# Presentation: 752793

## An Explicit-Implicit Analysis Scheme in a General-Purpose FEA Environment

- Abed M. Khaskia
- Mallett Technology, Inc.
- Laurel, Maryland
- (301) 725-0060

## Outline

-  Introduction
-  System of Equations  [Equations of Motion]
-  Explicit Solution Scheme
-  Implicit Scheme
-  Mixed Explicit – Implicit
-  Illustrative Case

## Introduction - Applications

-  Vibration analysis
-  Impact analysis. Crashworthiness, Drop test
-  Rotating elements and machinery
-  Earthquake analysis
-  Explosives
-  Metal Forming/stamping/rolling
-  Random Vibration

## Applications

## Applications

## Applications

## Introduction - Challenges

-  Large systems
-  Material and geometrical behavior
-  Unknown material properties
-  Loading and system boundary conditions
-  Multiphysics and multiple domains
-  Available testing and verifications issues
-  Changing technologies in numerical analysis

## System of Equations

-  General Equations of Motion

-  Solutions:
-  Implicit
-  Explicit
-  Mixed dictated by physics and numerical behavior

## Implicit Scheme

## Implicit Scheme

## Explicit Scheme

## Comparisons/Issues

-  Stability
-  Time step size
-  Nonlinear effects
-  Computations
-  Convergence
-  Mass matrices

## Mixed Scheme / Explicit - Implicit

-  Solution Steps

## Mixed Scheme / Explicit - Implicit

-   Solution Process on Material Model

## Explicit to Implicit

- Case Study – Cup Stamping

-  System Description and FE Model

## Explicit to Implicit

- Case Study – Cup Stamping

-  Modeling Challenge
-  Mass scaling to speed solution
-  Solution accuracy and verifications
-  Damping
-  Friction effects
-  Element deformation and proper shape
-  Time point and process to go from explicit to implicit
-  Preventing Rigid body motion in implicit solution
-  Convergence of the nonlinear implicit solution

## Explicit to Implicit

- Case Study – Cup Stamping

-  Results
-  Animation of process
-  Quality of solution – Hourglass energy check
-  Force applied by punch and blank velocity
-  Fluctuation in stress and strain data
-  Deformed shape and plastic strains at end of explicit
-  Spring back shape after implicit switch

## Explicit to Implicit

- Case Study – Cup Stamping

-  Stamping Process

## Explicit to Implicit

- Case Study – Cup Stamping

-  Blank Velocity

## Explicit to Implicit

- Case Study – Cup Stamping

-  Stress and Strains

## Explicit to Implicit

- Case Study – Cup Stamping

## Explicit to Implicit

- Case Study – Cup Stamping

-  Implicit FE Model

## Explicit to Implicit

- Case Study – Cup Stamping

-  Spring back shape

## Explicit to Implicit

- Case Study – Cup Stamping
- Conclusions

-  Experience shows that explicit/implicit is less than 25% of implicit CPU for same application
-  Implicit only is easier to validate and hence provides more confidence
-  Rigid body constraints in implicit part and time location for switch
-  Mass scaling and speed of process introduce simplifications
-  Certain aspects of the explicit/implicit process could be automated
-  Elements selections and compatibilities among them
-  Data management is important as time scale has two different meanings
-  The process is very promising for nonlinear applications as solvers will switch automatically between the two schemes based on solution behavior

## Acknowledgments/References

*Certain figures and images are courtesy of ANSYS, Inc. and  Livermore Software Technology Corporation.*