NUMERICAL-SOLUTION OF 2-DIMENSIONAL AND 3-DIMENSIONAL THERMOMECHANICAL PROBLEMS USING THE THEORY OF A COSSERAT POINT

In the present paper it is shown that the theory of a Cosserat point can be used to develop numerical solutions of two- and three-dimensional thermomechanical problems. Details have been provided for the use of triangular elements for two-dimensional problems and tetrahedrons for three-dimensional problems. However, higher order elements with many directors and temperature fields can be developed using similar methods to those discussed here. Most importantly, the basic balance laws are inherently nonlinear and they are valid for arbitrary material properties. With reference to three-dimensional problems, it is shown that the formulation using the theory of a Cosserat point can be related to the standard Galerkin method. However, in contrast with the Galerkin method, the theory of a Cosserat point places fundamental restrictions on constitutive equations which ensure that the balances of angular momentum and energy are identically satisfied for all thermomechanical processes. Also, the constitutive equations are restricted so that various statements of the second law are satisfied. In this sense, the theory of a Cosserat point can be used to complement the Galerkin method by providing a set of fundamental theoretical restrictions on the constitutive equations which can be used to evaluate different numerical integration schemes.