An adaptive concurrent two-scale FE model to predicting crack propagation in concrete

Finite element analysis including explicitly the details of the heterogeneities (finer-scale) can dramatically increase the numerical effort and memory demand. To minimize these drawbacks, a new concurrent adaptive multiscale model for concrete in two different scales of representation is proposed. In this approach, the macroscale stress is used as an indicator to properly update the model from the macro to the mesoscale model in the critical regions. The concrete is initially modeled as a homogenous material and then is gradually replaced by a heterogeneous representation, consisting of three phases: coarse aggregates, mortar matrix and Interfacial Transition Zone (ITZ). The use of Coupling Finite Elements (CFEs) is proposed to enforce the continuity of displacements between the non-matching meshes corresponding to the two different scales. These CFEs can ensure the connection between the finer and coarser scales without increasing the number of degrees of freedom of the problem. The mesoscopic scale is constructed using a mesh fragmentation technique in order to simulate the crack propagation process. This technique is based on the insertion of standard finite elements with high aspect ratio between all regular finite elements of the mortar matrix and in between the mortar matrix and aggregate elements, representing the ITZ. In the limit case, when the thickness of interface elements tends to zero and consequently the aspect ratio tends to infinite, these elements present the same kinematics as the Continuum Strong Discontinuity Approach (CSDA), being suitable to represent the formation of discontinuities associated to cracks, using a continuum tensile damage constitutive model. Numerical examples with complex crack patterns are carried out to validate the proposed adaptive multiscale model and show its efficiency and accuracy when compared to the full mesoscale model.