Constitutive modelling of aggregate interlock in concrete

Abstract

SUMMARYA model for formed cracks in concrete is presented. The model can be used in isolation for existing cracks or linked with other damage or plasticity models and applied once a crack has fully formed. It can be applied directly to interface finite elements or used to control the behaviour of crack planes in more general constitutive models that are applied to 2D and 3D continuum elements. The focus of the present development is on aggregate interlock and crack closing behaviour, which is examined from available experimental data. A contact function is derived and is used to differentiate between three contact states. These states are named open, where there is no contact, interlock, for which the stresses depend upon the nearest distance to the contact surface and closed, for which the stresses depend upon the relative displacements directly. The model is developed within an elasto-plastic framework using effective stresses, which are related to the total stresses via a contact proportion function. The relationship between the effective normal and shear yield stresses is found to be parabolic and the yield shear stress to be dependent upon the opening and embedment displacements. The performance of the model is assessed against experimental data from shear-normal tests and it is concluded that the model is able to represent the key characteristics of the behaviour of formed cracks in concrete.

A plastic-damage constitutive model for the finite element analysis of fibre reinforced concrete

“…The work described in reference [40] demonstrated that the locus of these contact points could reasonably be represented by a conical shaped 'contact function'  in u  space. Furthermore, by assigning a normal and shear stiffness to the interface, the stress developed after contact could be based on the embedment displacement, defined as the nearest distance to the contact surface in u  space.…”

“…Considering the contact assumptions from [40], the stress transferred across the crack plane due to the crack faces regaining contact ( σ  c ) depends upon the contact state as follows:…”

A Review on Studies of Fracture Parameters of Self-compacting Concrete

“…The crack tip opening displacement dropped when the aggregates with coating were used. In 2002, Jefferson [26] produced a model to demonstrate the formed cracks in concrete. The main aim of the model was to understand the interlocking of aggregates and crack closing behaviour.…”

A multi‐asperity plastic‐contact crack plane model for geomaterials

“…Several models have been proposed to simulate the transfer of stresses across rough cracks. These models use, to varying degrees, combinations of empirically based relationships and mechanistic models to describe the morphology of the crack surfaces and the contact expressions, which govern the stress–displacement relationships . Related models, which simulate concrete‐rebar interfaces, also have been developed .…”

“…More recently, Jefferson developed a two‐dimensional model, based on a type of smooth contact theory, in which the crack surface was modelled as a series of triangular asperities. The model employed a contact function based on the data of Walraven and Reinhardt , which was used to describe three contact states.…”