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Some general remarks on hyperplasticity modelling and its extension to partially saturated soils. (English) Zbl 1457.74030

Summary: The essential ideas and equations of classic plasticity and hyperplasticity are successively recalled and compared, in order to highlight their differences and complementarities. The former is based on the mathematical framework proposed by R. Hill [The mathematical theory of plasticity. Oxford: Clarendon Press (1950; Zbl 0041.10802)], whereas the latter is founded on the orthogonality hypothesis of H. Ziegler [An introduction to thermomechanics. 2nd, rev. ed. Amsterdam-New York-Oxford: North-Holland Publishing Company (1983; Zbl 0531.73080)]. The main drawback of classic plasticity is the possibility of violating the second principle of thermodynamics, while the relative ease to conjecture the yield function in order to approach experimental results is its main advantage. By opposition, the a priori satisfaction of thermodynamic principles constitutes the chief advantage of hyperplasticity theory. Noteworthy is also the fact that this latter approach allows a finer energy partition; in particular, the existence of frozen energy emerges as a natural consequence from its theoretical formulation. On the other hand, the relative difficulty to conjecture an efficient dissipation function to produce accurate predictions is its main drawback. The two theories are thus better viewed as two complementary approaches. Following this comparative study, a methodology to extend the hyperplasticity approach initially developed for dry or saturated materials to the case of partially saturated materials, accounting for interface energies and suction effects, is developed. A particular example based on the yield function of modified Cam-Clay model is then presented. It is shown that the approach developed leads to a model consistent with other existing works.

MSC:

74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
74L10 Soil and rock mechanics
74A15 Thermodynamics in solid mechanics
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