Abstract—This scientific research proposes a fundamental application of constructal theory developed by prof. Adrian BEJAN of Duke University in order to prove in a mathematical sense that the mechanical maximum work principle used by the theory of continuum media plasticity can be regarded as a solution of a general variational optimization problem. According to the first and second thermodynamics laws, the constructal principle search to complete the natural tendency for all finite-size system to raise the entropy obtaining specific optimal system design or material flow configurations. In accord with the constructal theory “all system searches to flow more and more easily over time using specific distribution of imperfections in order to maximize entropy and to minimize the losses”. In this sense, concerning the field of forming processes, all material flows under specified boundaries, loading and processing conditions are those which minimize the sum of dissipated deformation and friction power. Thus all the corresponding mechanical variables (velocities, stress, strain, strain rate) of the real mechanical state as those that minimizes the total dissipated power. It can be then obtained a variational constrained minimization problem. Equivalent form of the maximum work principle is proved also for the friction stresses together with the convexity properties of plastic or friction potential. An application in the case of a cylindrical upsetting shows the feasibility of the proposed minimization problem formulation to find analytical solution. To valid this theory, comparisons are made using the classical analytical analysis based on upper and lower bound theorems, slices method and numerical Finite Element Modelling (FEM).
Index Terms—Constructal theory, continuum media plasticity, maximum work principle, variational optimization.
A. Gavrus is with the National Institute of Applied Sciences of Rennes, Rennes, F-35708 France (e-mail: adinel.gavrus@insa-rennes.fr).
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Cite: A. Gavrus, "Application of Constructal Theory to Write Mechanical Maximum Work Principle and Equilibrium State of Continuum Media Flow as a Solution of a Variational Optimization Problem," International Journal of Modeling and Optimization vol. 8, no. 4, pp. 页, 2018.
