The Dynamic Lattice Method - Vibrations and Wave Propagation in Discontinuous and Heterogeneous Media

Abstract

The development of a new dynamic lattice element method (dynamicLEM) as well as its application in the simulation of wave propagation in discontinuous and heterogeneous media is the focus of this research paper. The conventional static lattice models are efficient numerical methods to simulate crack initiation and propagation in cemented geomaterials. The advantage of the LEM and the developed dynamic solution, such as simulation of arbitrary crack initiation and propagation, illustration and simulation of existing inherent material heterogeneity as well as stress redistribution upon crack opening, opens a new engineering field and tool for material analysis. To realize the time dependency of the dynamic LEM, the governing Newton's second law is solved while using the Newmark-β method and implementing the non-linear Newton-Raphson Jacobian. The method validation is done according to the results of a boundary element method (BEM) in the plane P-SV-wave propagation within a plane strain domain. Further validation tests comparing the generated wave types, simulation and study of crack discontinuities as well as inherent heterogeneities in the geomaterials are conducted to illustrate the accurate applicability of the new dynamic lattice method. The results indicate that with increasing heterogeneity within the material, the wave field becomes significantly scattered and further analysis of wave fields according to the wavelength/heterogeneity ratio become indispensable. Therefore, in a heterogeneous medium, the application of continuum methods in relation to structural health monitoring should be precisely investigated and improved. The developed dynamic lattice element method is an ideal simulation tool to consider particle scale irregularities, crack distributions and inherent material heterogeneities and can be easily implemented in various engineering applications.