According to character of procession of concrete material having size effect rule,effective crack propagation of concrete was investigated with size effect rule of fracture toughness of concrete,formula of effective crack propagation was obtained which reflected size effect rule,and then effective crack model of multi-crack concrete was obtained which was relative with dimension of the specimen.

According to the results on large scale specimens, an equivalence crack fracture model for large volume concrete is built, linking the stresses attribution on fracture process zone with the softening rules of the main crack when it is steady opening, by means of normalization.

For the two kinds of failing mode, this paper establishes the interface failing model and bundle fracture failing model.

Size effect is the essential property of quasi-brittle materials,All kinds of fracture models of concrete are discussed,joined with Bazant size effect law,the formulas of size effect under different fracture models are achieved.

This paper presents a fracture model of concrete,band damaging crack model (BDCM).

Ice ductile property can be described by damage model and ice brittle property by fracture model.

Elastic equivalent model of complex fiber reinforced plastic pavement deck;

Markov Reliability Equivalent Model of Breakers in Reliability Evaluation of the Main Wirings;

Mechanical properties of MEMS film resonator analyzed by equivalent model;

The results show that a linear relationship between the equivalent fracture strain and the small punch energy is established.