Introduction to Computational Materials Science Fundamentals to Applications

Suppose we have an object under some prescribed load (i.e., an applied force).We can describe how the object will deform in response to that load with the results of elasticity theory. For the purposes of this textbook, we will restrict the discussion to the regime of small displacements, in which we can use a linear version of elasticity theory. The fundamental assumptions of linear elasticity are that (1) the displacements (strains) are small and (2) there are linear relationships between the strains and their associated stresses (we define stress and strain hereinafter). The assumption of linear elasticity is reasonable for many applications and is used extensively in structural analysis.

We note that there is a further restriction to linear elasticity. The applied stress must be low enough so that yielding does not occur, i.e., so that the material does not undergo permanent deformation. Consider a thin metal rod, for example. If one applies a small force to the rod, it deforms but springs back to its original state when the force is removed. If you keep increasing the force, eventually the rod bends and does not return to the original state when the force is removed. That deformation is caused by the movement of linear defects called dislocations, which are described in Appendix B.5.We also describe a basic model of plastic deformation in terms of dislocation motion in that section. Later in this chapter, in Appendix H.5, we discuss the relationship between elastic and plastic strain.