The simulation of crack opening-closing and aggregate interlock behaviour in finite element concrete models

Abstract

The ability to model crack-closure behaviour and aggregate interlock in finite element concrete models is extremely important. Both of these phenomena arise from the same contact mechanisms, and the advantages of modelling them in a unified manner are highlighted. An example illustrating the numerical difficulties that arise when abrupt crack closure is modelled is presented, and the benefits of smoothing this behaviour are discussed. We present a new crack-plane model that uses an effective contact surface derived directly from experimental data and which is described by a signed-distance function in relative-displacement space. The introduction of a crack-closure transition function into the formulation improves its accuracy and enhances its robustness. The characteristic behaviour of the new smoothed crack-plane model is illustrated for a series of relative-displacement paths. We describe a method for incorporating the model into continuum elements using a crack-band approach and address a previously overlooked issue associated with scaling the inelastic shear response of a crack band. A consistent algorithmic tangent and associated stress recovery procedure are derived. Finally, a series of examples are presented, demonstrating that the new model is able to represent a range of cracked concrete behaviour with good accuracy and robustness. Figure 10. Uniaxial opening and closing response.Figure 11. Cracks opened in uniaxial tension and subsequently loaded in shear. EMBEDDED CRACK PLANES IN A THREE-DIMENSIONAL CONSTITUTIVE MODEL Embedded smeared cracksWhen the crack-plane model is applied to continuum elements, cracks are effectively smeared over elements and are represented by directional damage. The term h is no longer employed directly to define the local strains; instead, the crack-band approach of Bazant and Oh [3] is used. This involves scaling the governing fracture softening stress-strain curve, using the fracture energy parameter .G f /, such that the energy consumed in fully opening a mode 1 crack is the same irrespective of the element size. A key assumption in this method is that (numerically) strains localise into a band of elements, one element wide, early enough in the fracture process for the fracture energy consumed outside this band to be negligible. If this assumption is valid, the inelastic fracture strain vector (i.e. the reduced form of the strain tensor) can be related to the inelastic relative-displacement vector . M u/ as follows:The characteristic length is equal to the length of the longest straight line that could be drawn within a finite element normal to the crack plane. This gives a length in between that is computed by 'Oliver's first and second methods', which are described in References [52] and [64].The element local strain vector .Q ©/ is then defined as the sum of the inelastic and elastic strain components:in which ı denotes a third-order-matrix vector contraction. The incremental fracture strains are then given by Equation (35):

A Continuum Coupled Thermo-Hygro Mechanical Time-Dependent Model for Concrete

“…This damage parameter is a function of an effective local strain parameter ζ, which in turn is a function of the local strains ( ε  ) (Jefferson and Mihai, 2015). Bazant and Oh's (1983) crack-band approach is used to regularise the model with respect to mesh grading.…”

“…The constitutive is based on a recently developed smoothed plastic-damagecontact model for concrete developed by Jefferson and Mihai (2015). The basic stress-strain relationship employed in the model is as follows;…”

“…This uses the ideas from Bazant et al's (1997) solidification creep model but introduces the idea of two age related material states, relating to short and long term creep behaviour. The basic mechanical constitutive model is based on a new smoothed plastic-damage-contact model (Jefferson & Mihai, 2015).…”

Regularised crack behaviour effects on continuum modelling of quasi-brittle materials under cyclic loading

“…• low regularity of the constitutive laws (discontinuous stiffness variations at stress sign changes) due to the consideration of stiffness recovery under cyclic loading, later leading to numerical robustness issues [19,20];…”

Modelling on crack propagation behaviours at concrete matrix‐aggregate interface

“…Therefore, researches on crack propagation behaviours in concrete is of great significance in engineering practice. A series of research has been initiated to improve the understanding of failure mechanism in concrete, especially from the perspective of fracture mechanics . In order to assess the failure, the concept of energy release rate (ERR or G ) or stress intensity factor (SIF or K ) in fracture mechanics are generally introduced, predicted, and compared with its critical value G c or K c ; fracture tests are necessitated for these experimental values.…”