Abstract

The most general stress function in three dimensions is given by the symmetric Beltrami tensor, which consists of six scalar functions. In this brief communication, we explore the possibility of expressing a three-dimensional state of stress by means of a single scalar function, in the spirit of the Airy stress function in two dimensions. The price to pay for such a severe restriction is a loss of generality, in the sense that not every divergence-free stress field can be derived from the single stress function. Clearly, any such single scalar function gives rise to a particular case of the Beltrami tensor. One of these particular cases exhibits an interesting analogy with the tensor of inertia of a rigid body.

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