Energy-Based Coarse Graining of the Lattice-Discrete Particle Model

Concrete is a complex heterogeneous material. Its internal structure controls its mechanical behavior through crack localization, branching, and coalescence. As a result, only models that represent its failure through fracture-mechanics-based formulations can physically account for such phenomena. Among these models, the lattice-discrete particle model (LDPM) has great success. By representing concrete through an assemblage of interacting coarse aggregate pieces, LDPM can successfully model concrete multiaxial behavior under various static and dynamic loading conditions. However, this fine detailing results in a large computational cost that hampers the use of LDPM in large structural scale applications. In this work, the formulation of a calibration-free coarse-graining technique is presented. In this technique, fictitiously larger aggregate pieces are used to replace the original concrete aggregate pieces, with linear scaling of aggregate diameters. The formulation accounts for the effect of coarse graining on the amount of energy dissipated during deformation under combined tension and shear (tension-shear). Because of coarse graining, less distributed cracking is represented during tension-shear deformation at the coarse scale. The proposed formulation recovers this energy-dissipating mechanism by introducing a transition function in the tension-shear constitutive law based on the coarse-graining factor and geometry, which eliminates the need to recalibrate the LDPM parameters for the coarser scale. The formulation is developed and initially validated using simulations of uniaxial compression and notched three-point bending tests, with coarse-graining factors up to 5. Then, using the same identified function without any change, extensive validation of the technique is demonstrated by simulating size effect tests of notched three-point bending tests, uniaxial compression of ultrahigh-performance concrete (UHPC) with various scaling factors, and flexural behavior of RC beams with different reinforcement ratios. The results show that the proposed technique is capable of replicating the same fine-scale response and failure patterns at a fraction of the fine-scale computational cost.