Numerical Simulations of Fracture Problems using Smoothed Floating Node Method

Abstract

Numerical Simulations of Fracture Problems using Smoothed Floating Node Method Umed Singh Ensuring the safety and dependability of a wide array of engineering applications is of utmost importance, particularly in fields like aerospace, civil infrastructure, and mechanical components. It is imperative to accurately comprehend and forecast the onset and spread of cracks within engineering structures to prevent potentially disastrous failures with severe consequences. As materials are utilized in practical scenarios, their strength may diminish based on variables such as loading conditions, material composition, and environmental factors. The presence of flaws such as cracks, voids, holes, inclusions, discontinuities and manufacturing defects introduces complexity, thus requiring the utilization of fracture mechanics to tackle these complexities. Also changes in temperature within a material can lead to the development of thermal stresses, which may result in cracks and failure of the structure. Beyond cracking, temperature variations also result in alterations in the material's microstructure, and these changes significantly affect its mechanical properties and behaviour. Researchers have developed computational techniques, including both analytical and numerical methods, to tackle these challenges. In the field of computational analysis, two main approaches are highlighted in existing literature: Smeared Crack Approach and Discrete Crack Approach. Smeared or continuous methods, demonstrated by continuum damage mechanics, forecast material degradation by tracking the accumulation of damage in the material. On the other hand, discrete crack approaches consider cracks as interfaces, proving especially valuable for dealing with complex crack patterns. Linear elastic fracture mechanics simplifies the fracture behaviour analysis for materials that behave linearly elastic, but in practical applications, challenges frequently arise due to the presence of nonlinearities in the problems, such as in quasi-brittle materials (concrete, rock, bone, ice, and various composites) with nonlinear fracture process zone ahead of the crack tip. Many advanced numerical methods are reported in the literature to solve fracture mechanics problems involving arbitrary crack propagation without the use of remeshing to tackle the strong discontinuity. This thesis aims to develop a formulation based on discrete crack approach using floating node method in combination with strain smoothening technique to solve the fracture mechanics problems having strong discontinuity. The crack inside the specimen finds its true position with the help of floating nodes rather than tackling the crack by virtual nodes positioned on the standard nodes by using the special enrichment functions. The initial focus of this thesis is to develop a Smoothed Floating Node Method (SFNM) that accurately traces the crack real position by utilizing floating nodes based on the crack propagation direction criterion. A strain smoothing technique is employed, replacing area integral with a line integral to handle the integration scheme. Here, to mitigate challenges related to element distortion and convexity, a cell-based smoothing approach is adopted which eliminates the need of Jacobian matrix in the numerical calculations. The method's precision and convergence are thoroughly analysed, and error norms are calculated based on both energy and stress Intensity factors. Another contribution of this thesis is the incorporation of the nonlinear behaviour of the fracture process zone into the smoothed floating node method. The zero thickness cohesive element used in this work, acts as a medium to transfer the cohesive forces through the partially damaged materials in cohesive zone. The potential based intrinsic cohesive zone modelling formulation is aligned to the proposed SFNM method for the analysis of fracture behaviour of the quasi brittle materials. First, the numerical framework is validated through the patch test of a two-dimensional specimen subjected to both mode I and mode II loading conditions. Following this verification, the framework is further applied to address two-dimensional standard fracture problems considering the cohesive strengths of the material, both in the normal and tangential directions. The assessment of the SFNM coupled with CZM is conducted for scenarios involving straight and curved crack growth. Next, the formulation of the Smoothed Floating Node Method is extended to address fracture problems occurring within a thermally loaded environment, while considering the influence of mechanical boundary constraints. The analysis involves examining cracked specimens subjected to both isothermal and adiabatic crack thermal loading conditions. The fracture failure of the specimen is attributed to the thermal stresses induced in this setting. The cohesive zone model is employed to account for the combined thermo-mechanical effects. The nonlinear fracture process zone is examined both under thermal loading and mechanical loading separately, as well as in their combined state. Various homogeneous and bi-material problems are effectively solved using the proposed methodology, and the obtained results are compared with the existing literature results. Finally, comprehensive findings are presented for cases involving a combination of thermal and mechanical loads, specifically focusing on quasi-brittle materials.