Advanced Finite Element Methods Quiz 1

A material point undergoes hydrostatic compression.

 What does the deformation gradient tensor F look like?

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Which statement is False?

where :

F–deformation gradient,

E–Green-Lagrange strain tensor,

I–identity tensor

• F=I for rigid-body translation of a body in space

• F=0 for rigid-body rotation of a body in space

• Determinant of F = 1 for rigid-body rotation of a body in space

• E=0 for rigid-body translation of a body in space

Which statement is true for the 2nd Piola-Kirchoff stress tensor?

• It shows the actual (real) stress in a body

• Unlike 1st Piola-Kirchoff stress tensor, it is symmetric

• Opposed to Cauchy stress tensor, it has a physical meaning

Which statement is always true?

• Large displacement implies large rotation

• Large displacement implies a large strain

• Large strain implies large deformation

Which statement is true for the 1st Piola-Kirchoff stress tensor?

• P=F/a

• P=Fa

• P=F/A

• P=FA

In which case does the non-linear part of the Green-Lagrange strain tensor become relevant?

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• 

What is the true stress that material „feels“?

• Cauchy stress σ

• 1st Piola-Kirchhof stress P

• 2nd Piola-Kirchhof stress S

Correlate the following material types with their force-displacement (F-u) response in uniaxial tension test.  

• 1- Rubber, 2 – steel, 3 - concrete

• 1 – Steel, 2 - rubber, 3 - concrete

• 1 – Steel, 2 – concrete, 3 - rubber

Which statement is FALSE for the weak form in the total Lagrangian formulation?

• We integrate over the initial volume of the body

• We work with Cauchy stress instead of 2nd Piola-Kirchoff stress

• δW_int is non-linear in terms of displacements

The sources of non-linearity in Finite Element Analysis are (multiple answers are allowed)

• Boundary conditions

• Solution scheme

• Material law

• Expression for B operator

• Kinematics