In this paper, research progress on numerical models for self‐healing cementitious materials (SHCMs) is discussed. Models developed specifically for SHCMs, as well as other relevant work, are considered. A summary of current self‐healing (SH) techniques is provided along with descriptions of the processes that govern their behavior. Models for mechanical self‐healing, transport processes in materials with embedded healing systems, fully coupled models, and other modeling techniques used to simulate SH behavior are discussed. The mechanics models discussed include those based on continuum–damage–healing mechanics (CDHM), micromechanics, as well as models that use discrete elements and particle methods. A considerable section is devoted to the simulation of carbonation in concrete since the essential mechanisms that govern this process are applicable to SH systems that employ calcite as a healing material. A number of transport models for simulating early‐age self‐healing are also considered. This highlights the fact that there are currently very few papers that describe fully coupled models, although a number of approaches that couple some aspects of transport and mechanical healing behavior are discussed. This article closes with a discussion that highlights the fact that many models are presented with limited or no experimental validation.

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The paper presents results from two groups of experimental tests on a pressurised vascular self-healing cementitious material system, in which low viscosity cyanoacrylate was employed as the healing-agent. The first group comprised three series of tests on plain concrete notched prismatic beams. These tests examined the effects on the mechanical response of varying the healing period, the rate of loading and the healingagent pressure. The second group involved two series of direct tension tests on doubly notched prismatic specimens, each of which had a different crack opening displacement during the healing period. In this second group of tests, healing was allowed to take place in cracks that were held stationary for a period of time, with the degree of mechanical healing being measured for different healing periods. The paper also presents a simplified damage-healing model that is used to interpret the test results and to bring clarity to the indices used to evaluate the degree of healing. The tests were designed to provide new data on simultaneous damage-healing behaviour as well as on the effects of varying pressure, static healing periods and cracking configurations on the mechanical response of this self-healing cementitious material (SHCM) system. These data have been used to guide the development of a new numerical model for SHCMs (reported elsewhere) and should be useful to others who are developing design procedures and/or computational models for similar material systems.

A new model for simulating the transport of healing agents in self-healing (SH) cementitious materials is presented. The model is applicable to autonomic SH material systems in which embedded channels, or vascular networks, are used to supply healing agents to damaged zones. The essential numerical components of the model are a crack flow model, based on the Navier-Stokes equations, which is coupled to the mass balance equation for simulating unsaturated matrix flow. The driving forces for the crack flow are the capillary meniscus force and the force derived from an external (or internal) pressure applied to the liquid healing agent. The crack flow model component applies to non-uniform cracks and allows for the dynamic variation of the meniscus contact angle, as well as accounting for inertial terms. Particular attention is paid to the effects of curing on the flow characteristics. In this regard, a kinetic reaction model is presented for simulating the curing of the healing agent and a set of relationships established for representing the variation of rheological properties with the degree of cure. Data obtained in a linked experimental programme of work is employed to justif the hoi e a d fo of the o stituti e elatio ships, as ell as to ali ate the odel s evolution functions. Finally, a series of validation examples are presented that include the analysis of a series of concrete beam specimens with an embedded vascular network. These examples demonstrate the ability of the model to capture the transport behaviour of this type of SH cementitious material system.

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The formation of cracks in quasi-brittle materials such as concrete produces a degradation in mechanical performance in terms of both stiffness and strength. In addition to this, the presence of cracks leads to significant durability problems, such as reinforcement corrosion and calcium leaching [1]. Self-healing systems are designed to mitigate these issues by introducing crack 'healing' mechanisms into the material that result in a recovery of both mechanical performance and durability properties. There is now a significant body of work on the numerical simulation of self-healing systems [2-19], as highlighted in a recent review article [20]. The numerical treatment of damage-healing behaviour in mechanical self-healing models has varied, with many utilising a continuum damage-healing mechanics framework (e.g. [5, 7]). Alternative approaches have included a model based on micromechanical theories [11], the discrete element method (DEM) [13], the extended finite element method (XFEM) [12] and embedded discontinuity elements (EFEM) [17]. In addition to this, the treatment of the healing itself has varied, ranging from treating the healing as a thermodynamic

This paper gives an overview of a combined experimental-numerical study on vascular self-healing (SH) systems for cementitious composite materials. The work aimed to bridge the gap between numerical and experimental investigations for this type of SH system and to provide a set of data for developing, calibrating and validating a finite element model for these materials. The study investigated both healing-agent transport and mechanical damage-healing processes, including healing-agent curing. The experimental programme included mechanical tests on notched concrete beams and compact direct-tension specimens with inbuilt vascular healing systems, as well as tests to measure the transport properties of healing-agent within discrete concrete cracks and through the concrete matrix. The new coupled model employs elements with embedded strong discontinuities to simulate cracks and mechanical healing behaviour. A damage-healing constitutive model is described that simulates multiple damage-healing ‘events’. This mechanical model is coupled to discrete and continuum flow models that simulate healing-agent transport. The transport model accounts for pressurised and capillary flow, as well as curing-dependent flow properties. The main focus of this contribution is to show how these parallel programmes of work were combined so that the experimental observations guided the numerical developments and modelling questions were answered using experimental findings.

Summary A number of effective models have been developed for simulating chemical transport in porous media; however, when a reactive chemical problem comprises multiple species within a substantial domain for a long period of time, the computational cost can become prohibitively expensive. This issue is addressed here by proposing a new numerical procedure to reduce the number of transport equations to be solved. This new problem reduction scheme (PRS) uses a predictor‐corrector approach, which “predicts” the transport of a set of non‐indicator species using results from a set of indicator species before “correcting” the non‐indicator concentrations using a mass balance error measure. The full chemical transport model is described along with experimental validation. The PRS is then presented together with an investigation, based on a 16‐species reaction‐advection‐diffusion problem, which determines the range of applicability of different orders of the PRS. The results of a further study are presented, in which a set of PRS simulations is compared with those from full model predictions. The application of the scheme to the intermediate‐sized problems considered in the present study showed reductions of up to 82% in CPU time, with good levels of accuracy maintained.