lattice modelling approach

Comparing to the continuum-based models, lattice model is well adapted to map the ordered or random anisotropic microstructure of composite materials. The other advantage of lattice model is the simplicity of the physical interpretation of a phenomenon like fracture in each step of the analysis.

The main idea of lattice model is simulation of the material structure and mechanical properties by construction of a network of interconnected discreet line elements. The defined network can be two-dimensional or three-dimensional and has random or regular structure.

This approach was first developed to study the theory of elasticity (Hrennikoff 1941). Later lattice model was used in modeling the fracture process by removing the elements reaching a strength criterion at different loading steps. VanMier were one among of the first who used the lattice fracture model in concrete, aiming to simulate the quasi-brittle material behavior (Schlangen and VanMier 1992). In this model, beam elements were chosen in such a way that they represented the different phases of concrete (aggregates, matrix and interfaces). After that, the lattice fracture model was applied for several years in analyzing the concrete and sandstone fracture. All these studies confirmed that lattice fracture model is successful in predicting the influence of material microstructure on the pre-peak and softening behavior of force-displacement curve and crack propagation paths.

Now, lattice model is a well known approach in analysing the mechanical behavior and mechanism of fracture in cellular and fibrous structure such as wood, bone and soft tissues.