What is Continuum Mechanics?

After generating a continuum (by mathematically representing a real material), the mechanical behaviour of such continuum can then be studied. This is continuum mechanics - the study of materials' mechanical behaviour using mathematical models.

     Solid mechanics and fluid mechanics are two special cases of continuum mechanics.

Physical Laws vs. Constitutive Equations

See also

What are Constitutive Equations?

Physical Laws of Continuum Mechanics

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

Reynolds' Transport Theorem

The physical laws of continuum mechanics can be generalised using Reynolds' Transport Theorem as follows: