Đang chuẩn bị nút TẢI XUỐNG, xin hãy chờ
Tải xuống
(BQ) Part 2 book "Introduction to the mechanics of a continuous medium" has contents: Fluid mechanics, linearlzed theory of elasticity. Invite you to reference. | CHAPTER 6 Constitutive Equations 6.1 Introduction Ideal material Up to this point we have considered the mathematical descriptions of stress strain and rate of deformation. We have also developed in Chap. 5 a number of general theorems applicable to all continuous media. We now consider equations characterizing the individual material and its reaction to applied loads such equations are called constitutive equations since they describe the macroscopic behavior resulting from the internal constitution of the material. But materials especially in the solid state behave in such complex ways when the entừe range of possible temperatures and deformations is considered that it is not feasible to write down one equation or set of equations to describe accurately a real material over its entire range of behavior. Instead we formulate separately equations describing various kinds of ideal material response each of which is a mathematical formulation designed to approximate physical observations of a real material s response over a suitably restricted range. Some of the ideas involved in formulating simple equations for such ideal materials will be illustrated below in two examples the ideal elastic Hookean solid and the ideal viscous Newtonian fluid. These two especially simple ideal materials will be considered in some detail in two separate sections subsequent sections present some of the classical constitutive equations of viscoelasticity viscoplasticity and plasticity. These classical equations were introduced separately to meet specific needs and made as simple as possible oversimplifying many physical situations. The modern continuum theory of constitutive equations which has flourished in the last 15 years is guided by a different philosophy it begins with very general functional constitutive equations seeks to determine the limits imposed on the forms of the equations by certain general principles and specializes the equations as late as possible and as little as .
