Establishment Of Finite Element Model And Study On Size Effect Of Concrete Flexural Strength Based On Plane Cosserat Theory

Although the classical continuum theory has made great achievements in engineering practice,there are obvious limitations in describing the mechanical properties of materials at different scales,such as macro and micro scale,which can not explain the size effect under different scale.The Cosserat continuum theory is a kind of micropolar continuum mechanics which is different from the traditional continuum theory.It treats the object as a continuous distribution of micropolar particles which have a certain size and the intrinsic scale of material is introduced into the physical equation,thus the relationship between macro scale and meso scale is established.Therefore,when the Cosserat continuum theory is used to analyze the mechanical properties of micrometer scale or macroscopic scale composed of granular materials,it shows high precision and good simulation effect.The main contents and achievements of this paper are as follows:(1)The equilibrium equations,geometric equations and physical equations of general Cosserat theory for plane problems are derived,the Cosserat finite element model of quadrilateral eight node is constructed of which the line displacement and rotation angle are independent of each other.The FORTRAN language is used to compile and adjust the numerical simulation program CFEM.The numerical simulation of the pure bending cantilever beam is simulated,the numerical solution is compared with the analytical solution based on the classical elastic theory and the numerical solution of ANSYS which is a general finite element software,the correctness of Cosserat finite element model and program is verified.(2)On the basis of general Cosserat theory,when the micro angle of the micro particles is neglected,and the angular displacement is not equal to the macroscopic angular displacement,then the theory is reduced to the constrained rotational Cosserat theory.In this paper,the basic equations of the constrained rotational Cosserat theory are derived,the stress component is taken as the basic unknown function to solve the pure bending of rectangular beam,and the corresponding stress solution is given.(3)The finite element program CFEM is used to simulate the pure bending cantilever beam,the effects of different intrinsic parameters and macro dimensions on the mechanical properties of the components are studied.Research shows that,the couple stress is constant along the cross section,with the increase of the intrinsic size,the couple stress increases gradually,and the vertical displacement,the rotation angle and the normal stress in the mid-span section decrease gradually.When the intrinsic dimension is constant,with the increase of the macro dimension,the normal stress at the lower edge of the mid-span section increases gradually.(4)The numerical simulation of concrete flexural members is carried out by the program CFEM,the value of intrinsic size parameters of different strength grades of concrete is studied,and the reasonable range of value is determined.(5)The size effect of flexural strength of concrete is studied by numerical simulation.Research shows that,the smaller the ratio of the minimum macro size to the intrinsic length is,the more obvious the size effect is;The bigger the ratio is,the weaker the size effect is.The higher the concrete strength is,the more obvious the size effect is.