Meshless methods for nonlinear continuum mechanics - Graça, Ana Augusta Bernardo da (2018)
In the past two decades, meshless methods have been successfully implemented to solve numerous problems in engineering and science. The main characteristic of these methods is that the approximation functions do not require an established node connectivity (mesh) as is the case with Finite Element Methods (FEM). This new class of methods has shown great potential in the situations where the mesh becomes a critical issue. For instance, in the presence of large deformations, sometimes it is necessary to rede ne the mesh during simulation. Remeshing represents additional computational costs to the overall solution. Meshless methods have become not only an alternative to a conventional FEM but were also introduced in FEM as mixed formulations. The main goal of this work is to investigate and validate the Element Free Galerkin (EFG) method applied for nonlinear continuum mechanics problems considering the plastic anisotropy of metals. Hence, the Element Free Galerkin (EFG) method was implemented to solve the problems in two-dimensional and three-dimensional geometries. First, the convergence of the EFG method was investigated for di erent integration rules, polynomial basis and weight functions in 2D. Next, a 3D subspace analysis was conducted to identify the linear independent deformation modes. The goal was to use these results in the Enhanced Assumed Strain (EAS) method, formulated in the scope of the EFG method, and reduce the locking e ects arising in a nearly incompressible state, which was accomplished with success. Additionally, comparison between the EAS and the B-bar methods was investigated. To study the problems of nonlinear continuum mechanics, an iterative Newton-Raphson procedure was developed with an implicit formulation with the nonlinear equation system. As for the constitutive models, di erent yield criteria were implemented to predict the e ects of plastic anisotropy. Lastly, uniaxial-tension simulations were performed to predict the r -values of two aluminium alloys