Constitutive Relations - Lesson 3

Elements of linear elliptic partial differential equations are further discussed in this lesson and after that, the discussion is focused on constitutive relations. The discussion starts with writing a differential equation for the problem of the bar used in the previous lesson. The equation holds for the domain of 0<x<L and the endpoints x=0 and x=L are excluded. This is the case for most of the differential equations. The constitutive relation for the bar problem is written and discussed. The relation of linear elasticity is shown. Similarly, based on the discussed bar problem the constitutive relations along with Dirichlet boundary condition is written for heat flow and mass diffusion problems in one dimension.