** **

**Problems for Chapter 1**

** **

**Objectives and Methods of Solid
Mechanics**

** **

**1.1. ****Defining a
problem in solid mechanics**

** **

1.1.1.
For each of the
following applications, outline *briefly*:

- What would you calculate if you were asked to model the component for a design application?
- What level of detail is required in modeling the geometry of the solid?
- How would you model loading applied to the solid?
- Would you conduct a static or dynamic analysis? Is it necessary to account for thermal stresses? Is it necessary to account for temperature variation as a function of time?
- What constitutive law would you use to model the material behavior?

1.1.1.1. A load cell intended to model forces applied to a specimen in a tensile testing machine

1.1.1.2. The seat-belt assembly in a vehicle

1.1.1.3. The solar panels on a communications satellite.

1.1.1.4. A compressor blade in a gas turbine engine

1.1.1.5. A MEMS optical switch

1.1.1.6. An artificial knee joint

1.1.1.7. A solder joint on a printed circuit board

1.1.1.8. An entire printed circuit board assembly

1.1.1.9. The metal interconnects inside a microelectronic circuit

1.1.2. What is the difference between a linear elastic stress-strain law and a hyperelastic stress-strain law? Give examples of representative applications for both material models.

1.1.3. What is the difference between a rate-dependent (viscoplastic) and rate independent plastic constitutive law? Give examples of representative applications for both material models.

1.1.4. Choose a recent publication describing an application of theoretical or computational solid mechanics from one of the following journals: Journal of the Mechanics and Physics of Solids; International Journal of Solids and Structures; Modeling and Simulation in Materials Science and Engineering; European Journal of Mechanics A; Computer methods in Applied Mechanics and Engineering. Write a short summary of the paper stating: (i) the goal of the paper; (ii) the problem that was solved, including idealizations and assumptions involved in the analysis; (iii) the method of analysis; and (iv) the main results; and (v) the conclusions of the study