Bayly, B. 2000. Deformation with Diffusion: the Growth of Augen. In: (Ed.) Mark Jessell, and Janos Urai, Stress, Structure and Strain: a volume in honour of Win D. Means, Journal of the Virtual Explorer, Electronic Edition, ISSN 1441-8142, volume 2, paper 2, doi:10.3809/jvirtex.2000.00005

## Deformation with Diffusion: the Growth of Augen

**Abstract**

Stiff resistant inclusions in a deforming rock generate local stress concentrations and stress gradients. The resulting diffusive mass transfer is partly along grain interfaces and partly through grain interiors. For the latter effect, two different sets of fundamental ideas are in use. In either version, the effect of diffusion is to enhance strain rates and to moderate stress concentrations. In the first version, local diffusive loss is isotropic and can change an infinitesimal spherical element only to a smaller sphere whereas in the second, local diffusive loss can be anisotropic and can change a sphere to an ellipsoid.

The problem used as illustration is that of a highly viscous embedded cylinder in pure shear. Each version yields predictions of diminished stress concentrations and enhanced strain rates, and invites further development. The second version is favored; by extension, a material component’s chemical potential at a point is seen as being like the normal stress at a point, i.e. multivalued, every planar element through the point having its own associated value.

This paper is preserved in its original format.

**Table of Contents**

- Editor's Note
- Introduction
- The classical solution extended
- Diffusive Gain or Loss not Isotropic
- Discussion and conclusions
- Acknowledgments
- References
- Appendix A. An embedded cylinder in pure shear
- Appendix B. The characteristic length L
- Appendix C. Anisotropic gain or loss
- Appendix S1. The Laplacian operator in polar coordinates modified
- Appendix S2. Diffusion and shear stress
- Appendix S3. Tensor Expressions