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In this proposed research, the time response of a beam structure containing a sharp crack and subjected to a time varying loading is considered. In overcoming known crack surface closure difficulties, a process of material homogenization is proposed aiming at establishing the effective orthotropic, non linear mechanical response of the cracked domain. Robust geometry meshing algorithms are developed and used in conducting fundamental numerical finite element homogenization studies. Crack surface closure effects are addressed and comparisons to known analytical, numerical and experimental results will be carried out. In addition to the above, an eigenvalue approach as well as a time dependent response method are considered as a means of evaluating the response of cracked structures.