Tensor-based matrices in geometrically non-linear FEM

In the framework of the object-oriented paradigm, advantages of using the index-free tensor notation in combination with the concept of generalized tensor-based matrix are considered as being the most corresponding to the paradigm. The advantages reveal itself in the disappearance of a semantic gap between various stages of creation of FEM applications (theoretical inferences, use of the numerical methods, object-oriented software implementation) and, as a result, use of the unified object model in all the stages, as well as simplification of theoretical transformations. Based on the considered approach, a new FEM equation for large strain analysis is developed and its solution technique is outlined