Meso-element equivalent method for the simulation of macro mechanical properties of concrete

A meso-element equivalent method is proposed to investigate the macro mechanical properties of concrete. The randomly distributed aggregates with different sizes and shapes are built by using the Monte Carlo simulation approach, and they are discretized into a finite number of identical elements with a characteristic element size. Each meso-element formed is then processed to be a homogeneous and isotropic unit based on homogenization theory of composite materials. There are two key issues emphasized in the present research, they are the equivalence of the mechanical behaviors of the aggregated concrete material and the determination of the mesh-element size, respectively. The classical Voigt parallel approach is applied to establish the equivalent mechanical behaviors of the meso-elements containing the two-phase medium composed of aggregates and mortar matrix. Since the macroscopic nonlinearity of concrete material is essentially attributed to the inherent heterogeneities, the non-homogeneity of concrete is described by the dispersion coefficient of the effective elastic moduli of concrete meso-elements. And the characteristic element size is introduced and determined by means of a statistical analysis of the aggregate sizes and taken as an appropriate mesh size of concrete specimens. The proposed approach reflects the fact that the concrete nonlinearity originates from the inherent heterogeneity. Several two-dimensional samples of concrete specimens are carried out to verify the feasibility and the accuracy of the proposed meso-element equivalent method. Furthermore, the damage process and the deformation of a three-dimensional four-point bending concrete beam are studied. The numerical results show the high efficiency and accuracy of the proposed method. Compared with other meso-mechanical methods, the advantage of the present meso-element equivalent method is that the degrees of freedom of the concrete specimens reduce significantly, making the computational efficiency improved drastically, especially for three-dimensional problems, while the accuracy of the numerical results is acceptable.