Biaxial Stress‐Strain Relation for Concrete

Abstract

A constitutive law for concrete under monotonic biaxial loading up to peak stress is presented in the form of a total, explicit relation between stresses and strains. Explicitness is achieved by expressing the bulk and shear moduli of elasticity as nonlinear functions of the first two invariants of the strain tensor. Since in the plane‐stress states the transversal deformation, which appears as principal strain component in the definition of these invariants, is different from zero, it must be eliminated in order to obtain a biaxial formulation. This, in general, would require the solution of a nonlinear implicit equation; but explicitness has been preserved by finding an empirical, but very accurate, expression of the transversal component of strain as a function of the in‐plane principal components. The resulting stress‐strain relation depends only on three parameters, which characterize the concrete, initial elastic moduli, and compressive strength. Its use is very simple and leads to accurate predictions of the experimental results even close to the peak stress, where inelastic dilatancy occurs.