A composite beam theory for modeling nonlinear shear behavior. (15th January 2018) - Jiang, Fang; Deo, Ankit; Yu, Wenbin
Highlights: An efficient beam theory capturing the nonlinear shear behavior of composites. The variational asymptotic method is used to minimize the loss of accuracy. Nonlinear 3D stress fields including the free-edge effects are rigorously captured. Drawbacks of calibrating material model by plane stress assumption are exposed. The theory provides a rigorous calibration with measurements using slender coupons. Abstract: Accurate predictions of physically nonlinear elastic behaviors of a material point in the structure are essential to the further analyses which are beyond the linear elasticity regime, for example, the progressive damage and the failure. In light of substantial experimental evidence of nonlinear shear stress-strain responses in composites, it is necessary to consider them in the structure-level simulations rigorously. A variational asymptotic beam model is developed for this purpose. The three-dimensional continuum is rigorously reduced to a two-dimensional cross-sectional analysis and a one-dimensional Euler-Bernoulli beam analysis. The original three-dimensional continuum features material nonlinearities in longitudinal shear. The unknown cross-sectional warping is solved by finite element method using the principle of virtual work. Nonlinear beam constitutive relation and three-dimensional stress and strain fields are obtained.