TAILIEUCHUNG - A Principles of Hyperplasticity Part 6

Tham khảo tài liệu 'a principles of hyperplasticity part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 110 6 Advanced Plasticity Theories when these two surfaces come in contact with each other. The modulus can for instance be specified by an expression of the form a . h 8 H 1- 1 h - H 160 J where as before 8 PR is the distance from the current stress point to the image point. The form ensures that h 0 H and h 80 h0. This formulation is very close in concept to bounding surface plasticity. This form of plasticity however avoids the problem inherent in the bounding surface models of ratcheting for small cycles of unloading and reloading. The more sophisticated rules for defining the image point and the translation of the inner yield surface provide a more realistic way for describing hysteretic behaviour and the effect of past loading history. This process can be taken a step further by introducing a set of nesting surfaces within the domain between f 0 and F 0. These surfaces can translate and expand or contract due to plastic straining. They are capable of encoding in a more subtle way the details of the past stress history. The relative motion between each adjacent surface is defined by rules similar to to ensure that they remain nested. The hardening modulus can be defined by an interpolation formula such that it is h0 on the innermost yield surface and equal to H on the outermost surface. For instance it can be assumed if the stress point is in contact with n surfaces out of a total of N h H NTTJh - H The configuration of the nesting surfaces and therefore the subsequent stiffness for a particular stress path depends on the past history of loading. The material response for any loading history may be studied by following the evolution of the configurations of the nested surfaces. This model possesses a multi-level memory structure because for cyclically varying stress only a certain number of surfaces undergo translation the other surfaces may change only isotropically. This approach can be extended to an infinite number of surfaces although for .

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