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Lattice Boltzmann simulation of antiplane shear loading of a stationary crack. (English) Zbl 1464.74411
Summary: In this work, the lattice Boltzmann method is applied to study the dynamic behaviour of linear elastic solids under antiplane shear deformation. In this case, the governing set of partial differential equations reduces to a scalar wave equation for the out of plane displacement in a two dimensional domain. The lattice Boltzmann approach developed by G. Yan [J. Comput. Phys. 161, No. 1, 61–69 (2000; Zbl 0969.76076)] is used to solve the problem numerically. Some aspects of the scheme are highlighted, including the treatment of the boundary conditions. Subsequently, the performance of the lattice Boltzmann scheme is tested for a stationary crack problem for which an analytic solution exists. The treatment of cracks is new compared to the examples that are discussed in Guangwu’s work [loc. cit.]. Furthermore, the lattice Boltzmann simulations are compared to finite element computations. Finally, the influence of the lattice Boltzmann relaxation parameter on the stability of the scheme is illustrated.
MSC:
74S99 Numerical and other methods in solid mechanics
74R10 Brittle fracture
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