A Simple Galerkin Meshless Method, the Fragile Points Method (FPM) Using Point Stiffness Matrices, for 2D Linear Elastic Problems in Complex Domains with Crack and Rupture Propagation

TL;DR

The paper introduces the Fragile Points Method (FPM), a simple meshless Galerkin approach using point stiffness matrices, for accurately simulating complex 2D elastic problems, including crack and rupture propagation, without remeshing.

Contribution

It presents a novel, element-free FPM formulation for linear elasticity, emphasizing point-based trial functions and numerical flux corrections, enabling efficient modeling of complex fracture phenomena.

Findings

FPM accurately models crack initiation and propagation.

Demonstrates robustness and efficiency in complex geometries.

No remeshing needed for fracture simulations.

Abstract

The Fragile Points Method (FPM) is an elementarily simple Galerkin meshless method, employing Point-based discontinuous trial and test functions only, without using element-based trial and test functions. In this study, the algorithmic formulations of FPM for linear elasticity are given in detail, by exploring the concepts of point stiffness matrices and numerical flux corrections. Advantages of FPM for simulating the deformations of complex structures, and for simulating complex crack propagations and rupture developments, are also thoroughly discussed. Numerical examples of deformation and stress analyses of benchmark problems, as well as of realistic structures with complex geometries, demonstrate the accuracy, efficiency and robustness of the proposed FPM. Simulations of crack initiation and propagations are also given in this study, demonstrating the advantages of the present FPM in modeling complex rupture and fracture phenomena. The crack and rupture propagation modeling in FPM is achieved without remeshing or augmenting the trial functions as in standard, extended or generalized FEM. The simulation of impact, penetration and other extreme problems by FPM will be discussed in our future papers.