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.