Deviatoric Shape of Concrete Failure Surface based on Bezier curves

FOLINO, P

San diego

Congreso; 13th. US National Congress on Computational Mechanics; 2015

IACM

Inthis work the suitability of Bezier polynomials for representing an appropriatedeviatoric shape to be considered mainly in failure surfaces and also inyielding surfaces of concrete like materials is explored. Three differentoptions are evaluated, involving quadratic, cubic and rational quadratic Beziercurves, as an alternative to the classical and extensively used ellipticalinterpolation between the compressive and tensile meridians proposed by Willam& Warnke (1974). Like the latter, the three proposals lead to a deviatoricshape similar to a triangle with rounded corners, with a C1 continuity type. It iswell known that failure and mechanical behaviour of concretelike materials depend on all the three invariants and therefore yielding andfailure surfaces involving a circular deviatoric shape, neglecting theincidence of the third invariant, cannot accurately represent the main featuresobserved in concrete experimental tests, particularly when low confinementlevels and load scenarios leading to different Lode angles are considered.Several deviatoric shapes involving the third invariant have been proposed inthe literature. Most of them present a lack of smoothness and therefore, arenot convenient for numerical implementations. Among the proposals considering aC1 continuity type, outstands the above mentioned proposal by Willam &Warnke (1974), consisting in a deviatoric shape described by three ellipses. Themotivation of this work aims to improve the available numerical tools forconsidering the third invariant in constitutive models for concrete. On the onehand, it has been demonstrated in Folino and Etse (2011) that when theelliptical interpolation fails to accurately predict peak stress under biaxialstress states particularly in the compression-compression quadrant, thenumerical approach does not present any tool permitting to improve thisaccuracy, and thus, any contribution in this sense was the first objective ofthis work. On the other hand, the complexity involved in numerical approaches consideringthe third invariant usually discourages it application, and then, the secondobjective was to explore other possible mathematical descriptions of thedeviatoric shape. Herein, three different types of Bezier curves are consideredfollowing these two main purposes. It is demonstrated that the rationalquadratic type can be considered the most appropriate alternative to theelliptical interpolation.