Plastic Damage Model Of Concrete Based On Strain Gradient Theory And Size Effect Of Compressive Strength

Compressive strength is one of the important basic mechanical properties of concrete.A large number of experimental studies show that the compressive strength of concrete decreases with the increase of specimen size,and there is an obvious size effect.However,the classical continuum theory cannot explain this phenomenon.Strain gradient theory is a new theory developed to explain the phenomenon of size effect of materials at mesoscale.On the basis of the classical continuum theory,the effect of strain gradient is considered,and the intrinsic size of the material is introduced.In this paper,the plastic strain gradient is taken into account in concrete yield function and intrinsic dimension,and for the crack of concrete introduction of concrete damage constitutive relation,based on concrete damage mechanics model of plastic strain gradient theory,the finite element numerical analysis program,the analysis of concrete compressive strength size effect rule.The main contents and achievements of this paper are as follows:(1)based on the generalized continuum theory,the equilibrium equation,geometric equation and constitutive equation of the strain gradient theory for plane problems are derived systematically.And the strain gradient in the yield function,considering the influence of the adjacent point to its itself hardening parameter,adopt the method of weighted average in adjacent area will include intrinsic size and plastic strain gradient of the hardening parameter is introduced into the yield function,contains material intrinsic dimension parameters was deduced and the plastic yield model in terms of strain gradient.On this basis,the yield function of Mises,Drucker-Prager and Mohr-Coulumb and the constitutive relation of gradient plasticity are derived.(2)describe the development of concrete cracks and the phenomenon that the concrete at the cracks gradually loses the bearing capacity and exits the work,and describe the concrete stiffness degradation phenomenon with damage parameters.Meanwhile,the stress damage model of concrete,Loand model,Mazars model,piecewise linear model,piecewise curve model and bifold line model were analyzed and applied to the finite element model.(3)the finite element solution format was established based on the principle of minimum potential energy,so as to establish the concrete damage model based on the theory of plastic strain gradient.The finite element program was compiled in Fortran,and the concrete compression specimen was simulated numerically.Considering the intrinsic dimensional parameters of the material,the numerical results are in good agreement with the experimental results,so as to verify that the plastic strain gradient theory concrete damage model can effectively solve the phenomenon of concrete compressive strength size effect.(4)through the comparative analysis between the simulated value and the experimental value of the finite element model,the values of the intrinsic size parameters of concrete with different grades were studied,and the reasonable value range was determined.The influence of the composition of concrete materials on the intrinsic size parameters was also studied.(5)By numerical simulation analysis,the influence of size parameters(including the intrinsic size of micro materials and the size of macro structures)on the compressive strength is analyzed.The results show that when the macroscopic size of the specimen remains unchanged,the larger the intrinsic size parameter is,the higher the compressive strength of the concrete will be,which reflects the influence of the internal microstructure of the material on the compressive strength.When the composition of concrete material remains unchanged,that is,when the intrinsic size value is maintained,the larger the specimen size is,the lower the compressive strength of concrete will be.