Modelling crack initiation and propagation in heterogeneous solid microstructures with interfaces

In Structural Health Monitoring (SHM) of large concrete structures like bridges, optimal sensor placement is crucial due to high installation costs and the challenges of managing large data volumes generated by sensors. The FE2 framework provides an effective solution to address this issue by simulating bridge responses under various load conditions. This enables precise identification of critical sensor locations and enhances the cost-efficiency of SHM by reducing the number of sensors required. The FE2 framework requires small-scale simulations of concrete’s heterogeneous microstructure, which consists of at least three solid phases and involves non-linear, complex fracture dynamics. Consequently, the development of a modeling framework that requires the least computational cost is a major step in the FE2 framework. To this end, a numerical study was conducted to determine the best numerical framework for fracture simulation of concrete microstructures in terms of computational cost and implementation complexity. Among various frameworks, the Cohesive Zone Model (CZM), the Phase-field Fracture Model (PFM), and a hybrid of these approaches were analyzed. Specifically, the intrinsic CZM was selected from the CZM approach, while the standard and cohesive phasefield fracture approaches were chosen from the phase-field fracture framework. Within the hybrid model, the CZM is used for interface debonding, while the Cohesive Phase-field Fracture Model (CPFM) is employed for matrix cracking. The numerical study revealed that the computational cost of a complete mesoscale finite element fracture simulation of concrete was lower in CPFM simulations than in CZM simulations when the same resources were utilized. While CPFM simulations showed initial promise, a full simulation still required an average of 3.5 hours using five CPUs, each capable of 2.43 × 108 FLOPS (floating-point operations). This computational demand remains excessively high for the FE2 framework, indicating that its use in the SHM of large structures, such as bridges, remains impractical. These computationally intensive simulations exceed current resources, making FE2 application to large structures like bridges infeasible and hindering optimal sensor placement. Advancements in computational power, especially with modern GPUs, have enabled deep learning-based surrogate models to address computationally intensive problems in mechanical engineering and materials science. These surrogate models can predict physical phenomena in a fraction of a second instead of hours, bringing the realization of an online FE2 framework closer to feasibility. To this end, the CPFM model is employed to generate the required data to train deep learning-based surrogate models. In the first attempt, data-driven surrogate models were developed to predict fracture in concrete microstructures. Following the successful training and testing of the data-driven surrogate model, the computational cost was reduced by a factor of 3315, with each fracture simulation taking just 3.8 seconds. This substantial reduction in computational cost indeed brings the FE2 framework closer to practical implementation. However, a major limitation of data-driven models is their reliance on training data on conditions that is generated on, limiting their generalization to unrepresented boundary conditions. This necessitates generating new training data and retraining the model, making their use in SHM of bridges under the FE2 framework impractical. To address this limitation, the Neural Operator (NO) framework has been proposed. NOs learn operators that map functional parametric dependencies to their solutions, enabling generalization across various functional spaces, including different initial and boundary conditions. This overcomes the dependency issues of data-driven models and provides system responses in fractions of a second, bringing an online FE2 framework for bridges closer to realization. It should be noted that no neural operator models have been developed or implemented in this dissertation. Instead, they are suggested as a future research direction to address the challenges associated with data-driven models.

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