An Explicit Finite Element Primer

This Primer is one of many documents produced to help new and experienced analysts solve a range of problem types. It complements the books entitled A Finite Element Primer and NAFEMS Introduction to Non-linear Finite Element Analysis and is the first NAFEMS’ booklet on explicit analysis.

Explicit finite element codes have become increasingly more accessible to analysts and engineers for the solution of dynamic problems that are both non-linear and transient in nature. The functionality of these codes has also seen rapid development, as new applications are defined and older ones better understood. This primer document attempts to outline the theory behind some of the more common functionality, and, where possible to present objective methods on how best to apply it in analyses.

The document is basically divided into three sections:

Chapters 1 and 2 provide an introductory overview of the evolution and philosophy on how an explicit finite element code is arranged.
Chapters 3 to 6 describe the basic functionality used in the generation of a model, namely material properties, loading and boundary conditions, contact and results selection. Contact is included as a separate chapter because it was (and still is) one of the main drivers for the development of explicit codes.
Chapters 7 and 8 offer some guidance on methods of optimising the computational performance of a model and on alternative solution sequences that can be used to overcome problems of extreme mesh deformation.

The primer is targeted at readers with one to two years of experience using general finite element packages. It is impossible in a short document such as this to cover all aspects of the functionality and subtleties of each and every commercial code. Consequently, we have deliberately kept the subjects of each chapter general in nature. Additionally, we have deliberately refrained from exhaustive theoretical discourse on material models, preferring to indicate texts that treat this subject in a more rigorous manner in a bibliography section. We have tried to bring out the salient points of the topics of each chapter and where possible present a description of what can go wrong with an analysis, how to identify the problems and most importantly how to correct or minimise them. Finally, the primer is not intended as a substitute for the theory and user manuals of commercial programs and we would always recommend that these be consulted as the first point of reference before commencing the solution to a problem.

1.0 Introduction	1
1.1 Setting the Scene	1
1.2 Explicit Versus Implicit Time Integration	2
1.2.1 Implicit Integration	2
1.2.2 Explicit Integration	3
1.3 Problems Suited to Explicit Analysis	4
1.4 Historical Development of Explicit Finite Element Methods	8
1.5 Stress Wave Propagation Example	9
1.6 Consistent Units of Analysis	13
1.7 Code Precision	15
2.0 Theoretical Overview	17
2.1 Background	17
2.2 Element Formulations	17
2.2.1 Common Element Classes	17
2.2.2 Reduced Element Integration	18
2.2.3 Hourglass Control	20
2.3 Time Integration Loop	23
2.4 Time Integration Stability	24
2.5 Elemental Time Step Calculation	27
2.6 Damping Control	31
2.6.1 Viscous Damping	31
2.6.2 Artificial Bulk Viscosity	33
3.0 Material Modelling	35
3.1 Elastoplastic Material Response	36
3.1.1 Post Yield Stress Variation with Strain	38
3.1.2 Material Yield Criteria and Plastic Straining	41
3.1.3 Dynamic Material Response	46
3.1.4 Material Failure	50
3.2 Hyperelastic Material Response	52
3.3 Viscous Material Response	54
3.4 Rigid Body Response	55
4.0 Loading and Boundary Conditions	59
4.1 Nodal and Element Variables	59
4.1.1 Follower Forces	59
4.1.2 Stability Effects of Nodal Forces and Boundary Conditions	60
4.2 Initial Conditions	62
4.2.1 Nodal Constraints with Failure Criteria	63
4.2.2 Body Forces	65
4.3 Stress Initialisation	65
4.4 Transmitting Boundaries	69
5.0 Contact Modelling	71
5.1 Contact Definitions	72
5.2 Sorting Algorithms	75
5.3 Penetration and Contact Force Evaluation	76
5.3.1 Friction Force Calculation	77
5.4 Special Cases of Contact	77
5.4.1 Plane Rigid Surface Contact	77
5.4.2 General Rigid Body Contact	78
5.4.3 Tied Contact	79
5.4.4 Contact Combined with Material Erosion	80
5.5 Potential Problems in Contact Modelling	81
5.5.1 Penalty Method Contact	81
5.5.2 Contact Stability	83
5.5.3 Penetration Tracking	84
6.0 Selection of Analysis Results	87
6.1 Introduction	87
6.2 Data Sampling Rates	89
6.3 Energy Results	91
6.4 Nodal Results	92
6.5 Element Results	92
7.0 Model Optimisation	95
7.1 Maximising an Analysis Time Step	96
7.1.1 Time Step Scaling	96
7.1.2 Mass Scaling	96
7.2 Minimising Computational Time per Time Step	97
7.2.1 Mixed Time Integration	98
7.2.2 Activation and Deactivation of Analysis Functionality	101
7.2.3 Rigid and Deformable Material Switching	101
7.2.4 Parallel Processing	102
7.3 Restart File Usage	103
7.4 Coupling to External Analysis Codes	104
8.0 Mesh Adaptivity, Rezoning & Euler Solutions Seqs.	105
8.1 Mesh Adaptivity	105
8.2 Rezoning	107
8.3 ALE (Arbitrary Lagrangian Eulerian) Mesh Updating	108
8.4 Euler Solution Sequence	109
9.0 Concluding Remarks	111
10.0 Bibliography	113
11.0 References	117
Appendix 1 Numerical Example of Wave Propagation

Document Details

Reference	R0085
Authors	Jacob. P Goulding. L
Language	English
Audience	Analyst
Type	Publication
Date	1st January 2002
Region	Global

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