Conservation Principles

Question 1

Intensive quantity

Answer 1

A quantity that does not depend on the amount of material. Example is density.

Question 2

Extensive quantity

Answer 2

A quantity that depends on the amount of material. Example is mass.

Question 3

Pull back operation

Answer 3

An operation that takes an eulerian tensor and converts it into a lagrangian tensor.

Question 4

Push forward operation

Answer 4

An operation that takes a lagrangian tensor into an eulerian tensor.

Question 5

Additive decomposition of D

Answer 5

D = D^e + D^P’

Question 6

Define L

Answer 6

L = Fdot F^-1
L = D + W
L = partial of v with respect to x (spatial velocity gradient)

Question 7

Material derivative of a line element

Answer 7

dxdot = Ldx

Question 8

Material derivative of a volume

Answer 8

dVdot = tr(L) dV

Question 9

Material derivative of an area element

Answer 9

dadot = tr(L) da - da.L

Question 10

Material derivative of J

Answer 10

Jdot = J Tr(L) = Jdiv(v)

Question 11

First piola kirchoff stress

Answer 11

P = F^T*sigma

P is a non-symmetric tensor

Question 12

P^T (piola kirchoff stress transposed)

Answer 12

P^T = JsigmaF^-T

P is a non symmetric tensor