A Principles of Hyperplasticity Part 5 ppt

... 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 ... Models The main features of hyperplasticity are the compactness of the formulation and a clear link to conventional plasticity. As an illustration of these features, the...

Ngày tải lên: 10/08/2014, 11:21

... 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) and the temperature. ... that the above relations are applicable only within a certain range of temperatures for which the ideal gas idealisation is reasonable, and that at a sufficiently low temperature, mod...

Ngày tải lên: 10/08/2014, 11:21

... ¬ ¼       (5. 13) which can of course be manipulated into a variety of other forms. 5. 1 .5 Hierarchy of Isotropic Elastic Models An advantage of the hyperelastic approach (here extended ... instance, often forms a central part of a finite element analysis. Therefore, one of the most important criteria that needs to be applied to the formulation of any mode...

Ngày tải lên: 10/08/2014, 11:21

... 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 i...

Ngày tải lên: 10/08/2014, 11:21

... comparative advantage explains the gains from trade Consider how everyone can benefit when people trade with one another Learn the meaning of absolute advantage and comparative advantage Apply ... and consumes 2 1/2 pounds of potatoes and 20 pounds of meat. SPECIALIZATION AND TRADE After several years of eating combination B, the rancher gets an idea and goes to talk to the farmer: R...

Ngày tải lên: 15/12/2013, 11:15

... 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...

Ngày tải lên: 10/08/2014, 11:21

... 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

... certain materials more 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 ... 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 ma...

Ngày tải lên: 10/08/2014, 11:21

... 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 ... Following approach (b) above, the generalisation of Equations (9. 25) and (9.31) that we seek for the function f must consist of a quadratic function of * v H and s H , raised to...

Ngày tải lên: 10/08/2014, 11:21