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SIAM Chapter Meetings 2013-2014


These meetings take place in Room M/2.06, Senghennydd Road, Cardiff, from 3pm, unless otherwise stated. Everyone is welcome to attend. If you wish to give a talk, please email

26th November 2013

Speaker: Iulia Mihai (Cardiff School of Engineering)

Title: Micromechanics based constitutive models for cementitious composite materials.

Abstract: Extensive research has been carried out over the last few decades in order to explain and model damage phenomena in quasi-brittle materials such as concrete. It is generally accepted that the heterogeneous structure of such materials observed at nano, micro and meso levels determines their complex macroscopic behaviour and failure mechanisms.

A micromechanical constitutive model for concrete is presented which employs the classic Eshelby inclusion solution and a Mori-Tanaka homogenization scheme to simulate a two-phase composite comprising a matrix phase representing the mortar and spherical inclusions representing the coarse aggregate particles. Furthermore the material contains randomly distributed circular microcracks. The onset of cracking is addressed in a microcrack initiation criterion, governed by an exterior-point Eshelby solution, in which microcracks are assumed to initiate in the interfacial transition zone between aggregate particles and cement matrix. The adopted solution captures tensile stress concentrations in the proximity of inclusion matrix interfaces in directions lateral to a compressive loading path. An advantage of the two-phase formulation is that it is able to predict the build-up of tensile stresses within the matrix phase under uniaxial compression stresses thus allowing the model to naturally simulate compressive splitting cracks. The implementation of the microcrack initiation criterion into the constitutive model enables the use of realistic material properties in order to obtain a correct cross-cracking response.

The model combines these solutions with a rough crack contact component which enables it to capture the dilatant behaviour of concrete subject to compression. The formulation can be readily extended in order to simulate the behaviour of fibre reinforced concrete by considering the crack bridging action of randomly distributed short fibres. The influence of fibres is incorporated into the model at a crack-plane level in a local constitutive relationship via an equivalent damage parameter that characterises the crack bridging state of the fibres. The evolution of the equivalent damage parameter for fibres is based on the micromechanics based crack bridging model of Lin and Li 1997.

Numerical results obtained with the proposed micromechanical constitutive model are compared against experimental data. Good correlation between numerical and experimental responses demonstrates the potential of the model to capture key characteristics of the mechanical behaviour of plain and fibre reinforced concrete.