A new specialised finite element for simulating the cracking and healing behaviour of quasi-brittle materials is presented. The element employs a strong discontinuity approach to represent displacement jumps associated with cracks. A particular feature of the work is the introduction of healing into the element formulation. The healing variables are introduced at the element level, which ensures consistency with the internal degrees freedom that represent the crack; namely, the crack opening, crack sliding and rotation. In the present work, the element is combined with a new cohesive zone model to simulate damage-healing behaviour and implemented with a crack tracking algorithm. To demonstrate the performance of the new element and constitutive models, a convergence test and two validation examples are presented that consider the response of a vascular self-healing cementitious material system for three different specimens. The examples show that the model is able to accurately capture the cracking and healing behaviour of this type of self-healing material system with good accuracy.

A new model for the multi-scale simulation of solute transport in concrete is presented. The model employs plurigaussian simulations to generate stochastic representations of concrete micro- and meso-structures. These are idealised as two-phase medium comprising mortar matrix and pores for the micro-structure, and mortar and large aggregate particles for the meso-structure. The generated micro- and meso-structures are employed in a finite element analysis for the simulation of steady-state diffusion of solutes. The results of the simulations are used to calculate effective diffusion coefficients of the two-phase micro- and meso-structures, and in turn, the effective diffusion coefficient at the macro-scale at which the concrete material is considered homogenous. Multiple micro- and meso-structures are generated to account for uncertainty at the macro-scale. In addition, the level of uncertainty in the calculated effective diffusion coefficients is quantified through a statistical analysis. The numerical predictions are validated against experimental observations concerning the diffusion of chloride through a concrete specimen, suggesting that the generated structures are representative of the pore-space and coarse aggregate seen at the micro- and meso-scales, respectively. The method also has a clear advantage over many other structural generation methods, such as packing algorithms, due to its low computational expense. The stochastic generation method has the ability to represent many complex phenomena in particulate materials, the characteristics of which may be controlled through the careful choice of intrinsic field parameters and lithotype rules.

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.