Deformation and long-term damage of homogeneous and composite materials of stochastic structure (Review)

The studies of mathematical models for the coupled processes of deformation and long-time damage of stochastic composite materials are systematized. Damage is modeled by stochastically arranged micropores. The damage of a single microvolume is characterized by its stress-rupture strength determined by the dependence of the time to brittle fracture on the difference between the equivalent stress and its limit, which is the ultimate strength, according to the Huber–Mises or Schleicher–Nadai criteria, and assumed to be a random function of coordinates. The equation of damage balance at an arbitrary time and the equations relating macrostresses and macrostrains constitute a closed system. Algorithms of calculating the time dependence of microdamage and macrostresses are developed. The effect of temperature and nonlinearity on the curves is studied