Variational Formulation of a Material Ageing Model
A material ageing parameter, i.e. an additional internal variable, is introduced as the conjugate to the Canonical Energy Momentum Tensor. Ageing is manifested in variation of basic material characteristics such as density, moduli of elasticity, yeald stress, strength and toughness.
Four-dimensional intrinsic (material) Riemannian metric G of the material 41) space-time continuum P is utilized as the characteristic of the processes developing in the material. The ageing process is modeled as the evolution of the metric G (most importantly of its time related component) of the material space-time P embedded into 4D Absolute (Newtonian) space-time with Euclidian metric.
The kinetic equation for material ageing parameter is derived by following the classical variational approach. The formulation of a Lagrangian for an ageing elastic media and the derivation of a system of coupled elastostatics and ageing equations constitute the central part of the work. The external and internal Balance Laws associated with certain symmetries of internal (material) and external (Absolute) space-time geometries are briefly reviewed from a new viewpoint presented in the paper. A few examples that provide a basis for experimental examinations of the proposed model are also discussed.
KeywordsVariational Formulation Energy Momentum Tensor Ageing Equation Deformation History Tensor Density
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