A Principles of Hyperplasticity part 13 ppt

... kk I J aa a aa a aa a aa a III I aaa aaa aaa aaa aa a aa a aa a aaa §· cccc   ¨¸ ©¹ §·    ¨¸ ©¹      aaaa (B.10) 304 15 Concluding Remarks current (rather weak) theorems ... one of a number of possible approaches. In particular, we chose to treat ˆ w as if it were an external kinematic variable. An alternative would be to treat ˆ w as an in...

Ngày tải lên: 10/08/2014, 11:21

... internal energy expression is related to a par- ticular aspect of the physical behaviour of the material. Once a familiarity is established with the aspects of behaviour that are related to particular ... is that the state of a material is entirely determined by the values of a certain set of independent variables: the kinematic variables (strain and internal variables)...

Ngày tải lên: 10/08/2014, 11:21

... strains ( e. g. incompressible behaviour) or on the rates of the internal variables ( e. g. dilational constraints for granular materials). A full treatment of constraints would not be appropriate ... Elastic and Plastic Models in Hyperplasticity they represent the areas shown in the figure. For the special case that the energy functions are quadratic functions, the areas f a...

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... de- termined by calibration against experimental unloading-reloading curves. A variety of forms have been suggested in the literature. The advantage of the bounding surface approach is that, apart from ... discrete set of internal variables are introduced. A direct application of this generalisation is the thermomechanical formulation of kinematic hardening plasticity with an...

Ngày tải lên: 10/08/2014, 11:21

... similar variables o a initial value of a  a rate of a with time, {w w  aat  a material derivative, { ,  ii aaav ˆ a any function of the internal variable K ,  {K ˆˆ aa ... is certainly large, and can encompass a very wide range of rate- independent materials within a single framework. It should also be stated that, as far as the authors are aware, i...

Ngày tải lên: 10/08/2014, 11:21

... 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. ... plastic strains have become well established over many years, but they are based on empirical observation, first of metals and later of many other materials. The concept of a y...

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... is that it requires the specification of a tensor-valued functional (the stress as a functional of the strain history). This is clearly a challenging task. An advantage of the approach adopted ... instead expresses the response in terms of functionals of the history of the material (usually through the history of strain and temperature). Both approaches have advantages...

Ngày tải lên: 10/08/2014, 11:21

... accurately across a wide range of strain amplitudes. This is important, for instance, in modelling geo- technical materials (Houlsby, 1999). The disadvantage is that a large number of material ... the above example, we showed how the choice of a particular pair of func- tionals leads to a material model with a specific stress-strain curve. In certain circumstances, it may...

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... Elasticity and Small Strains 177 reproduce the characteristic S-shaped curve in a plot of normalised secant shear stiffness o GG against shear strain  log J and to generalise this variation ... linked to another important effect that the elastic strains may have on the plastic behaviour of coupled materials. Collins (2002) demonstrated that for coupled materials, derivation of...

Ngày tải lên: 10/08/2014, 11:21

... the laws of thermodynamics, and at the same time account for many important aspects of soil behaviour. Houlsby and Mortara (2004) explore an approach to the behaviour of fric- tional materials ... plastic dissipation for geotechnical materials. Hyper- plasticity is used to analyse the stress–dilatancy relation for shear deformations of frictional, granular materials. Central to this...

Ngày tải lên: 10/08/2014, 11:21