Damage Mechanics in a Uniaxially-Loaded Elastic Tapered Bar

The principles of damage mechanics are used to predict the displacements and stresses in a uniaxially-loaded one-dimensional elastic tapered bar. The variation of the damage variable along the length of the bar is studied. A random distribution of the damage variable along the length of the bar is also considered. It is shown how the displacements and stresses are obtained in closed-form solutions whenever possible. Otherwise, finite element analysis is employed to solve the resulting problem. The computer algebra system MAPLE is used to write a symbolic finite element program specifically for this problem with the random distribution of the damage variable for which there is no closed form solution.