This paper presents an extension of the recently developed smoothed floating node method (SFNM) with cohesive zone approach to model crack growth in elastic materials under thermo-elastic loading conditions. The SFNM utilizes floating nodes to accurately model the crack by activating dormant nodes at intersection points of crack path and the corresponding element edges. Through the activation of floating nodes, the cracked element transforms into sub-elements, facilitating separate integration of each sub-element. A smoothing cell-based integration technique is employed to convert the area integral to line integral which mitigates the element distortion issues. The temperature distribution is initially determined across the entire domain, and then imposed as thermal loads in the 2D domain. The thermal stress intensity factor is calculated for both homogeneous and bi-material specimens using the interaction energy integral approach, and the crack propagation is predicted using circumferential stress criterion. The accuracy of the proposed framework is demonstrated with several benchmark problems of fracture mechanics. The develop framework yields comparable results with the available literature with less modeling complexity.

This paper presents a numerical framework for implementation of cohesive zone model with smoothed floating node method (SFNM) for failure analysis of quasi-brittle materials. The nonlinear behavior of material inside the fracture process zone in front of the crack tip is modeled with a potential-based intrinsic cohesive zone approach. Here, SFNM is used to represent the kinematics of crack and the crack front inside the domain without the requirement of remeshing and discontinuous enrichment functions during crack growth, hence resolves the issues associated with the existing discrete numerical methods. A strain smoothing technique is adopted over the domain through which classical domain integration changes to line integration along each boundary of the smoothing cell, hence derivative of shape functions are not required in the computation of the field gradients, thus resolves the issue of element distortion. The proposed numerical framework is firstly verified using the patch test of the two-dimensional specimen under mode I and mode II loading conditions and subsequently extended for solving the two-dimensional standard fracture problems. The effectiveness of the proposed framework is checked by comparing the computational results with the available literature results.

In this work, Floating Node Method (FNM), first developed for fracture modelling of laminate composites, is coupled with cell-wise strain Smoothed Finite Element Method (SFEM) for modelling 2D linear elastic fracture mechanics problems. The proposed method is termed as Smoothed Floating Node Method (SFNM). In this framework, FNM is used to represent the kinematics of crack and the crack front inside the domain without the requirement of remeshing and discontinuous enrichment functions during crack growth. For smoothing, a constant smoothing function is considered over the smoothing domains through which classical domain integration changes to line integration along each boundary of the smoothing cell, hence derivative of shape functions are not required in the computation of the field gradients. The values of stress intensity factor are obtained from the SFNM solution using domain based interaction integral approach. Few standard fracture mechanics problems are considered to check the accuracy and effectiveness of the proposed method. The predictions obtained with the proposed framework improves the convergence and accuracy of the results in terms of the stress intensity factors and energy norms.

The presence of a nonlinear fracture process zone (FPZ) plays a crucial role in governing the failure response of a quasi-brittle structure. One such influence is the structural size and boundary effect phenomenon, where the growth and interaction of FPZ with the boundary has a considerable impact on the load-carrying capacity of the structure. In this article, a numerical study is conducted using a micromorphic stress-based localizing gradient damage model [1], recently proposed by the authors, to capture the structural size effect phenomenon during quasi-brittle failure of geometrically similar concrete beams. The main objective is to reproduce the results of independent experimental investigations on the size effect in quasi-brittle structures using a single set of material and numerical parameters. Generally, a quasi-brittle fracture process starts with a diffuse network of microcracks, which eventually localizes in a narrow process zone before forming a macroscopic crack during the final stages of failure. To comply with this description, the micromorphic stress-based localizing gradient damage model incorporates evolving anisotropic nonlocal interactions throughout the loading process through an anisotropic interaction tensor and a damage dependent interaction function. A new arc-length control method based on rates of the internal and dissipated energy approach [2] is modified as per the localizing gradient damage formulation and implemented to trace the nonlinear behavior in numerical simulations. The damage model successfully reproduces the experimental results with localized damage profiles using low-order finite elements for both mode-I and mixed-mode cases.