Methodologies are developed for analyzing failure initiation and crack propagation in highly heterogeneous concrete mesostructures. Efficient algorithms are proposed in Python to generate and pack geometric features into a continuous phase. The continuous phase represents the mortar matrix, while the aggregates and voids of different sizes represent the geometric features randomly distributed within the matrix. The cohesive zone model (CZM) is utilized to investigate failure initiation and crack propagation in mesoscale concrete specimens. Two-dimensional zero-thickness cohesive interface elements (CIEs) are generated at different phases of the concrete mesostructure: within the mortar matrix, aggregates, and at the interfacial transition zone (ITZ). Different traction–separation laws (TSL) are assigned to different phases to simulate potential crack paths in different regions of the mesoscale concrete specimen. The mesoscale finite element simulations are verified using experimental results from the literature, with a focus on implementing mixed-mode fracture and calibrating its corresponding parameters with respect to the experimental data. In addition, the current study addresses the limited exploration of void effects in mesoscale concrete simulations. By investigating voids of diverse sizes and volume fractions, this research sheds light on their influence on the mechanical behavior of concrete materials. The algorithms for generating cohesive interface elements and concrete microstructures are described in detail and can be easily extended to more complex states. This methodology provides an effective tool for the mesostructural optimization of concrete materials, considering specific strength and toughness requirements.

In this study, we develop a novel multi-fidelity deep learning approach that transforms low-fidelity solution maps into high-fidelity ones by incorporating parametric space information into an autoencoder architecture. This method’s integration of parametric space information significantly reduces the amount of training data needed to effectively predict high-fidelity solutions from low-fidelity ones. In this study, we examine a two-dimensional steady-state heat transfer analysis within a heterogeneous materials microstructure. The heat conductivity coefficients for two different materials are condensed from a 101 $$\times $$ × 101 grid to smaller grids. We then solve the boundary value problem on the coarsest grid using a pre-trained physics-informed neural operator network known as Finite Operator Learning (FOL). The resulting low-fidelity solution is subsequently upscaled back to a 101 $$\times $$ × 101 grid using a newly designed enhanced autoencoder. The novelty of the developed enhanced autoencoder lies in the concatenation of heat conductivity maps of different resolutions to the decoder segment in distinct steps. Hence the developed algorithm is named microstructure-embedded autoencoder (MEA). We compare the MEA outcomes with those from finite element methods, the standard U-Net, and an interpolation approach as an upscaling technique. Our analysis shows that MEA outperforms these methods in terms of computational efficiency and error on representative test cases. As a result, the MEA serves as a potential supplement to neural operator networks, effectively upscaling low-fidelity solutions to high-fidelity while preserving critical details often lost in traditional upscaling methods, such as sharp interfaces features lost in the context of interpolation approaches.

This study evaluates four widely used fracture simulation methods, comparing their computational expenses and implementation complexities within the finite element (FE) framework when employed on heterogeneous solids. Fracture methods considered encompass the intrinsic cohesive zone model (CZM) using zero-thickness cohesive interface elements (CIEs), the standard phase-field fracture (SPFM) approach, the cohesive phase-field fracture (CPFM) approach, and an innovative hybrid model. The hybrid approach combines the CPFM fracture method with the CZM, specifically applying the CZM within the interface zone. The finite element model studied is characterized by three specific phases: inclusions, matrix, and the interface zone. This case study serves as a potential template for meso- or micro-level simulations involving a variety of composite materials. The thorough assessment of these modeling techniques indicates that the CPFM approach stands out as the most effective computational model, provided that the thickness of the interface zone is not significantly smaller than that of the other phases. In materials like concrete, which contain interfaces within their microstructure, the interface thickness is notably small when compared to other phases. This leads to the hybrid model standing as the most authentic finite element model, utilizing CIEs within the interface to simulate interface debonding. A significant finding from this investigation is that within the CPFM method, for a specific interface thickness, convergence with the hybrid model can be observed. This suggests that the CPFM fracture method could serve as a unified fracture approach for multiphase materials when a specific interfacial thickness is used. In addition, this research provides valuable insights that can advance efforts to fine-tune material microstructures. An investigation of the influence of interfacial material properties, voids, and the spatial arrangement of inclusions shows a pronounced effect of these parameters on the fracture toughness of the material.

In this study, we develop a novel multi-fidelity deep learning approach that transforms low-fidelity solution maps into high-fidelity ones by incorporating parametric space information into a standard autoencoder architecture. This method's integration of parametric space information significantly reduces the need for training data to effectively predict high-fidelity solutions from low-fidelity ones. In this study, we examine a two-dimensional steady-state heat transfer analysis within a highly heterogeneous materials microstructure. The heat conductivity coefficients for two different materials are condensed from a 101 x 101 grid to smaller grids. We then solve the boundary value problem on the coarsest grid using a pre-trained physics-informed neural operator network known as Finite Operator Learning (FOL). The resulting low-fidelity solution is subsequently upscaled back to a 101 x 101 grid using a newly designed enhanced autoencoder. The novelty of the developed enhanced autoencoder lies in the concatenation of heat conductivity maps of different resolutions to the decoder segment in distinct steps. Hence the developed algorithm is named microstructure-embedded autoencoder (MEA). We compare the MEA outcomes with those from finite element methods, the standard U-Net, and various other upscaling techniques, including interpolation functions and feedforward neural networks (FFNN). Our analysis shows that MEA outperforms these methods in terms of computational efficiency and error on test cases. As a result, the MEA serves as a potential supplement to neural operator networks, effectively upscaling low-fidelity solutions to high fidelity while preserving critical details often lost in traditional upscaling methods, particularly at sharp interfaces like those seen with interpolation.

A spatiotemporal deep learning framework is proposed that is capable of 2D full-field prediction of fracture in concrete mesostructures. This framework not only predicts fractures but also captures the entire history of the fracture process, from the crack initiation in the interfacial transition zone to the subsequent propagation of the cracks in the mortar matrix. In addition, a convolutional neural network is developed which can predict the averaged stress-strain curve of the mesostructures. The UNet modeling framework, which comprises an encoder-decoder section with skip connections, is used as the deep learning surrogate model. Training and test data are generated from high-fidelity fracture simulations of randomly generated concrete mesostructures. These mesostructures include geometric variabilities such as different aggregate particle geometrical features, spatial distribution, and the total volume fraction of aggregates. The fracture simulations are carried out in Abaqus, utilizing the cohesive phase-field fracture modeling technique as the fracture modeling approach. In this work, to reduce the number of training datasets, the spatial distribution of three sets of material properties for three-phase concrete mesostructures, along with the spatial phase-field damage index, are fed to the UNet to predict the corresponding stress and spatial damage index at the subsequent step. It is shown that after the training process using this methodology, the UNet model is capable of accurately predicting damage on the unseen test dataset by using 470 datasets. Moreover, another novel aspect of this work is the conversion of irregular finite element data into regular grids using a developed pipeline. This approach allows for the implementation of less complex UNet architecture and facilitates the integration of phase-field fracture equations into surrogate models for future developments.