Study On Elastic-Plastic Constitutive Based On The Least Energy Dissipation Principle And Numerical Simulation Of Crack Propagation

The simulation, prevention and disaster reduction of engineering disasters have been ofimportance for decades in engineering and academia. Due to the multiple influencing factorsto mechanical properties of concrete, it is still a challenge to predict concrete component ofthe yield and failure, and to design numerical simulation program with powerful nonlinearanalysis ability. Based on the least energy dissipation principle, the general expression onflowing criterion of plastic strain is deduced, which clearly reveals the intrinsic mechanismon shearing dilation character of quasi-brittle materials. Following that the three dimensionelastic-plastic extended finite element expansion is obtained based on the least energydissipation principle. Furthermore, the numerical simulation program with powerfulnonlinear analysis ability is compiled which can be used in the crack growth across the tracksimulation. Finally, the analysis of interface crack propagation in FRP-steel-concrete beamis performed. The numerical method based on this new flow rule is of widely applicationforeground. The main conclusions and achievements in the thesis are summarized asfollows:(1) In this flowing criterion formula of plastic strain, there is a cross couple item aboutthe current stress and the plastic softness increment matrix which does not occur in classicplastic flowing criteria. Due to the presence of the cross couple item, the plastic deformationdoes not always flow along the normal direction of the yield function surface. It clearlyreveals the intrinsic mechanism on shearing dilation character for quasi-brittle materials.(2) Based on the plastic strain flowing equation, the FEM increment iterative form isconducted. Due to the symmetric character of the stiffness matrix, the calculation efficiencyis greatly improved compared with that of the non-associated flowing rule where thestiffness matrix is unsymmetrical.(3) By using Legendre orthogonal polynomial as base function, the fitting curve of thestress and strain from the clay experimental data is achieved by the least square method. Itprovides a very practical way for the constitutive relation of the nonlinear numerical analysis.(4) The evolvement process of plastic deformation is subsequently simulated for soilsamples when the samples are subjected to axial and surrounding press. The fracture form ofsimulation is nearly similar to that of the experimental phenomena.(5) The slippage fracture process of a soil slope is modeled with the flowing criterion ofplastic strain based on the least energy dissipation principle. The fracture form conforms tothe practical case, implying that the flowing rule is rational and reliable. The results modeledby associated flow rule is almost show on shearing dilation effect, while the shearingdilation effect is very apparent with the non-associated flow rule and the cross couple itembased on the least energy dissipation principle. The simulation process and result show thatthe cross couple item conducted from the least energy dissipation principle not only exhibitsthe effect of shearing dilation, but also possesses solid theoretical foundation and highercalculation efficiency because of the symmetric stiffness matrix compared with thenon-associated flow rule.(6) The three dimension elastic-plastic extended finite element expansion is obtainedbased on the least energy dissipation principle. Incremental iteration format for the extendedfinite element method is deduced. Following that the elastic-plastic extended finite elementprogram is compiled based on open source program for the study on the development of3dcrack and destroy form to provide the foundation for future application.(7) Displacement function is structured through the crack surface element and theadded discontinuous additional function. With the merit of simulation crack propagation ofthe grid without decomposing, it will overcome the difficulties in traditional finite elementmethod with high-density grid points in the crack tip.(8) Based on the least energy dissipation principle, simulation of the interface crackpropagation and interface crack evolution in FRP-Steel concrete beam is performed. Thedestroy form of concrete development along the interface is the exfoliate of thedestruction.The fracture form of simulation is almost similar to the actual damage forms.This shows that the expanded finite element simulation crack propagation is effective andfeasible. In the end, we reviewed the future application and prospect of the thesis results.