Thermo-Inelasticity and Damage: Coupling of Damage and Internal Friction

Damage in quasi-brittle materials takes place progressively with a nonlinear response and greater strength under compression than tension. This damage behavior may be interpreted as an effect of micro-crack nucleation and growth inside an elastic matrix. Because these materials sustain mainly compressive stresses, the resulting stress field in the microstructure turns out to be compressive and the opposite edges of the micro- cracks are closed. Because of the roughness of the micro-crack edges, their contact is characterized by friction that is coupled with damage mecha- nisms. Consequently, the mechanical response of these materials to compressive stress states is nonlinear and dissipative due to the simultaneous presence of two coupled deformation processes consisting of the progressive propagation of micro-cracks together with the frictional sliding between the crack faces. This interpretation of the micro-crack effects on the mechanisms of inelas- tic deformation makes clear the role of internal friction on vibration damping, rather than being due to the viscoelastic phase in the material. The hysteretic response of some quasi-brittle mate- rials is shown and the micro-cracked model with internal friction is described in a simplified ver- sion in order to clarify the role of the damage and internal friction.