Explicit Finite Element Methods for Large Deformation Problems in Solid Mechanics

2007 ◽  
Author(s):  
David J. Benson
Keyword(s):  
Finite Element ◽  
Large Deformation ◽  
Finite Element Methods ◽  
Solid Mechanics ◽  
Explicit Finite Element ◽  
Large Deformation Problems

Periodic Symmetry for Explicit Methods for Large Deformation Twisting and Stretching

2003 ◽  
Author(s):  
Don R. Metzger
Keyword(s):  
Finite Element ◽  
Large Deformation ◽  
Finite Element Methods ◽  
Dynamic Equilibrium ◽  
Explicit Methods ◽  
Element Formulation ◽  
Kinematic Constraints ◽  
Explicit Finite Element ◽  
Internal Forces ◽  
External Forces

The presence of repetitive symmetry in continua and structures allows for the modeling of a single symmetric cell. Typically, the symmetry conditions are enforced with homogeneous kinematic constraints, but these may preclude some otherwise admissible response. Also, in large deformation situations, the original symmetric boundaries can distort significantly. The objective of this work is to provide a means for explicit finite element methods to ensure periodic symmetry while resultant loads may be prescribed on the symmetric boundaries. A method is devised to determine external forces that concurrently maintain dynamic equilibrium of the system with compatible deformations at the boundaries. The method requires only internal forces and nodal positions, which are accessible in an explicit finite element formulation.

Application of the particle finite element method for large deformation consolidation analysis

2019 ◽  
Vol 36 (9) ◽  
pp. 3138-3163 ◽  
Author(s):  
Wei-Hai Yuan ◽  
Wei Zhang ◽  
Beibing Dai ◽  
Yuan Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Large Deformation ◽  
Excess Pore Pressure ◽  
Triangular Element ◽  
Particle Finite Element Method ◽  
Content Type ◽  
Modified Cam Clay ◽  
Large Deformation Problems ◽  
Element Method

Purpose Large deformation problems are frequently encountered in various fields of geotechnical engineering. The particle finite element method (PFEM) has been proven to be a promising method to solve large deformation problems. This study aims to develop a computational framework for modelling the hydro-mechanical coupled porous media at large deformation based on the PFEM. Design/methodology/approach The PFEM is extended by adopting the linear and quadratic triangular elements for pore water pressure and displacements. A six-node triangular element is used for modelling two-dimensional problems instead of the low-order three-node triangular element. Thus, the numerical instability induced by volumetric locking is avoided. The Modified Cam Clay (MCC) model is used to describe the elasto-plastic soil behaviour. Findings The proposed approach is used for analysing several consolidation problems. The numerical results have demonstrated that large deformation consolidation problems with the proposed approach can be accomplished without numerical difficulties and loss of accuracy. The coupled PFEM provides a stable and robust numerical tool in solving large deformation consolidation problems. It is demonstrated that the proposed approach is intrinsically stable. Originality/value The PFEM is extended to consider large deformation-coupled hydro-mechanical problem. PFEM is enhanced by using a six-node quadratic triangular element for displacement and this is coupled with a four-node quadrilateral element for modelling excess pore pressure.

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