Particle based methods can be employed as an alternative to Continuum-mechanics based approaches for modeling crack nucleation and its subsequent propagation in materials. Discrete Element Method (DEM) offers implicitly the ability to describe crack nucleation as the breakage of bonds between two material points that were previously bonded together upon reaching a certain failure criteria. However, the range of materials that can be represented within DEM is in general restricted to values of Poisson's ratio under 0.25. Also, within this range, a stiffer response of the structure is observed. This is especially prominent under bending dominated problems.
Since an accurate elastic material response is a prerequisite for subsequent analysis, the development of a bond model that accurately captures the linear elastic domain for values of Poisson's ratio in the range 0 to under 0.5 is of utmost importance. To overcome this limitation, a bond model inspired by the Continuum mechanics description of engineering shear strain has been proposed. This proposed model overcomes the inability of the standard bond model to distinguish between rigid-body rotation and shear deformations. With the eigenvalues of a square unit-cell it is possible to understand the underlying behavior of the employed bond model. The normalized eigenvalues are plotted as a function of the Poisson's ratio for the standard and modified bond model. Here the eigenvalue λ_3 corresponds to rigid-body rotations.
Pure bending is investigated comparing the results obtained with the standard and modified bond models against the analytical solution for two different values of Poisson's ratio.
To overcome the limitation to structured discretization of the domain the proposed bond model is extended to unstructured meshes employing triangles. The results of a Cook's cantilever bending example employing the modified bond model show good agreement with an equivalent Finite Element model.
Further research includes the extension of the proposed model to 3D. Also, upon selection of a suitable damage criteria, the model must be employed to predict the damage evolution in a quasi-brittle material such as concrete.
The project is part of the DFG programme GRK 2075 - Modelling the constitutional evolution of building materials and structures with respect to aging.