A damaged non homogeneous Timoshenko beam model for a dam subjected to the aging effects due to diffusion of a fluid

A variational method [1] for a non homogeneous Timoshenko beam model with the inclusion of the phenomenon of the aging damage due to the diffusion of a aging fluid is proposed.In addition to the classic kinematic descriptors, such as the axial dispacement w, the transversal displacement u and the rotation q of the section, also the concentration c of the aging fluid for every section of the beam and the damage w [2] have been considered.The effects of the damping, by means of a proper Rayleigh functional, has been considered introducing damping factors.The investigated example is a dam that is subjected not only to distributed forces and couples but also to the distributed dual of the concentration ( ), that drives the incoming flow of the aging fluid, that is, for this purpose coupled with the damage evolution.As an outlook we will consider the 2D and 3D cases within granular micromechanics.