The simulation of transport processes in cementitious materials with embedded healing systems

Abstract

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.

Mechanical response of a vascular self-healing cementitious material system under varying loading conditions

“…Much less experimental work has been directed towards the specific requirements of design and numerical models for a range of loading scenarios [3,45]. The lack of a comprehensive data set for any one autonomic healing system became evident to the authors whilst writing a review of numerical models for self-healing cementitious materials [3] and during the development of the new numerical model described in Reference [50]. Thus, the aim of the present research programme was to gather a consistent new set of data on healing-agent transport, curing and mechanical healing for a range of loading rates that could be used to develop numerical and design models for autonomic self-healing cementitious material systems.…”

“…It is emphasised that this model is not intended to be predictive, it is simply introduced as a tool for aiding the interpretation of the notched beam results presented in this paper. A separate paper [50] describes a full coupled nonlinear finite element model for these material systems, which does not have the aforementioned restrictions.…”

A specialised finite element for simulating self-healing quasi-brittle materials

“…Various forms of healing model are described in Jefferson et al [20] and a specific model (see "Healing agent transport and curing model" and "Crack-plane constitutive model" sections for an overview) is presented in Freeman and Jefferson [19] and Jefferson et al [70]. The aim here is to show how a general form of local healing model may be incorporated into the element with an embedded strong discontinuity.…”

“…This leads to a reaction front which propagates into the glue, which, experimental evidence shows is diffuse in nature [75,78]. This can be described by [19]:…”

“…In this study, the EFEM approach is employed and a specialised element is presented that takes healing into account at the element level. The element-based strong-discontinuity approach for simulating both cracking and healing is preferred to the smeared approach of Zhang and Zhuang [17] because the former provides a more accurate description of the crack geometry and crack displacements, which is particularly important in the present work, in which the mechanical model is coupled to a transport model for the flow of healing agents through the discrete cracks [19]. The approach adopted for this work ensures that the healing is consistent with the internal degrees of freedom introduced to represent the crack and allows for a variational derivation.…”