ABAQUS Secondary Development Of Finite Element Method Based On Cosserat Theory And Its Application In Fracture Mechanics

In recent years, more new materials with micro-structure have been applied in engineering.Classical continuum mechanical theories cannot explain the size effect of micro materials. In this case, strain gradient theory is presented which has the constitutive model where a material constant (the internal length scale) L that can reflect the size effect of materials is introduced, and builds a relationship between macro classical continuum mechanics and micro mechanics.The Cosserat theory is the one of strain gradient theory and usually thought to have two kinds:the constrained Cosserat theory and the non-constrained Cosserat theory, and the former theory is adopted by the paper. Here, the finite element method is applied and governing equations and finite element formulations of plane non-constrained Cosserat elasticity are derived for the numerical calculations. The application of the finite element method based Cosserat theory combined with ABAQUS secondary development in fracture mechanics is researched, and user element subroutine based on eight-node plane isoparametric finite element is written.At first, the cantilever beam bending problem and stress concentration at a small hole are researched to validate the finite element method. The results shows that if the material constant L is close to the characteristic size, the scale effect is clearly,and couple-stress must be considered. Compared with the classical elasticity theory, the bending deflection of cantilever beam in center line and stress concentration factor of the small hole are less.Then, the finite element method based Cosserat theory is combined with linear elasticity fracture mechanics. The paper analyzes how the material constant L influences initial crack propagation condition and direction, the length of crack propagation step. It is found that couple-stress doesn’t change the initial cracking angle in center I crack and reduces the initial cracking angle in center45°-inclined crack.In addition, couple-stress has a certain influence on the the length of crack propagation step and rupture load.Lastly, the effect of two classical anchoring schemes on45°-inclined rock crack propagation is analyzed. It’s found that when the model has the bolt, rupture load is increased to some extent and the cracking angle and length of crack propagation step are little changed when the model has the bolt. The results also shows that rupture load increases with an increase in the modulus of elasticity of the bolt.