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The contact searching is computationally intensive and its memory requirement is highly demanding; therefore, it is significant to develop an efficient contact search algorithm with less memory required. In this paper, we propose an efficient global contact search algorithm with linear complexity in terms of computational cost and memory requirement for the finite element analysis of contact problems. This algorithm is named LC-Grid (Lei devised the algorithm and Chen implemented it). The contact space is decomposed; thereafter, all contact nodes and segments are firstly mapped onto layers, then onto rows and lastly onto cells. In each mapping level, the linked-list technique is used for the efficient storing and retrieval of contact nodes and segments. The contact detection is performed in each non-empty cell along non-empty rows in each non-empty layer, and moves to the next non-empty layer once a layer is completed. The use of migration strategy makes the algorithm insensitive to mesh size. The properties of this algorithm are investigated and numerically verified to be linearly proportional to the number of contact segments. Besides, the ideal ranges of two significant scale factors of cell size and buffer zone which strongly affect computational efficiency are determined via an illustrative example.

A novel adaptive combined DE/FE algorithm is proposed to simulate the fracture procedure of brittle materials of plane stress problems. The main concept of the approach is that a model is composed of the finite element completely at the initial stage without any discrete element generated until portion of the model grid becoming severely deformed; and then the model is fragmented into two subdomains, the finite element (FE) and the discrete element (DE) subdomains. The interface force between the two subdomains is calculated by using the penalty method. An extrinsic cohesive fracture model is employed to simulate the brittle fracture procedure only in the DE subdomain. The adaptive algorithm may allow for the use of the accurate and efficient FEs in the lower distorted region and the DEs which are automatically generated in the severely deformed FE region . The feasibility of the adaptive algorithm is validated by the impact fracture simulation of a glass beam. The comparison of calculation time consumption shows that the adaptive algorithm has a higher efficiency than the DEM. At last, the impact fracture behavior of a laminated glass beam is simulated, and the cracks propagation is compared with the experimental results showing that the adaptive algorithm can be implemented to capture some fracture characteristics of brittle materials.

An algorithm combining three-dimensional (3D) discrete and finite element methods is proposed. This new approach is conducted by decomposing the calculation domain into a finite element (FE) calculation domain and a discrete element (DE) calculation domain; the interaction between the two sub-domains is processed by using a penalty function method. Following the established model that combines spherical DEs and FEs, the corresponding numerical code is developed. The vibration process of two cantilever beams under dynamic force is simulated. By comparing the results calculated with different penalty factors set and also with that calculated by the finite element code LS-DYNA, it is found that the calculated results are unanimous and the precision is almost the same as LS-DYNA, as long as the penalty factor is large enough. Moreover, the vibration processes of two plates under impact of rigid spheres are simulated and the accuracy of the model proposed in this paper is further proved in the field of contact mechanics by comparing the simulating results with that calculated by using LS-DYNA. Finally, the impact fracture behavior of a laminated glass plate is simulated, with the influence of model parameters taken into consideration. And the numerical experiments show that the combined model can be used to predict some macroscopical physical quantities, such as the impact force of impactor.

A three-dimensional discrete element model of laminated glass plane is presented and a 3D numerical analysis code, which can simulate the impact fracture behavior of automobile laminated glass, is developed. The impact process of a single glass plane and a laminated glass plane are calculated in the elastic range by the code. Comparing its results with those calculated by the commercial FEM code LS-DYNA in the same condition, the validity of the 3D laminated glass model and the 3D discrete element method are proved. Furthermore, the impact fracture process of a single glass plane and a laminated glass plane are simulated respectively. The entire failure processes in detail are presented. By comparing the impact force and reduction of kinetic energy of impact body between those two models, the numerical method is applied to demonstrate the advantage of laminated glass in passenger’s safety.