Multi-linear stress-strain and closed-form moment curvature response of epoxy resin materials

A simplified multi-linear stress-strain approach has been used to obtain the closed form nonlinear moment curvature response for epoxy resin materials. The model consists of constant plastic flow in tension and compression. The multi-linear stress-strain model is described by two main parameters in addition to four non-dimensional tensile and six non-dimensional compressive parameters. The main parameters are modulus of elasticity in tension and strain at the proportional elastic limit point in tension. The ten non-dimensional parameters are strain at the ultimate tensile stress, maximum strain, post elastic proportionality stiffness, and post peak strength in the tension model and strain at the proportionality elastic limit, strain at yield strength point, maximum strain, initial elastic stiffness, post elastic proportionality stiffness, and post peak strength in the compression model. Explicit expressions are derived for the stress-strain behavior of the epoxy resins. Closed form equations for moment curvature relationship are presented. The results of tension, compression, and bending tests using digital image correlation technique are presented. Load deflection response of flexural three point bending (3PB) samples could be predicted using the moment curvature equations, crack localization rules, and fundamental static equations. The simulations and experiments reveal that the direct use of uniaxial tensile and compressive stress-strain curves underestimates the flexural response. This model gives an upper bound estimate for flexural over-strength factor.