Chandrasekhar Annavarapu Sri

We demonstrate the ability of a stabilized finite element method, inspired by the weighted Nitsche approach, to alleviate spurious traction oscillations at interlaminar interfaces during composite delamination. The method allows for the use of any value for the cohesive stiffness and obviates the need for ad hoc approaches to estimate the minimum penalty stiffness for accurate analysis. Simulation studies involving constant strain patch tests and benchmark delamination tests under mode-I, mode-II, and mixed-mode loadings show evidence of traction oscillations with the standard method. In contrast, the stabilized method is able to alleviate traction oscillations, which illustrates its efficacy and robustness.

We develop a numerical strategy based on a weighted Nitsche’s approach to model a general class of interface problems with higher-order simplex elements. We focus attention on problems in which the jump in the field quantities across an interface is given. The presented method generalizes the weighted Nitsche’s approach of Annavarapu et al. (Comput. Meth. Appl. Mech. Eng. 225–228:44–54, 2012) to higher-order simplices. Specifically, for higher-order simplex elements, we derive closed-form analytical expressions for the stabilization parameter arising in Nitsche’s variational form. We also prescribe corresponding weights for the discrete fluxes in the consistency terms present in Nitsche’s variational form. The prescribed choice of weights is shown to be optimal such that it minimizes the stabilization parameter while ensuring coercivity of the bilinear form. In the presence of large contrasts in material properties and mesh sizes, the proposed weighting yields better conditioned systems than the traditional Nitsche formulation by bounding the maximum eigenvalue of the discrete system from above. Further, the geometrical representation of curved interfaces is improved through a hierarchical local renement approach. Several numerical examples are presented with quadratic triangles to demonstrate the efficacy of the presented method.