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

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.

Microstructural dimension involved in the damage of concrete-like materials: An examination by the lattice element method

With the lattice element method, it is required to introduce a length via, for example, a non-local approach in order to satisfy the objectivity of the mechanical response. In spite of this, the mesoscale structuring of inclusions within a matrix conveys the natural origin of the internal length for a fixed mesh. In other words, internal length is not explicitly provided to the model, but rather governed by the characteristics of the meso-structure itself. This study examines the influence that the meso-structure of quasi-brittle materials, like concretes, have on the width of the fracture process zone and thus the fracture energy. The size of the fracture process zone is assumed to correlate with a microstructural dimension of the quasi-brittle material. If a weakness is introduced by a notch, the involvement of the ligament size (a structural parameter) is also investigated. These analyses provide recommendations and warnings that could be beneficial when extracting, from material meso-structures, a required internal length for nonlocal damage models. Among the observations made, the study suggests that the property that best characterise a meso-structure length would be the spacing between inclusions rather than the size of the inclusions themselves. It is also shown that microstructural dimension and the width of the fracture process zone have comparable order of magnitude, and they trend similarly with respect to microstructural sizes such as the inclusion interdistances.

Numerical Platform

An essential scientific goal of the GeomInt project is the analysis of potentials and limitations of different numerical approaches for the modelling of discontinuities in the rocks under consideration in order to improve the understanding of methods and their synergies with regard to theoretical and numerical fundamentals. As numerical methods, the “Lattice Element Method” (LEM), the non-continuous discontinuum methods “Discrete Element Method” (DEM), the “Smoothed Particle Hydrodynamics” (SPH), the “Forces on Fracture Surfaces” (FFS) as well as the continuum approaches “Phase-Field Method” (PFM), “Lower-Interface-Method” (LIE), “Non-Local Deformation” (NLD) and the “Hybrid-Dimensional Finite-Element-Method” (HDF) will be systematically investigated and appropriately extended based on experimental results (Fig. 3.1).