Numerical implementation aspects of a constitutive model for concrete with a deviatoric shape of yielding surfaces based on Bézier curves

FOLINO, P.

Montreal

Congreso; 14th. US National Congress on Computational Mechanics; 2017

IACM

Theaim of this work is to present some details related to the numericalimplementation of a highly non- linear 3D constitutive formulation for concreteso called the Performance Dependent Model [Folino & Etse 2012] in a finiteelement code. One of the relevant features of the model is it C-1 continuousyielding surface. While the meridians are described by second order polynomials,the deviatoric views were originally described by the well-known ellipticalinterpolation between the compressive and tensile meridians proposed by Willam& Warnke (1974). Afterwards, an alternative geometrical description of thedeviatoric shape was explored, using Bézier polynomials. Although threedifferent options were evaluated, involving quadratic, cubic and rationalquadratic Bezier curves, only the two latter were found suitable forrepresenting a real alternative to the elliptical interpolation approach.Thenumerical implementation of complex constitutive models taking into account theincidence of the third invariant, still nowadays, can be considered achallenge. It is usual to find in the literature that this incidence is neglectedand circular deviatoric shapes are considered even for concrete like materials,particularly when non local formulations are considered or multiscaleapproaches are used.Inthis case, for the stress integration of the model, the backward Euler methodwas applied. A direct method was used that leads to a single iteration process,while full consistency condition was used for the determination of the plasticmultiplier. The consistent tangent operator was obtained and used in thenumerical approach. At the finite elements level, the arc length methodcombined with Newton?s method was applied. In this work, some details of thisimplementation are presented, with focus on the comparison of differentnumerical aspects when Bézier curves are considered versus the ellipticalinterpolation approach.