Size Effect Of Bending Performance Of Quasi-brittle Materials Such As Concrete On Cosserat Theory

ABSTRACT:Quasi-brittle materials such as concrete have mechanical properties such as high compressive strength,weak tensile strength,and brittle fracture.A large number of experimental results show that there is a significant size effect on bending performance of quasi-brittle materials,that is,as the size of the specimen increases,its bending performance will gradually decreases.However,according to classical continuum theory,this phenomenon cannot be explained.The Cosserat continuum theory is a generalized continuum theory developed on classical continuum theory.The intrinsic size parameters of the material are introduced in the physical equations,so the size effect of the bending performance of quasi-brittle materials can be solved.The research content and main results of this paper are as follows:(1)Based on Cosserat linear elasticity theory,the maximum tensile stress failure criterion was adopted and a method for determining the intrinsic size of a quasi-brittle material was proposed.By numerically simulating bending test specimens of concrete and other quasi-brittle materials and comparing them with experimental results,the values of the intrinsic size parameters of the five quasi-brittle materials of zirconia ceramics,alumina ceramics,nuclear graphite,fiber reinforced plastics and concrete were determined.(2)Considering that the bending failure of the quasi-brittle materials is accompanied with a certain deformation and energy release,the material in the bent tension region has already entered plasticity.Therefore,in accordance with the principle of equivalent bearing capacity;using the equivalent tensile strength failure criterion considering partial plasticity,the values of intrinsic size parameters of five quasi-brittle materials such as concrete were further revised.(3)By numerically simulating the bending performance of quasi-brittle materials with different sizes,it is verified that the Cosserat numerical solution considering the intrinsic size parameters is more consistent with the experimental results,and it also shows that the Cosserat theory makes up for the shortcomings of the classical continuum theory and can explain the size effect phenomenon of quasi-brittle material bending performance.(4)Cosserat finite element numerical model was used to numerically simulate the size parameters of the quasi-brittle materials such as concrete from the microscopic and macroscopic scales.The influence of dimensional parameters on the bending performance of concrete and other quasi-brittle materials was studied.The results show that the bending property increases with the increase of the dimensionless ratio of the intrinsic size to the specimen height.And at the meso-level,the bending strength and bending stiffness of the material gradually increase with the increase of intrinsic size,and at the macroscopic level,the height of the specimen has significant influence on the size effect of bending performance,while the span has little effect on the size effect of bending performance.(5)Based on the finite element model of Cosserat theory,numerical simulation equations of the size effect of the nominal bending strength and the nominal bending stiffness of five quasi-brittle materials such as concrete were obtained.