Certain materials are atomically structured such that they can deform and polarize as they do so. This is a useful property that allows us to convert energy between mechanical and electrical domains. Examples of such materials include SiO2​ (Quartz) and BaTiO3​ (Ceramic).
A Compression force on Quartz Generating a a Charge Dipole
When dealing with piezoelectric materials we are usually concerned about the relative amount, direction, and type of force that corresponds to a particular polarization vector. The relation between tense forces ( T1​,T2​,T3​ ) and shear forces ( T4​,T5​,T6​ ) are represented in a piezoelectric coefficient matrix ( D ) with a polarization output vector shown below: