  Citation: Wang, J.; Jivkov,A.P.; Engelberg, D.L.; Li, Q. Image-Based vs. Parametric Modelling of Concrete Meso-Structures. Materials 2022, 15, 704. https://doi.org/10.3390/ ma15030704 Academic Editor: Jong Wan Hu Received: 3 December 2021 Accepted: 12 January 2022 Published: 18 January 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). materials Article Image-Based vs. Parametric Modelling of Concrete Meso-Structures Jiaming Wang 1, * ,† , Andrey P. Jivkov 1, * , Dirk L. Engelberg 2 and Qingming Li 1 1 Department of Mechanical, Aerospace and Civil Engineering, University of Manchester, Manchester M13 9PL, UK; Qingming.Li@manchester.ac.uk 2 Materials Performance Centre, Department of Materials, University of Manchester, Manchester M13 9PL, UK; D.Engelberg@manchester.ac.uk * Correspondences: jiaming.wang@sheffield.ac.uk (J.W.); andrey.jivkov@manchester.ac.uk (A.P.J.) † Current address: Department of Civil and Structural Engineering, University of Sheffield, Sheffield S10 2TN, UK. Abstract: Damage initiation and crack propagation in concrete are associated with localisation of energy dissipation by the concrete meso-structure. Meso-scale models are, therefore, required for realistic analysis of concrete non-linear behaviour. Such models are constructed either from X-ray Computed Tomography images (image-based modelling) or by in silico meso-structure generation (parametric modelling), while both approaches are widely used and their advantages and disadvan- tages are recognised, little work is done on comparing their performance in predicting measured macroscopic behaviour with equivalent constitutive relations for meso-structural features. This work uses microstructure characterisation and mechanical behaviour data to construct, validate and com- pare the two modelling approaches. The macroscopic behaviour obtained with both meso-structural models is found to be in good agreement with experimental data. Differences are observed only between the predicted distributions of damage within specimens. These outcomes suggest that the computationally simpler parametric meso-structures are sufficient to derive stress–strain behaviour for engineering-scale models in the absence of other environmental factors. The observed differences in damage distribution could be important for analysis of coupled behaviour, e.g., mass transport and chemical reactions affecting local mechanical properties and being affected by local damage. Establishing the importance of damage distribution is such cases requires further research. Keywords: meso-scale; concrete damage plasticity model; cohesive zone model; zero-thickness ITZ; X-ray computed tomography; quasi-static loadings; energy dissipation 1. Introduction The macro-cracks of concrete are developed through micro-crack initiation, propa- gation and coalescence. The reliable prediction of concrete component failure requires in-depth understanding of the localized crack evolution of concrete heterogeneous com- position. Compared with the homogeneity at macro-scale, meso-scale concrete consists of heterogeneous phases, including coarse aggregates, mortar (cement paste with sand and fine aggregates embedded) as matrix, and entrapped air voids. Interfacial transition zone (ITZ) is not observable at meso-scale, but provides both preferable locations for crack initia- tion and easier pathways in the damage evolution. ITZ has lower stiffness and strength compared with mortar, because it is a thin layer of higher-porosity mortar coating around aggregates with thickness between 10 and 100 μm[1,2]. The aggregate distribution of meso-scale concrete can be obtained by digital image acquisition of realistic size and location of aggregates or by random spatial distribution of aggregates of given shapes with prescribed size distribution. As a non-destructive imaging method, X-ray computed tomography (XCT), has been widely used for acquisition of concrete meso-structures [3–5]. Different phases can be identified by threshold of grey Materials 2022, 15, 704. https://doi.org/10.3390/ma15030704 https://www.mdpi.com/journal/materials