called characteristic length is given and compared to the converged numerical results. Finally, a two-dimensional example is treated with a damage with or without the delay effect.