Qualitative and quantitative analysis of vorticity, strain and area change in general non-isochoric 2D deformation

• A simplified non-isochoric 2D deformation characterised by two components of the velocity gradient tensor is considered.
• A qualitative understanding of the stretch and rotation history of linear elements is obtained in polar coordinates.
• In a reference frame where deformation decomposes into a progressive pure shear and rotation, finite strain is simplified.
• A numerical procedure for estimation of the velocity gradient tensor components, finite strain and area change is developed.

A scale free representation of a general non-isochoric 2D deformation is presented which is amenable to mathematical analysis. By describing deformation in 2D in terms of polar coordinates the stretching and rotational histories of linear elements separate and are easily analysed both qualitatively and quantitatively. An analysis of finite strain combined with dynamical considerations allows the derivation of equations which may be used to estimate finite strain, area change and kinematic vorticity number. Numerical investigation of method developed here was carried out and it was found to perform well unless large area changes occur in combination with large components of simple shear. A re-analysis of natural data indicates the method is consistent.

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