FE Thermomechanics and Material Sampling Points

The thermomechanics of finite elements of continuous media is discussed. The novel key concept introduced is that of material sampling points attributed to each finite element. Similar to representing the spatial interactions by a finite number of nodal quantities, the state of a finite element is represented by the set of local states at its sampling points. The fully algebraic, thermomechanical equations of the discrete model are formulated using Biot’s variational approach. The constitutive description in this finite element theory pertains to formulating the constitutive equations locally at all sampling points. A linear elasticity problem and a heat conduction problem illustrate the theory.