Study Of Constitutive Relations Of Materials In DDA Method

The Discontinuous Deformation Analysis(DDA)is a powerful numerical method to simulate the deformations,failures and large displacements of discontinuous materials.It has been widely used in the simulation of the failures and instabilities of rock mass structures.However,the linear elastic model was the only constitutive model in the DDA method,which is an important factor to deviate the simulation results from reality in many occasions involving nonlinear stress-strain phenomena.Therefore,in this paper,three nonlinear constitutive models,including the elastic brittle model,the elastic damage model and the Johnson-Cook model,have been coupled in the DDA to enhance the practical applicability of this numerical method.First,as a commonly used constitutive model in the field of rock mechanics,the elastic brittle constitutive model is coupled in the DDA based on the DDA sub-block joint surface fracturing modeling algorithm,which has already been successfully used to simulate many static and dynamic rock fracturing problems,such as the Brazil splitting and drilling blasting of rock.With the elastic brittle constitutive model,the compression test of square rock specimens is simulated and the influence of the residual stress coefficient on the simulation results is discussed.Second,an elastic damage constitutive model is coupled in the DDA from the point of view of damage.To verify the coupled damage constitutive model,the simulated stress-strain curves of a long element model are compared with the corresponding theoretical curves under different loading histories.Thereafter,the compression test of square rock specimens is simulated with the damage model.The influence of the critical fracturing damage value and the number of cracking edges on the simulation results are investigated.With a critical damage value of 0.8 and three cracking edges(using triangular sub-blocks),the DDA simulation results are close to those by other numerical simulation methods.Third,the Johnson-Cook constitutive model that is widely used to describe the stress-strain relationship of metal materials is coupled in the DDA method.The simulated stress-strain curves of a long element model are compared with the experimental results,and the proper values of the reference strain rate under different loading rates are obtained.Then,the tensile test of a long rod model is simulated.The results are in close agreement with the corresponding experimental and finite element simulation results.Finally,the three coupled constitutive models are applied in the simulation of a projectile penetration test.As compared with the only linear elastic constitutive model in the original DDA,the simulation results indicate that with the three more constitutive models coupled in this paper,the DDA method becomes more effective to simulate some practical complicated problems.