B free

The linearized strain matrix and the matrix of material elasticities — commonly referred to as the B and D matrices — have been traditionally presented as convenient operators that enable the matrix formulation and finite element implementation of field theories in continuum mechanics. In this article it is argued that the opposite is true: neither matrix is necessary, they both complicate the finite element formulation of field theories and, moreover, they do not necessarily lead to the most efficient implementations. Examples are provided to back this statement in the context of infinitesimal and finite strain solid mechanics. For these problems, the finite element equilibrium equations and their linearization are fully derived using a formulation which is simpler, more compact, often computationally cheaper … and free of both B and D matrices.