An extended Hamilton principle as unifying theory for coupled problems and dissipative microstructure evolution
Abstract
An established strategy for material modeling is provided by energybased principles such that evolution equations in terms of ordinary differential equations can be derived. However, there exist a variety of material models that also need to take into account nonlocal effects to capture microstructure evolution. In this case, the evolution of microstructure is described by a partial differential equation. In this contribution, we present how Hamilton's principle provides a physically sound strategy for the derivation of transient field equations for all state variables. Therefore, we begin with a demonstration how Hamilton's principle generalizes the principle of stationary action for rigid bodies. Furthermore, we show that the basic idea behind Hamilton's principle is not restricted to isothermal mechanical processes. In contrast, we propose an extended Hamilton principle which is applicable to coupled problems and dissipative microstructure evolution. As example, we demonstrate how the field equations for all state variables for thermomechanically coupled problems, i.e., displacements, temperature, and internal variables, result from the stationarity of the extended Hamilton functional. The relation to other principles, as the principle of virtual work and Onsager's principle, is given. Finally, exemplary material models demonstrate how to use the extended Hamilton principle for thermomechanically coupled elastic, gradientenhanced, ratedependent, and rateindependent materials.
 Publication:

Continuum Mechanics and Thermodynamics
 Pub Date:
 July 2021
 DOI:
 10.1007/s0016102101017z
 arXiv:
 arXiv:2010.09440
 Bibcode:
 2021CMT....33.1931J
 Keywords:

 Coupled processes;
 Multiphysics;
 Variational modeling;
 Local and nonlocal effects;
 Condensed Matter  Materials Science;
 Physics  Classical Physics
 EPrint:
 doi:10.1007/s0016102101017z