Lomnitz was born to a Jewish family in
Cologne, Germany. He graduated as engineer from the
University of Chile in 1948. He then studied with
Karl von Terzaghi in
Harvard University and obtained a
Master's degree in
soil mechanics. Lomnitz received his doctorate from
Caltech in 1955 with a dissertation on creep measurements in igneous rocks. Its principal thesis, a logarithmic creep behavior observed in rocks, was reformulated as the "Lomnitz Law" by Harold Jeffreys in 1958. The Lomnitz law is expressed as,\varepsilon\left(t\right)=\frac{\sigma}{E_{0}}\left[1+q\ln\left(1+at\right)\right],\text{ }t\geq0, where, \varepsilon(t) is the time-varying
creep (or, strain), \sigma is the constant
stress load on the material, E_{0} is the
shear modulus, a is a positive material constant, and q is the creep constant. Though the Lomnitz law was inferred empirically from rheological measurements on rocks, its validity was firmly established by Pandey and Holm by deriving it from the physical principles in the framework of
fractional calculus. They had used a time-varying
Maxwell model in their analysis and found that the underlying physical mechanism in rocks that led to the Lomnitz law was a linearly time-varying
viscosity, \eta\left(t\right), \eta\left(t\right)=\eta_{0}+\theta t, where \eta_{0} is the constant part of the viscosity and \theta t is the time-varying part of the viscosity, such that \theta=d\eta(t)/dt > 0. Such a property with increasing viscosity with time corresponds to
rheopecty, or anti-
thixotropy, a special class of
Non-Newtonian fluid. Pandey and Holm extracted the physical interpretation of the parameters of the Lomnitz law as follows:q=\frac{E_{0}}{\theta}\text{ and } a=\frac{1}{\tau}=\frac{\theta}{\eta_{0}}where, \tau is the relaxation time during which the transition from the elastic- to creep-type deformation occurs. The mechanism underlying the Lomnitz law is that the time-varying part increases linearly with time and dominates over the constant part, \theta t \gg \eta_{0}. Further, since q \ll 1, for igneous rocks this implies the time-varying part of the viscosity dominates over the elasticity of the rocks, i.e., \theta \gg E_{0}. Interestingly, the relaxation modulus of the time-varying Maxwell model was identified as the Nutting law from rheology. This physical justification has been lacking in both Nutting's law and Lomnitz's law since their inception in 1921 and 1956 respectively. As a result of these findings a useful physical interpretation of the fractional
dashpot and hence the
fractional derivatives was obtained. ==Career==