Numerical modelling of elastic behaviour of concrete reinforced with steel short fibres in plane stress conditions

This work describes a numerical model of fibre reinforced concrete elastic behaviour implemented using the finite elements method (Hughes, 2000). In structures made of this material, each point is formed by steel fibres embedded into a simple concrete matrix. The reinforced concrete is represented inside a finite element as an orthotropic material having random material direction based on the vanishing diameter fibre model (Dvorak and Bahei-el-Din, 1982) and the mixing theory modified for short length reinforcement (Oller, 2003). Statistical analysis consisted of repeating the problem's numerical simulation where the direction of fibres was modified by a random function to set up a sampling database from the results and measure their variability. A sensitivity study of finite element size and the number of sampling data was then carried out in terms of total strain energy. Finite element size and sampling data are recommended. The average structural response of a reinforced concrete beam with different quantities of steel fibres where minimum data dispersion was observed is given as an example of applying the above.