Nonlinear Elastic Effects on High-Strength Concrete Stress Invariants

Computational modeling of concrete behavior and most failure criteria for concrete strongly rely on the use of invariants of stress. These invariants allow a straightforward geometric interpretation of stress states and concrete failure surfaces in the three-dimensional Haigh-Westergaard stress space. Although second-order linear elastic relations have been traditionally applied to evaluate stresses in concrete, the magnitudes of concrete third-order parameters based on finite deformation theory—Murnaghan parameters l, m, n—are such that, if nonlinear stress-strain relations are considered, the stress invariants’ magnitudes are directly affected. In this work, acoustoelastic stress-strain relations for a general triaxial stress state and ultrasonically calculated second- and third-order elastic parameters are used in the evaluation of three high-strength concrete mixtures with compressive strengths: f′_c = 43.0, 44.8, and 56.0 MPa (6.2, 6.5, and 8.1 ksi, respectively). The results demonstrate that nonlinear elastic effects introduce anisotropy when uniaxial stresses are applied and the magnitudes of concrete elastic and shear moduli change because of the applied stress field. When triaxial loads are considered, all stress invariants—first (I₁), second (I₂), and third (I₃)—also undergo variations in their magnitudes. The stress-induced anisotropy due to uniaxial loading application and also the changes in the stress invariants’ magnitudes calls attention to the importance of considering nonlinear third-order effects in cement-based materials’ stress-strain relations and failure criteria.