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Tham khảo tài liệu 'a principles of hyperplasticity part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 1.3 Notation 5 Lemaitre and Chaboche 1990 Maugin 1992 1999 Coussy 1995 . In this context what we call a hyperplastic material has much in common with what the French authors define as a standard material although we believe we have adopted a rather stricter formalism for the necessary definitions. There are numerous other works in which the thermodynamics of continua are addressed. Many attempt great generality e. g. the works by Eringen 1962 Truesdell 1977 and Holzapfel 2000 describing the mechanics in terms of appropriate tensor notation for large strain analysis and often developing a somewhat axiomatic approach in which thermodynamics is introduced at a very general level. The disadvantages of this approach are twofold. Firstly these works are impenetrable to all but the highly specialised reader. Secondly we have found that despite their generality their treatment of plasticity theory is often superficial. Plasticity theory does not sit easily within formulations oriented principally toward the treatment of materials in which the dissipation is viscous rate dependent . Often the authors of more general texts revert to conventional analysis of plasticity problems and make little connection between plasticity and thermodynamics. Our approach is different in that a thermodynamics and hyperplasticity are intimately connected and b we make our ideas more accessible by adopting just small strain analysis which makes much of the presentation more straightforward. 1.3 Notation This book makes much use of vectors and tensors and for these we use the subscript notation. Thus ơj is a shorthand for a second-order tensor which could Ơ11 Ơ12 Ơ13 be written out in full in matrix form as Ơ21 ơ22 23 _ơ31 ơ32 ơ33 _ tion convention over a repeated index so . We adopt the summa- that for instance Cịi Ơ11 ơ22 ơ33. Although the subscript notation can become rather cum- bersome at times and many authors prefer the boldface notation in which the above tensor would simply be written .
