Smoothed floating node method for modelling 2D arbitrary crack propagation problems. (February 2022)

• Record Type: Journal Article
• Authors: Singh, Umed; Kumar, Sachin; Chen, Boyang
• Is Part Of: Theoretical and applied fracture mechanics. Volume 117(2022)
• Publication Date: 2022-02
• Subjects: Floating node method -- Smoothed finite element method -- Smoothing domain -- Stress intensity factors -- Line integration; Fracture mechanics -- Periodicals; 620.1126
• DOI: 10.1016/j.tafmec.2021.103190
• Languages: English
• ISSNs: 0167-8442

Abstract

Highlights: The proposed framework does not require remeshing and enrichment functions to model static and dynamic crack behaviour. The framework is element distortion insensitive due to absence of isoparametric mapping. Shape function derivatives are not required for the field variable gradient matrix. Its implementation is straight forward and can be applied to triangular or quadrilateral or any distorted elements. Its Integration is simple as domain integration is transformed into line integration. Abstract: 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.