A derivative-free phase-field theory for capturing local buckling induced damage in architected plates

Abstract

Architected plates are commonly used to enhance the load-bearing capacity and stability of structures such as ship hulls and aircraft components. Local buckling-induced damage in these plates are critical events that occur when the plate is subjected to external transverse loading. Performing the analysis to accurately capture this damage and estimation of local buckling load requires explicit 3D- modeling of the architected plate, which is computationally expensive. We address this issue by proposing a derivative-free phase-field theory to capture local buckling-induced damage in architected plates. Here the architected plate is modeled using the shear deformable plate theory and the internal web-core structure is preserved in terms of length scale parameters. The numerical value of the length scale parameter depends on the shape of the webcore structure so that any complicated shape of the webcore is handled based on this parameter. This approach makes the analysis simple to predict the damage behavior with a lesser number of degrees of freedom. The extra energy required to attenuate the zero energy mode-induced oscillations in the solution is estimated from the in-plane buckling analysis of the architected plate. To showcase the efficiency, simulations are conducted based on the proposed approach with different loading cases. The local buckling load and the induced damage behavior of the webcore are compared with the 3D-finite element solution obtained from ABAQUS. The comparison shows that the damage variable is an equivalent estimator of out-of-plane stretch of the webcore in predicting the buckling behavior of the webcore with reduced computational cost and time.