On the brittle fracture of a pin-jointed frame

Abstract

The aim of the paper is to report some preliminary results concerning rupture through damage accumulation of a simple pin-jointed frame under tension. Under the elastic and stationary creep conditions (at small strains) this is a well-known problem of strength of material and mathematical theory of creep. Here we assume additionally that damage also evolves in the rods, obeying the classical Kachanov's law, which essentially complicates the problem. In the brittle case, the only one, considered in detail in this paper, the problem is formulated eventually as a coupled nonlinear system of differential equations for the damage variables in the rods. This system, in general, does not admit a close form analytical solution unlike the classical examples of continuum damage mechanics, so that numerical treatment is needed. That is why the special bu realistic case of a common "damage exponent" of the rods is only considered and a simple explicit solution for the damage evolution is found and discussed in more detail.