Keywords: three-dimensional lattice fracture analysis, element-by-element, MPI, cement paste, tensile behaviour, micro-crack evolution.

The three-dimensional lattice model is one of the important fracture models in the field of fracture mechanics. In lattice analysis, a piece of material is discretized into a frame structure which consists of beam elements. However, the generated structure to be analyzed is usually very large, for instance, the system consists of one million nodes, hence, the cost for computational resources is quite expensive in terms of time and memory. In order to reduce the computational time and analyze even larger structures, parallel computing must be a good choice.

In this paper, the algorithm of conventional sequential lattice analysis is parallelized. The resulting algorithm is based on the EBE (Element-By-Element) scheme and a Jacobi-preconditioned conjugate gradient solver is adopted. As the new algorithm operates on element stiffness matrices instead of the global stiffness matrix, it can be easily implemented on distributed memory architecture. The programming tool is the host language C++ in combination with the library MPI (Message Passing Interface). On the basis of the proposed algorithm, a parallel package is developed to perform the three-dimensional lattice fracture analysis.

For its application, some numerical experiments are carried out to simulate the tensile behaviour of cement paste and the micro-crack evolution at the micro-level. Furthermore, the correctness and efficiency of the package are verified and investigated in detail.

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