Elastoplastic-Stochastic Damage Constitutive Model And Numerical Algorithms Of Steel-Polypropylene Hybrid Fiber Concrete

With the development of The Belt and Road Initiative,and the requirement of the infrastructure construction becoming higher and higher,fiber reinforced concrete(FRC),as a new generation of composite material,is gradually replacing traditional concrete as one of the materials widely used in civil engineering,and has become a research hotspot in the field of cement-based composite materials.The research on the elastoplastic damage constitutive model of FRC is not only the intersection and combination of mechanics and material science,but also the frontier research field in the 21 st century.This is beacause the research on constitutive behavior is related to security issues,and also a challenge in the informatization and intellectualization process of civil engineering field because of its complex mechanism.Based on the project “Research on elastic-plastic damage constitutive relationship of steel-polypropylene hybrid fiber concrete”(Supported by the Youth Science Foundation of the National Natural Science Foundation of China;Project No.: 51608397),this paper studies the steel-polypropylene hybrid fiber concrete(HFRC)by the combination of experimental research,theoretical analysis and numerical simulation methods.The elastioplastic random damage constitutive model is established,and the corresponding numerical algorithm is proposed.The main work and results of this paper are as follows:(1)Considering the influencing factors,including confining pressure,steel fiber volume fraction and aspect ratio,polypropylene fiber volume fraction and aspect ratio,120 HFRC cylindrical specimens are designed and fabricated by single variable method.The conventional triaxial cyclic compression test at constant confining pressure is carried out.The mechanical properties such as multiaxial yield strength,transverse deformation,plastic deformation,stiffness degradation and damage characteristics of HFRC are statistically analyzed.Combined with Acoustic Emission and SEM tecnique,the mechanism of the damage behavior of HFRC under quasi-static loading is analyzed.The test results show that:the application of confining pressure and the addition of fiber not only effectively improve the strength and toughness of HFRC,but also significantly restrain the damage evolution process of the material;The cube compressive strength increased by 23.1% with the addition of steel fibers and decreased by 4.9% with the addition of polypropylene fibers;The axial peak strain increases slightly with the addition of steel fiber,and the maximum increase is about 24.4%under the same confining pressure;There are coupling effects between the confining pressure and steel fiber,steel fiber and damage mode,damage mode and material elastic constant evolution;The steel fiber bridging effect is more significant under a low level of confining pressure;The steel fiber bridging effect on the tensile cracks is much stronger than that on the shear cracks;The degradation of Young’s modulus and shear modulus are not synchronous;The shear modulus is more affected by the damage evolution,which means that under the same damage state,the degradation degree of shear modulus is more serious.(2)Based on the mechanism analysis and statistical analysis of the test results,and taking the confining pressure,the fibers bridging effects and the coupling effects between them into consideration,the multiaxial strength,transverse deformation,plastic deformation and stiffness degradation of HFRC are studied.The multiaxial strength model of HFRC under active constraint is established,as well as the empirical equation including material plastic evolution,damage evolution,and cyclic axial stress-strain relationship etc.are proposed.(3)Based on the framework of irreversible thermodynamics,elastictoplastic constitutive theory and concrete stochastic damage mechanics and the damage mechanism revealed by the test research in this paper,and taking the microscopic mechanism of random distribution and random orientation of steel fibers,energy consumption of steel fiber pull-out,fracture energy consumption of polypropylene fiber fracture and the influence of confining pressure into consideration,the evolution law of hardening and damage behaviours of HFRC in effective stress space are studied,and the corresponding criterion are proposed.Furthermore,the elastictoplastic statistics damage constitutive model of HFRC is established.The constitutive and damage behavior of HFRC under complex stress state can be scientifically and reasonably characterized by the proposed model,which is of strong universality and have the clear physical meaning parameters.(4)The commercial finite element software ABAQUS is redeveloped using UMAT,and the theoretical constitutive model of HFRC is numerically realized.In the process of numerical implementation,based on the traditional return mapping algorithm,a semi-implicit return mapping algorithm is proposed,of which the rationality is proved mathematically,and the computational efficiency and robustness are greatly improved.An analytical solution of the decomposition projection operator is strictly deduced and proposed,in which a priori cosine discriminant criteria is proposed to classify the stress tensor,so as to effectively avoid the singular solution generated by the computer when calculating the eigenvector of stress tensor.The proposal of this analytical algorithm can greatly reduce the computational cost caused by traditional Jacobi iterative methods.Verificated by the test data in this investigation and existing literature,the proposed theoretical constitutive model of HFRC has high prediction accuracy,and can be used for the finite element calculation of the material and serve as a guidance in the engineering design of HFRC materials.Finally,on the basis of summarizing the full paper,combined with the actual engineering needs and industry development trend in this field,some suggestions are put forward for the follow-up research of this subject.