What are Constitutive Equations?

Physical laws of continuum mechanics are valid for any continuum. Constitutive equations are mathematical relationships between kinetics and kinematics quantities of a specific continuum (recall that a continuum is just a mathematical idealisation of a material). In other words, constitutive equations describe the behaviour of a material subjected to certain loading conditions.

Examples
Consider two analyses:

1. With same loading conditions but using two different materials i.e. steel vs. aluminium
2. With same material but test at two different temperatures i.e. room temperature vs. 1000ºC

In the above examples, the constitutive equations are responsible for the the followings

1. Differing response for steel and aluminium under the same loading conditions
2. In practice, a material is only described over a range of conditions it is expected to encounter. Therefore, constitutive equations are formulated to describe different response of the same material over an acceptable range i.e. two different sets of equations for 10-30ºC and 900-1200ºC temperature range for the above analysis

Kinetics vs. Kinematics

A summary of the differences between a kinematics and kinetics study.

	Kinematics	Kinetics
Study of	Motion (Deformation and flow)	Forces (Surface and body)
Considers	Motion disregarding the forces and moments that cause the motion.	Motion and the forces underlying this motion.

See also

What is Kinetics?

What is Kinematics?

What is Kinematics?

Kinematics is the study of motion, disregarding the forces that cause the motion.

     In order to define the motion of a body (i.e. the deformation and flow of a solid or fluid body under external loading), a continuum can be broken down into multiple "particles" and the relative change of position of each particle is monitored (see Figure).

Figure. The kinematic quantities of a classical particle: mass (m), position (r), velocity (v), acceleration (a). Image adapted from Wikipedia.