Homogenization of Transport Processes and Hydration Phenomena in Fresh Concrete

Abstract

The problem of hydration and transport processes in fresh concrete is strongly coupled and non- inear, and therefore, very difficult for a numerical modelling. Physically accurate results can be obtained using fine-scale simulations, which are, however, extremely time consuming. Therefore, there is an interest in developing new physically accurate and computationally effective models. In this paper, a new fully coupled two-scale (meso-macro) homogenization framework for modelling of simultaneous heat transfer, moisture flows, and hydration phenomena in fresh concrete is proposed. A modified mesoscalemodelisfirstintroduced. Inthismodel, concreteisassumedasacompositematerialwithtwo periodically distributed mesoscale components, cement paste and aggregates. A homogenized model is then derived by an upscaling method from the mesoscale model. The coefficients for the homogenized model are obtained from the solution of a periodic cell problem. For solving the periodic cell problem, two approaches are used – a standard finite element method and a simplified closed-form approximation taken from literature. The homogenization framework is then implemented in MATLAB environment and finally employed for illustrative numerical experiments, which verify that the homogenized model provides physically accurate results comparable with the results obtained by the mesoscale model. Moreover, it is verified that, using the homogenization framework with a closed-form approach to the periodic cell problem, significant computational cost savings can be achieved.

Homogenization of discrete diffusion models by asymptotic expansion

“…Computational homogenization, 34 sometimes called FE 2 , has been developed to overcome complications related to nonlinear constitutive models or complex material internal structures. Vast literature about computational homogenization in heterogeneous materials is available and it spans from the homogenization of mechanical properties, [35][36][37] heat conduction, 38,39 transport phenomena, 40,41 flow, 42 and diffusion, 43 to coupled processes. 44 Motivated by a homogenized solution for discrete mechanical models, [45][46][47][48] the asymptotic expansion homogenization is employed here to develop a homogenization scheme for the discrete diffusion problem.…”

“…Computational homogenization [34], sometimes called FE 2 , has been developed to overcome complications related to nonlinear constitutive models or complex material internal structures. Vast literature about computational homogenization in heterogeneous materials is available and it spans from the homogenization of mechanical properties [35,36,37], heat conduction [38,39], transport phenomena [40,41], flow [42] and diffusion [43], to coupled processes [44].…”