TAILIEUCHUNG - A Principles of Hyperplasticity part 12

Tham khảo tài liệu 'a principles of hyperplasticity part 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 262 12 Behaviour of Porous Continua large strains fluid flow in porous media heat flow in porous media viscous effects inertial effects. Apart from this generalization the proposed framework places less stringent restrictions on the class of derived constitutive models in terms of the requirements of the Second Law of Thermodynamics. Within the framework of Chapter 4 the fact that the mechanical dissipation had to be non-negative resulted in a condition that is more stringent than the Second Law. Within the present framework it is the total dissipation including dissipation due to heat and fluid fluxes that has to be non-negative which is equivalent to the Second Law. As in the standard hyperplastic approach the entire constitutive behaviour is completely defined by specification of two scalar potential functions. However in the generalised framework these functions also include properties related to different phases of the media and their interaction. The fluid and heat conduction laws are also built into these potentials completing description of the constitutive behaviour of complex media. Chapter 13 Convex Analysis and Hyperplasticity Introduction So far we have avoided use of the terminology of convex analysis in the presentation of hyperplasticity. The reason has been to make this book as accessible as possible to engineers many of whom will not be familiar with the mathematical techniques of convex analysis. However this terminology is the most natural and rigorous for the description of many of the concepts we require. So in this chapter we re-present hyperplasticity in a convex analytical framework. This allows us to treat certain issues more rigorously where in previous chapters we have glossed over some problems. In general we follow the terminology employed by Han and Reddy 1999 in their book in which they make much use of convex analysis for conventional plasticity theory. We acknowledge too that the French school of plasticity has made much use .

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