Page 21 - Mechanics of Microelectromechanical Systems
P. 21
8 Chapter 1
Similarly to the normal strain, the shear strain is defined as:
A linear relationship also exists between shear stress and strain, namely:
where G is the shear modulus and, for a given material, is a constant amount.
Young’s modulus and the shear modulus are connected by means of the
equation:
where is Poisson’s ratio.
For a three-dimensional elastic body that is subject to external loading
the state of strain and stress is generally three-dimensional. Figure 1.7 shows
an elastic body that is subject to the external loading system generically
represented by the forces through In the case of static equilibrium, with
thermal effects neglected, an elementary volume can be isolated, which is
also in equilibrium under the action of the stresses that act on each of its
eight different faces.
Figure 1.7 Stresses on an element removed from an elastic body in static equilibrium
As Fig. 1.7 indicates, there are 9 stresses acting on the element’s faces, but
the following equalities, which connect the stresses, do apply:
