A Class of Constitutive Relations with Internal Variable Derivatives. Derivation from Homogenization and Initial Value Problem
نویسندگان
چکیده
A general framework for deriving and using a class of constitutive laws incorporating spatial gradients of internal variables is presented. It user two basic ingredients : a derivation of such models by homogenization techniques and a reformulation of the et~olution eyuation at the scale of the whole structure.
منابع مشابه
An analytic solution for a non-local initial-boundary value problem including a partial differential equation with variable coefficients
This paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients. At first, the non-self-adjoint spectral problem is derived. Then its adjoint problem is calculated. After that, for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined. Finally the convergence ...
متن کاملA Nonlinear Creep-damage Constitutive Model of Mudstone Based on the Fractional Calculus Theory
During the flood development in an oil field, the creep characteristic of mudstone is one of the important factors causing casing damage. In this study, based on the theory of fractional order differential and taking into account the creep damage evolution rules, a fractional nonlinear creep-damage model is proposed to reflect the instantaneous deformation in loading processes and the accelerat...
متن کاملA Unified Model for Hysteresis in Ferroic Materials
This paper provides a unified modeling framework for ferroelectric, ferromagnetic and ferroelastic materials operating in hysteretic and nonlinear regimes. Whereas the physical mechanisms which produce hysteresis and constitutive nonlinearities in these materials differ at the microscopic level, shared energy relations can be derived at the lattice, or mesoscopic, scale. This yields a class of ...
متن کاملAPPLICATION OF THE SINGULAR BOUNDARY VALUE PROBLEM FOR INVESTIGATION OF PISTON DYNAMICS UNDER POLYTROPIC EXPANSION PROCESS
In this paper a mathematical simulation of a simplified internal combustion engine is presented. To contribute engine kinematics and its geometry, simple relations are derived for constrained motions. The equation of motion for the piston forms a singular boundary value problem. The uniqueness of the solution was studied in the Banach space. For solving governing equations an iterative numerica...
متن کاملروشهای تجزیه مقادیر منفرد منقطع و تیخونوف تعمیمیافته در پایدارسازی مسئله انتقال به سمت پائین
The methods applied to regularization of the ill-posed problems can be classified under “direct” and “indirect” methods. Practice has shown that the effects of different regularization techniques on an ill-posed problem are not the same, and as such each ill-posed problem requires its own investigation in order to identify its most suitable regularization method. In the geoid computations witho...
متن کامل