The Proper Generalized Decomposition (PGD) as a numerical procedure to solve 3D cracked plates in linear elastic fracture mechanics

• Published in: International journal of solids and structures Vol. 50; no. 10; pp. 1710 - 1720
• Main Authors: Giner, Eugenio, Bognet, Brice, Ródenas, Juan J., Leygue, Adrien, Fuenmayor, F. Javier, Chinesta, Francisco
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 15.05.2013; Elsevier
• Subjects: Corner singularity; Corners; Cracked plate; Decomposition; Engineering Sciences; Finite element method; Fracture mechanics; Materials; Mathematical models; Mechanics; Plates; Proper Generalized Decomposition; Three dimensional; Finite element method; Proper Generalized Decomposition; Corner singularity; Cracked plate
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/j.ijsolstr.2013.01.039

► A 3D crack problem is decomposed into 2D and 1D domains plus extra-coordinates. ► The Poisson’s ratio and the plate thickness are considered as extra-coordinates. ► A single solution solves for a given range of Poisson’s ratio and plate thickness. ► The problem is solved at roughly the cost of a series expansion of 2D analyses. ► Refined discretizations are affordable, capturing the corner singularity behavior. In this work, we present a new approach to solve linear elastic crack problems in plates using the so-called Proper Generalized Decomposition (PGD). In contrast to the standard FE method, the method enables to solve the crack problem in an efficient way by obtaining a single solution in which the Poisson’s ratio ν and the plate thickness B are non-fixed parameters. This permits to analyze the influence of ν and B in the 3D solutions at roughly the cost of a series expansion of 2D analyses. Computationally, the PGD solution is less expensive than a full 3D standard FE analysis for typical discretizations used in practice to capture singularities in 3D crack problems. In order to verify the effectiveness of the proposed approach, the method is applied to cracked plates in mode I with a straight-through crack and a quarter-elliptical corner crack, validating J-integral results with different reference solutions.