Two-Dimensional Numerical Model of the Fracture Process in Steel Fibre Reinforced Concrete with the Continuum Strong Discontinuity Approach and Functional Data Analysis

Fabián Augusto Lamus,Rubén Darío Guevara,Dorian Luis Linero

doi:10.1590/1679-78255325

Abstract

Abstract This paper presents the formulation of a two-dimensional numeri-cal model able to describe the fracture process in structural mem-bers of steel fibre reinforced concrete (SFRC) from the volume ratio of the fibres and the mechanical properties of the compo-nents: a concrete matrix and a set of steel fibres with a random orientation. The relationship between the stress and the strain fields of the composite material is obtained using the mixture theory with a compatibility strain of its component materials. The concrete matrix is represented with a scalar damage constitutive model with a softening strain and a different strength in tension and compression. The mechanical strain of an insulated fibre and the slip between the fibre and the matrix are simultaneously de-scribed with a one-dimensional plasticity constitutive model. The cracking of the composite material indicates a jump in the dis-placement field and non-bounded values of the strain field, which are represented by the Continuum Strong Discontinuity Ap-proach. The model has been implemented in the framework of the nonlinear analysis with the Finite Element Method, using con-stant strain triangular elements. Moreover, the fibres distribution and orientation change randomly in each finite element and each simulation or observation. The structural responses of the simula-tions are treated as curves and analysed by tools from the Func-tional Data Analysis. Confidence intervals for the structural re-sponse are built using bootstrap methodology. Finally, experi-mental tests of SFRC members subjected to tension and bending are simulated. The structural response and the cracking patterns obtained from the numerical simulation are satisfactory.

Highlights

The mechanical behaviour of steel fibre reinforced concrete (SFRC) can be described by four types of approaches implemented with finite element methods, according to the analysis scale
The objective of this work is to estimate the median of the mechanical response and its confidence interval, for structural members of SFRC by means of a stochastic procedure that is based on the functional data analysis, which has proven to be adequate for similar problems
Each material point shows the macroscopic behaviour of the SFRC considering: the steel fibres uniformly distributed in the concrete matrix, the compatibility of the longitudinal strain between the materials, and the composite material stress equal to the weighted addition of the stress of each component material

Summary

Introduction

The mechanical behaviour of SFRC can be described by four types of approaches implemented with finite element methods, according to the analysis scale. Two-Dimensional Numerical Model of the Fracture Process in Steel Fibre Reinforced Concrete with the Continuum Strong Discontinuity Approach and Functional Data Analysis mesh of solid finite elements represents the plain concrete. Oliveira de Barros (1995) implements a non-linear constitutive model which represents the fracture process by a rotating smeared crack model. This approach has a low computational cost but requires knowing the mechanical properties of the SFRC for a defined amount of steel as an input data

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Conclusion