The fundamental equations of statics are that the sum of forces acting on a body are equal to zero and the sum of the moments acting on a body are equal to zero. These can be expressed in orthogonal coordinates as:
Fx = 0 Fy = 0 Fz = 0
Mx = 0 My = 0 Mz = 0

For planar (flat) structures three of these equations drop out and we are left with:
Fx = 0 Fy = 0 M = 0

The fundamental relationship in deformable body mechanics is Hooke's Law, which in its simplest form is: [stress] = E[strain]

Another basic principle of deformable body mechanics is the continuity of displacements: if a point within a body moves a certain amount, the amount of motion is the same for all parts of the body connected to that point.

The way a given material responds to forces is a property of the material. Material properties that are often measured include:

• Yield stress - the amount of stress that can be applied to a material without causing the material to permanently change shape.
• Ultimate stress - the amount of stress that can be applied to a material without causing it to break.
• Young's modulus - the value of E in Hooke's Law.
• Poisson's ratio - a measure of the change in volume of a material under stress.
• Modulus of thermal expansion - the amount a material expands when it is heated.