Physical Laws of Continuum Mechanics

Physical laws are empirical laws derived by repeated observation of physical phenomena. These laws established links between kinematics (of continua) and kinetics (of deformation) without considering the physical properties (such as elasticity, density, viscosity and thermal conductivity) of the continuum (of the material) itself. This means that they are valid for any continuum (any material).

     The most important physical laws that govern the mechanics of continua are:

1. Conservation of Mass - the mass of an isolated system will remain constant over time
2. Conservation of Momentum (Newton's Second Law) - rate of change of (linear/ angular) momentum is equal to the resultant (force/ moment) acting on the system
3. Conservation of Energy (First Law of Thermodynamics) - rate of change of energy is equal to the difference between rate of heat input and rate of work output

     Note that the above laws can be generalised using Reynolds' Transport Theorem.

Figure. An experiment illustrating the law of conservation of mass (adapted from Grade 8 EAP)

What is a Continuum?

In continuum mechanics, a continuum is an idealised mathematical representation of a real material such as solid, liquid or gas.

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 Kinetics?

Whilst kinematics deals with the motion and deformation of a body, kinetics studies the forces that produce motion. The two types of forces are:

1. Body forces (per unit mass or volume) are non-contact forces that act on the total mass of a continuum. Examples include gravitational force, electromagnetic force and inertial force.
2. Surface forces (per unit area) are contact forces that act across an internal or external surface of a body. Examples include pressure, contact forces and frictional forces.

Figure. Magnetic (non-contact) vs. frictional (contact) forces. Images adapted from Newtown High School and Joey's Blog.

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.

What is Deformation and Flow?

Materials (or continua) are generally classified as solids or fluids. Their main difference is that when subjected to external loading:

• a solid body will undergo time-independent deformation, and
• a fluid body will flow as a function of time.

     Materials that have both fluids and solids characteristics also exist. These include shear thickening materials such as custard (see Video), shear thinning materials such as blood, and other materials with time-dependent "visco" characteristics such as elastomers.

Video. The shear thickening effect of corn starch mixed with water.