Mesomechanics of deformation and short-term damage of linear elastic homogeneous and composite materials

The structural theory of microdamage of homogeneous and composite materials is generalized. The theory is based on the equations and methods of the mechanics of microinhomogeneous bodies with stochastic structure. A single microdamage is modeled by a quasispherical pore empty or filled with particles of a damaged material. The accumulation of microdamages under increasing loading is modeled as increasing porosity. The damage within a single microvolume is governed by the Huber-Mises or Schleicher-Nadai failure criterion. The ultimate strength is assumed to be a random function of coordinates with power-law or Weibull one-point distribution. The stress-strain state and effective elastic properties of a composite with microdamaged components are determined using the stochastic equations of elasticity. The equations of deformation and microdamage and the porosity balance equation constitute a closed-form system of equations. The solution is found iteratively using conditional moments. The effect of temperature on the coupled processes of deformation and microdamage is taken into account. Algorithms for plotting the dependences of microdamage and macrostresses on macrostrains for composites of different structure are developed. The effect of temperature and strength of damaged material on the stress-strain and microdamage curves is examined