FAILURE ANALYSIS OF ENGINEERING STRUCTURES USING LOCALIZING GRADIENT DAMAGE METHOD

Abstract

The structural integrity of a component/structure is an essential aspect of its design and service. The importance of structural integrity is further compounded for mission-critical components/structures. Therefore, the predictive knowledge of failure in a component/structure is paramount in today’s demanding applications. In addition, due to a significant decrease in product development time, the traditional methods (analytical/experimental) face many challenges in the overall design process. Therefore, it has become necessary to explore alternative methods that yield acceptable results quickly. As a result, computational modelling techniques provide solution at every level of product development. The rapid adoption of computational techniques is also catalyzed by the availability of computational tools and resources at a reasonable cost. Thus, in this thesis, the computational failure modelling methods are developed and applied to simulate various types of fracture problems. The computational failure modelling methods developed till date can be broadly categorized into discrete and smeared methods. As their name suggests, the discrete methods explicitly model a crack/discontinuity, either by using a conformal mesh (FEM) or through appropriate enrichments functions (extended FEM). On the contrary, in smeared methods, the cracks or discontinuities are represented through a finite width zone with very low or negligible stiffness. In other words, a sharp crack is smeared with finite width zone. As a result, unlike discrete methods, the smeared methods are able to model failure quite seamlessly without much numerical complexities. The frequently used smeared methods are the phase field method and gradient damage method. In this thesis, the gradient damage method is adopted for further development and application. The conventional gradient damage method (CGDM) exhibits several spurious effects, such as damage band widening and incorrect damage initiation, despite having remarkable regularizing capabilities. Consequently, a micromorphic framework based localizing gradient damage method (LGDM) is developed to avoid the spurious effects. The LGDM can avoid spurious effects by adopting a decreasing interaction region. An interaction region defines the quantum of interaction between micro and macro cracks and among the micro-cracks themselves during a fracture. This interaction region remains constant in the CGDM causing spurious effects. Therefore, with a micromorphic framework and decreasing interaction region, LGDM is able to simulate quasi-brittle and ductile fracture accurately. However, it is found that there is further scope of improvement in the LGDM. Hence, in this thesis, the LGDM is further improved to enhance its performance and efficiency. In addition, the improvements are also carried out to increase the applicability of LGDM to a broader range of fracture phenomena. Abstract iii The LGDM is a coupled nonlinear method that requires an incremental-iterative procedure to obtain the numerical solution. Besides, the minimum element size in LGDM is dictated by the length scale parameter adopted for the problem. Therefore, computational efficiency is essential for solving real-life practical problems with reasonable time and resources using LGDM. Hence, the LGDM is implemented in commercial software packages like MATLAB, ABAQUS, and COMSOL using FEM for increased computational efficiency and utility. Additionally, three adaptive refinement schemes are also developed for LGDM to increase the computational efficiency. The adaptive refinement schemes are hanging nodes based, template based and multiscale FEM based schemes. These refinement schemes are designed to simultaneously refine the strongly coupled biquadratic serendipity and bilinear elements used in the LGDM. The above-mentioned FE implementations and adaptive refinement schemes led to higher utility and a significant increase in the computational efficiency. Apart from increasing computational efficiency, the applicability of LGDM is also improved to simulate various types of fracture. Firstly, a thermo-mechanical formulation is developed to model quasi-brittle fracture under thermal and mechanical loads. For this, a coupled trivariate formulation is developed that uses displacement, micro-equivalent strain and temperature as the primary field variables. The coupled formulation incorporates the mechanical and thermal effects of steady-state and transient heat transfer. Secondly, the LGDM is used to simulate ductile fracture using localizing gradient plasticity (LGP). The LGP alleviated several spurious effects such as spreading and shifting of plastic strain localization region and ductile damage band found in the conventional gradient plasticity (CGP). Finally, the LGDM is coupled with XFEM (called XLGDM) to simulate fracture through a continuous-discontinuous framework. In this framework, a transition from LGDM to XFEM is carried out consistently. The transition is triggered when the damage reaches close to unity. To simplify the implementation, the decoupling of fully coupled LGDM is carried out through an operator-split methodology. The staggered solution scheme is employed to solve the obtained decoupled LGDM. The conversion of fully coupled LGDM to decoupled LGDM led to a notable decrease in the computation effort and complexity without compromising on the accuracy. The aforementioned improvements led to an increase in applicability of LGDM to various fracture phenomena that is evident from the results reported in this thesis.