In this dissertation, the solution of boundary value problems for materials with nonlocal behavior has been studied. Eringen's model of nonlocal integral elasticity is considered that it di ?ers from the The rest of the thesis is devoted to modeling of cracked problems with Eringen’s non-local integral model. It is observed that in the static cases with a full non-local behavior (i.e. when ) only some special kernel functions must be used. Afterward, a novel approach was introduced to model crack propagation and crack branching in brittle materials. The method is based on new shape functions, consisting of some modification factors. These shape functions are constructed with standard quadratic Lagrangian shape functions, applicable in collocation based methods. With the aid of the introduced shape functions, any discontinuity could be modeled in the domain only by altering the modification factors. Numerical simulations show the ability of the method in modeling of dynamic crack propagation.
