Theoretical Research On Distributed Cohesive Element Method And Multiscale Analysis Based On EAH

A new method called distributed cohesive element method is proposed. Some keyissues including theoretical foundation, structured mesh dependence, phenomenon basedcohesive law and multiscale analysis of the proposed distributed cohesive element methodare systematically studied by theoretical analysis, mathematical argument, numerical sim-ulation and experimental investigation. The main work and contributions are as follows.(1) The theoretical foundation of distributed cohesive element method is establishedand its capacity of solving fracture problem is shown. By attributing each node to onlyone single element, the rigidly cohesive nature of conventional finite element method isrevealed. Two cohesive element types including nodal cohesive element and interfacialcohesive element are obtained and their separation displacement fields are derived. Byconsidering the element interfacial energy term, the variational foundation of distributedcohesive element method is found based on Sub-Region Generalized Variational Princi-ple. The Virtual Work Principle of distributed cohesive element method is established fordynamics and the associated discretized momentum equations of the proposed methodare also given for further investigation.(2) The structured mesh dependence of distributed cohesive element method is s-tudied. For evaluating crack length deviation, the concept of EEB (Element Edge Basis)is proposed and the EEB solution of the local crack length deviation is established. Thecrack length deviations of5types of structured meshes in the cases including ideal s-traight crack, curved crack and random crack problems are investigated quantificationallyby the established EEB solution. Based on EEB solution the crack length deviation evalu-ation problem for2D structured mesh is solved. For evaluation crack shape deviation, theconcept of crack Hausdorff distance is introduced. The crack shape convergence is testedby numerical simulations based on the introduced crack Hausdorff distance. The studyshows that the finite crack length deviation could not be eliminated by structured meshrefinement except for those cased in which the cracks propagate along a limited numberof directions. The study also shows that the crack shape deviation vanishes which refiningthe mesh.(3) A consistently coupled cohesive rule is proposed and Xu-Needleman cohesive law is proved to be a non-consistently coupled cohesive law mathematically based onseparation work analysis. Based on the original form of Xu-Needleman cohesive law, aconsistently coupled cohesive law with better mechanical properties in mixed mode anal-ysis is proposed. A specific consistently coupled cohesive law for High Strength SteelQ460-C is established and the failure of High Strength Steel plate bolted connections isanalyzed by distributed cohesive element method. The calculation results match the ex-perimental results well and three typical failure modes including net section failure mode,bolt bearing failure mode and combined failure mode are reproduced in the simulationsuccessfully. The effectiveness and feasibility of the proposed method are validated.(4) The theory of EAH (Embedded Atom Hyperelasticity) is developed and in EAHthe closed form solution of atomistic stress calculation is obtained. Based on EAH theory,a multiscale mechanism based cohesive law is obtained and a multiscale distributed cohe-sive element method is developed. The validity and feasibility of the proposed multiscaledistributed cohesive element method are both validated by comparing with the results ofa large scale molecular dynamics simulation. It is shown that the multiscale distributedcohesive element provides satisfactory results with higher efficiency.