Tensor objects in finite element programming

This paper describes a novel programming tool, nDarray, which is designed using an Object Oriented Paradigm (OOP) and implemented in the C++ programming language. Finite element equations, represented in terms of multidimensional tensors are easily manipulated and programmed. The usual matrix form of the nite element equations are traditionally coded in FORTRAN, which makes it di cult to build and maintain complex program systems. Multidimensional data systems and their implementation details are seldom trans- parent and thus not easily dealt with and usually avoided. On the other hand, OOP together with e cient programming in C++ allows building new concrete data types, namely tensors of any order, thus hiding the lower level implementation details. These concrete data types prove to be quite useful in implement- ing complicated tensorial formulae associated with the numerical solution of various elastic and elastoplastic problems in solid mechanics. They permit implementing complex nonlinear continuum mechanics theories in an orderly manner. Ease of use and the immediacy of the nDarray programming tool in constitutive driver programming and in building nite element classes will be shown.