650:651 Mechanics of Inelastic Behavior (SM3)

12/7/01

650:651 Mechanics of Inelastic Behavior (SM3)

Homework No. 4

(Due Friday, December 14, 2001)

1. (a) For a Kelvin model under a constant stress, discuss how the stress transfers between

the spring and the dashpot.

(b) For a Maxwell model under a constant strain, discuss how the strain transfers between the spring and the dashpot.

2. i) Derive the governing differential equation (GDE) of the 4-parameter Burgers model.

ii) Solve the GDE for its creep compliance function J(t).

iii) Solve the GDE for its relaxation function E(t).

3. Carry out the Laplace transform of the following functions:

4. Carry out the Laplace inversion of the following functions:

5. Find the J(t) and E(t) of the Burgers model in Prob. 1 by the Laplace transform and the

Laplace inversion method.

6. For the creep function

(a) derive its governing differential equation;

(b) find its corresponding relaxation function E(t).

7. Derive the frequency-dependence of the real and imaginary parts of the complex Young’s

modulus E* for

(a) Maxwell model,

(b) Kelvin model,