## Preliminary Definitions

6 Work is defined as the product of a force and displacement f b

7 Energy is a quantity representing the ability or capacity to perform work.

8 The change in energy is proportional to the amount of work performed. Since only the change of energy is involved, any datum can be used as a basis for measure of energy. Hence energy is neither created nor consumed.

9 The first principle of thermodynamics (Eq. 6.44), states

The time-rate of change of the total energy (i.e., sum of the kinetic energy and the internal energy) is equal to the sum of the rate of work done by the external forces and the change of heat content per unit time:

s

U*0

A /

Uo

A

U*o

A

U0

Nonlinear

### Linear

Figure 13.1: *Strain Energy and Complementary Strain Energy where K is the kinetic energy, U the internal strain energy, W the external work, and H the heat input to the system.

10 For an adiabatic system (no heat exchange) and if loads are applied in a quasi static manner (no kinetic energy), the above relation simplifies to:

0 0