Splitting method and hybrid-Trefftz formulation for multisite damage analysis in two-dimensional domains

• Published in: International journal of solids and structures Vol. 104-105; pp. 50 - 64
• Main Authors: Argôlo, Higor Sérgio Dantas de, Proença, Sergio Persival Baroncini
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01-01-2017; Elsevier BV
• Subjects: Approximation; Boundary element method; Cracks; Damage assessment; Deformation; Finite element analysis; Finite element method; Fracture mechanics; Hybrid systems; Hybrid-Trefftz formulation; Iterative methods; Multiple site damage; Multisite damage analysis; Parallel processing; Splitting; Splitting method; Stress intensity; Stress intensity factors; Stress state; Two dimensional analysis; Hybrid-Trefftz formulation; Fracture mechanics; Splitting method; Multisite damage analysis
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/j.ijsolstr.2016.10.030

The aim of this paper is to present a new strategy for multiple-site damage analysis by combining the splitting method and hybrid-Trefftz stress formulation in a two-dimensional domain. The first is a decomposition method originally conceived to obtain the solution of a cracked solid. Accordingly, the given problem is split into three subproblems: an uncracked global problem (PG(0)), a local problem (PL(k)) considering a single crack located in a reduced domain and a global problem (PG(k)) aiming to account for the relative interaction effects among all the cracks. Most subproblems are independent and the solution results from a non-iterative strategy, which is one of the main benefits of this method. The hybrid-Trefftz stress formulation is a non-conventional finite element method where stresses and displacements are approximated, independently, in the domain and boundary of the element, respectively. The stress fields are hereby approximated by a basis function that solves the Navier equation and includes analytical fracture mechanics functions, so that the values of stress intensity factors are computed from the solution of the linear system. The hybrid-Trefftz formulation is used in the local problem PL(k) of the splitting method, therefore improving the performance of the method and providing accurate solutions with very coarse meshes. In conclusion, it is shown through the numerical examples that the splitting method and hybrid-Trefftz formulation framework hereby proposed allows conducing accurate analysis. Once exploring a parallel processing, taking advantage of the independence of each subproblem, the framework can be extended to consider different scenarios of multisite cracked solids with a low computation cost.