The Contact Theory Of DDA Based On Penalty Function Method?Bi-potential Theory And The Application Of High Order Displacement Model

DDA is a numerical method that can calculate the velocity and displacement of block system accurately when blocks moving.But the accuracy of the contact force,which based on Penalty Function Method,depends strongly on the parameters of contact stiffness,then,the mechanical energy of the black system may be wrong.In this paper,the variable stiffness method and the impulse-based method are used to deal with contact among blacks and the accuracy of mechanical energy can be improved.Meanwhile,the bi-potential theory and a high order polynomial displacement approximation theory are used to compute the contact forces and the block deformations.The detailed contents are as follows:DDA theory and the formation process of the integral equations are introduced.The key contents of the augmented Lagrange multiplier method are explained.The advantages and disadvantages of the penalty function method of contact theory are analyzed from the view of the conservation of mechanical energy and the friction loss.The variable stiffness method is used to deal with mechanical energy problems and the result is optimistic.The displacement correction formula is introduced.The influence of penalty value on mechanical energy was studied when the penalty method is used to deal with the contact.The change of mechanical energy within the system show strong dependence on the stiffness of the system in collisions.To solve the problem above,the impulse-based method is used to calculate the velocity after every collision.Based on the penalty method.Mohr-Coulomb's law and Maximum Tensile Stress Criterion are used to judge the contact status between blocks.A cantilever beam is discretized into regular polygons which contact with each other,and huge cohesive force and tensile strength are set to prevent sliding and creaking between blocks.DDA is used to simulate the deformation cased by the same load at different block sizes.Strain on the edge and cross section of beam is compared with theoretical solution.The conclusion is that the smaller relative size between regular polygons and cantilever beam,the higher accuracy of the calculation.Bi-potential and high order polynomial displacement approximation theories are used to calculate the contact force,stress and displacements of blocks.Seveal numerical examples which based on Matlab program are used to test the accuracy and effectiveness of the method above.It is found that the contact force andstress can be calculated accurately.