On the interpretation of the logarithmic strain tensor in an arbitrary system of representation

•We provide a new approach to the definition of the logarithmic strain tensor.•The logarithmic strains are the natural extension of the infinitesimal strains.•Both infinitesimal and logarithmic shear strains are correctly interpreted.•We show the limitations of some tests used to define a constitutive model.

Logarithmic strains are increasingly used in constitutive modelling because of their advantageous properties. In this paper we study the physical interpretation of the components of the logarithmic strain tensor in any arbitrary system of representation, which is crucial in formulating meaningful constitutive models. We use the path-independence property of total logarithmic strains to propose different fictitious paths which can be interpreted as a sum of infinitesimal engineering strain tensors. We show that the angular (engineering) distortion measure is arguably not a good measure of shear and instead we propose area distortions which are an exact interpretation of the shear terms both for engineering and for logarithmic strains. This new interpretation clearly explains the maximum obtained in some constitutive models for the simple shear load case.