Citation: Chidiac, S.E.; Reda, M.A. Performance Modeling of Spherical Capsules during Mixing of Self-Consolidating Concrete. Materials 2023, 16, 2379. https:// doi.org/10.3390/ma16062379 Academic Editor: Marjan Marinšek Received: 19 February 2023 Revised: 9 March 2023 Accepted: 14 March 2023 Published: 16 March 2023 Copyright: © 2023 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 Performance Modeling of Spherical Capsules during Mixing of Self-Consolidating Concrete Samir E. Chidiac * and Mouna A. Reda Department of Civil Engineering, McMaster University, 1280 Main Street West, Hamilton, ON L8S 4L7, Canada * Correspondence: chidiac@mcmaster.ca Abstract: Autonomous healing is a very promising technique in self-healing concrete systems. For capsules to achieve their anticipated performance, they should be able to survive the harsh mixing conditions of concrete, yet rupture upon concrete cracking. At present, there are no standard test methods, either experimental or analytical, for determining the capsule survival rate during concrete mixing. This study investigates the correlation between the capsules’ shell properties, concrete rheological properties, the capsules’ external forces, and capsule survival rate during concrete mixing. Finite element and statistical modeling techniques were employed to evaluate the capsule performance and predict the survival rate of capsules during concrete mixing, with 68% confidence. The results revealed that the capsules’ survivability during concrete mixing is highly influenced by the capsule’s radius-to-thickness ratio, the rheological properties of the fresh concrete, the average- paste-thickness (APT) of the concrete mix, the aggregate content and angularity, and the speed of the mixer. In brief, capsules with a radius-to-thickness ratio between 30 and 45 are likely to survive concrete mixing and yet still rupture upon concrete cracking. Keywords: self-healing; capsule survival rate; FE model; probability; rheological properties; concrete; concrete pan mixer 1. Introduction Encapsulation, which is employed to protect the healing agent during the mixing and casting of fresh concrete and to release the agent upon the cracking of hardened concrete [1,2], is a promising technique for the creation of autonomous self-healing concrete systems [3–22]. For the capsules to achieve their objective, the shell’s mechanical and geometrical properties need to be compatible with those of the concrete matrix. Ideally, the shell needs to be ductile to endure the harsh concrete mixing conditions and brittle to rupture upon concrete cracking. Different shell materials, including glass [5,21–29], ceramics [21,29], and polymers [2–4,9,12,14–16,18,19,30–41], have been investigated and tested in the literature. Test results revealed that glass and ceramics have low survivability during mixing [42,43], whereas polymers have “switchable” mechanical properties, with a higher survival ratio [13,44–47]. The robustness of capsules to survive mixing conditions requires not only their resistance to the shear forces applied by the concrete mixer, but also to the punching stress exerted by the aggregates [47–49]. The review of the literature revealed that there are no standard test methods for measuring the performance of capsules in terms of survivability during concrete mixing and placing. The studies documented in the literature, which are presented here, show inconsistencies in the results, as different test methods and measuring techniques are used to assess performance. Moreover, the survival rate of the capsules during mixing is found to be highly influenced by the geometrical and mechanical properties of the shell, the concrete rheological properties, and the speed and type of the concrete mixer. As such, there is a need to develop standard testing protocol to evaluate the performance of capsules in self-healing cementitious materials during the mixing and placing of concrete, as their performance impacts the efficiency and efficacy of Materials 2023, 16, 2379. https://doi.org/10.3390/ma16062379 https://www.mdpi.com/journal/materials