Implementation of Numerical Mesostructure Concrete Material Models: A Dot Matrix Method.

We develop a dot matrix method (DMM) using the principles of computational geometry to place aggregates into matrices for the construction of mesolevel concrete models efficiently and rapidly. The basic idea of the approach is to transform overlap detection between polygons (or polyhedrons) into checking the possibility of any intersection between the point sets within a trial placement aggregate and the already placed ones in mortar. Through the arithmetic operation of integer point sets, the efficiency of the underlying algorithm in the dot matrix method is higher. Our parking algorithm holds several advantages comparing with the conventional placement issues. First, it is suitable for arbitrary-shape aggregate particles. Second, it only needs two sets for examining if the overlap between a trial placement aggregate and the already placed ones. Third, it accurately places aggregates according to aggregate grading curves, by order of reduction, led to more efficiently reducing aggregate placement time. The present method is independent of the size of aggregate particles. Combing with 3D laser scanning technology, the present method can also be used to create mesostructure concrete models conveniently and flexibly. Several examples show that DDM is a robust and valid method to construct mesostructure concrete models.