Material Modelling and Fundamental Solutions

In addition to specifying the geometry of the problem, it is necessary to describe the physical response of the material in a mathematical way. This is done by defining the response characteristics of an infinitesimally small portion of the solid. The

constitutive

law establishes a relationship between heat flow and the temperature gradient or between strain and stress. The constants in such relationships are characteristic values or properties of the material. We distinguish between material properties which are direction independent (

isotropic

material), and those which are dependent on direction (

anisotropic

material). Furthermore, there are problems where the same properties apply everywhere (

homogeneous

problems) and where properties change from location to location (non-homogeneous problems).