Adaptive mesh refinement schemes for the localizing gradient damage method based on biquadratic-bilinear coupled-field elements

Abstract

In the present work, adaptive h-refinement schemes are developed for the localizing gradient damage method. In general, the existing adaptive refinement schemes have been developed using the bilinear quadrilateral (Q4) elements for the weakly coupled systems such as XFEM and Phase field method. In contrast to this, the presently developed refinement schemes are designed for simultaneous refinement of the strongly coupled biquadratic serendipity (Q8) and Q4 elements, which is a typical requirement of the localizing gradient damage method. This work addresses mainly two types of numerical complexities in the presently developed refinement schemes, first one is the strong coupling of primary variables in the localizing gradient damage method and other is the presence of mid-side nodes in the Q8 element. A detailed comparative study of three adaptive refinement schemes i.e. hanging nodes based, template based and multiscale FEM based, is carried out. The suitability and effectiveness of the refinement schemes are demonstrated through the study of various parameters like damage profile, load-displacement response, discretization error and computation time. Additionally, a comparison matrix of implementation complexity based on developed algorithm and coding is also presented to highlight the difficulties in their implementation. A novel oversampling data transfer scheme is proposed for the transfer of Gauss point’s state variables from unrefined to refined mesh.