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MISC

Comparison explicit and implicit time integrations

Explicit method Implicit method
Target problems Dynamic(transient) Static and dynamic(transient)
Damping Artificial damping Numerical damping
Time stepping method Matrix multiplication Linear algebra equations
Assemble stiffness matrix No Yes
Data storage requirement Small Large
Solving speed each step Quick Mediate
Iteration convergence No Yes
Solution Certain solution Could be uncertain solution
Stability Conditionally stable Unconditionally stable
Time step Small Large
Accuracy Low High
Strain-stress curve Suitable Mooney-Rivlin model Parameter requirement for positive definiteness
No inflection point (single curvature) 2- or 3-parameter C10 + C01 > 0
One inflection point (double curvature) 5-parameter

C10 + C01 > 0
C20 > 0
C02 < 0
C20 + C11 + C02 > 0

Two inflection points 9-parameter

C10 + C01 > 0
C30>0
C03 < 0
C30 + C21 + C12 + C03 > 0