Three-dimensional FEM Based On Cosserat Theory And Research Of Its Application On Fracture Mechanics

Cosserat theory is one of the theory which has the constitutive model where strain gradient is introduced to study its influence on properties of material. This thesis combines the three-dimensional Cosserat theory and FEM, and analyses the bending of three-dimensional cantilever beam and split of three-dimensional crack on the ABAQUS secondary development platform.The basic theory of fracture mechanics and classifications of crack is first introduced, followed by current crack criteria and maximum circle tensile stress principle.Then control equation of three-dimensional Cosserat theory, boundary condition, general equation of FEM based on minimum potential principle, isoparametric transformation equations, Gaussian integral function are derived. Before the procedures of display optimization are presented, method of secondary development on ABAQUS is introduced. Lastly, UEL is programmed on the ABAQUS secondary development platform.Before equations of stress alternation are derived, Post-processing method and stress optimization are presented, after which Fortran post-processing program is written.Finally bending of three-dimensional cantilever beam and split of three-dimensional crack is examined on the basis of UEL and Fortran post-processing program.The results of bending of three-dimensional cantilever beam reveal effects of couple stress on the deflection of cantilever beam depend on the internal length scale to model dimension ratio l/h. As the ratio increases, the deflection of cantilever beam decreases, size effect becomes more apparent. When the ration is very small, the deflection of cantilever beam under Cosserat theory is close to it under classical continuum mechanical theory, size effect can be ignored.The result of three-dimensional cantilever beam shows couple stress affects the initial crack angle and rupture load moderately. As the ratio l/h increases, crack angle decreases while rupture load increases, size effect becomes more apparent. The length h influences the crack parameters. When it is augmented, crack angle mounts while the crack propagation length and rupture load decrease. The length of crack in z axis direction L affects the initial crack angle, rupture load and propagation step. As L mounts, crack angle decreases while rupture load and propagation step show an upward trend. When L increases, edge effect becomes more apparent.