The paper initiated a new description of slow processes in materials by using energetic arguments rather than differential equations. This energetic formulation is much more flexible and allowed for applications in many other areas of material modeling such as damage, brittle fracture, dry friction, elastoplasticity, superconductivity, ferroelectricity, and ferromagnetism.

Based on the physical "postulate of realizability" we derived a new mathematical formulation of rate-independent processes, the so-called "energetic formulation." It is an abstract but very general mathematically clean way of describing a large class of rate-independent systems. It unifies many classical formulations and highlights the basic physical princicples, namely, suitable global, static stability and the total energy balance.

The evolution of rate-independent systems is very special as the dissipative forces depend on the direction of the rate of the internal variables but not on the modulus of the rate. This leads to genuinely nonsmooth multi-valued differential inclusions, which are difficult to handle analytically and numerically. The energetic formulation derived in our paper avoids the usage of rates and bases the theory on approximate time-incremental problems which are minimization problems.

The final time-continuous formulation is derivative-free and does not need a linear underlying structure. Thus, nonconvex problems like infinite-strain elasticity are accessible for the first time. Moreover, it is possible to transfer the modern developments in the theory of microstructures in static phase transformations to rate-independent evolutionary processes. In particular, the evolution of microstructure can be modeled, which is relevant for the understanding of the shape-memory effect and of hysteresis in magnetism.

The research originated from Valery Levitas’ interest in phase transformations, which induced the interdisciplinary project "Stress and Strain Induced Phase Transitions in Engineering Materials" coordinated by Professor Emeritus Erwin Stein (Hannover) and supported by Volkswagen-Stiftung in the years 1995 to 1998.