The future of structural geology

The theoretical root of structural geology is in continuum mechanics, founded by Euler (stress, 1776), Lagrange (strain, 1784), and Cauchy (1827). Compared with the principles of modern physics it is hopelessly obsolete. It completely ignores all the developments in physics after 1830, especially the rise of energetic thinking (starting 1840), physical work (Joule 1845), the First Law of thermodynamics (Mayer 1842), bonds in solids (Maxwell 1850), the mathematics of 3D space (Grassmann 1866), and others. It will be shown that Cauchy’s derivation of the stress tensor is invalid, and that strain is physically meaningless (Koenemann 2008, 2014). Continuum mechanics is as obsolete as a trilobite. It fails completely and systematically for simple shear in the elastic (Poynting 1909), viscous (Nikuradse 1933), and plastic field (Koenemann 2008). This is particularly relevant for geologists trying to understand mylonites. Any attempt to tackle simple shear with a theory that is older than the discovery of bonds is a waste of time. Mathematics and physics provided the full set of necessary conceptual tools (thermodynamics, vector algebra) starting in 1901. A realistic grasp of elastic and plastic deformation satisfying modern standards is plainly impossible without solid training in mathematics (differential equations, linear algebra, vector algebra, potential theory), physics (thermodynamics in scalar [P, V, T] and vector field form [f, r, T]), and material science.