A New Peridynamics Energy Release Rate And Its Effect On The Failure Behavior Of Brittle Materials

Traditional continuum mechanics has inherent shortcomings when dealing with cracks.The undefined equations of motion with differential displacement at the cracks and stress singularities make it difficult to solve them.In recent years,the peridynamics(PD)method,which has developed rapidly in recent years,is based on the principle of non-local action.The equation of motion uses spatial integration of displacement to solve the crack problem.The equation is still defined at the discontinuity and the form is continuous.They are exactly the same,realizing a unified solution to the mechanical behavior of continuum and discontinuous media.At present,the energy release rate used by PD is derived from fracture mechanics,and the object is a crack with no width,and the crack of PD has a certain width whether it is artificially prefabricated or naturally regenerated(referred to as the default width).The original PD energy release rate did not consider the influence of the default width of the crack,which led to a strong grid dependence of the PD method.For the same failure problem,using different grids,the failure results often differ greatly,and even based on The same grid,using different neighborhood radius,the local difference of damage is not small.The grid dependence makes the calculation results of PD damage very unstable,which undoubtedly reduces its credibility when simulating material damage.To this end,a modified peridynamics energy release rate is proposed.Starting from the crack itself,the effect of the volume of the material point at the crack on the energy release rate is considered.The results of the calculation example show that it can significantly reduce the PD simulation of brittle material failure Time dependence on the grid.First,the default width of horizontal cracks in PD is explored,and then a new energy release rate is derived based on the volume of the material point and the default width of the cracks.Finally,the effect of it on the failure behavior of brittle materials is studied,and the following research results have been obtained:(1)Through the study of horizontal prefabricated cracks under different grid arrangements,starting from the fracture of the material point bonds near the cracks,it is proved that the cracks in PD have real widths,and the default horizontal prefabricated cracks are determined The size of the width.(2)A modified energy release rate is proposed based on the volume of the material point and the default width of the crack.Co MPared with the energy release rate of traditional PD,the calculated results of the modified energy release rate are more consistent with the experimental situation,and the numerical simulation results are more consistent.In order to stabilize,the grid dependence of PD simulation material failure is greatly reduced.(3)The effect of the shape of the crack tip on the damage of the material is studied when the modified energy release rate is used.It is found that when the number of cracks is small,the shape of the crack tip has a great influence on the damage of the brittle material,which is a key factor.However,when there are multiple cracks,the effect of the shape of the crack tip is not significant.