Engineering Plasticity

Metal forming and the finite-element method

“…5. For further reference, the books that provide a wealth of solutions to many metal-forming problems using the above methods are listed in the References [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”

Theoretical model and solution for the rheological problem of anchor-grouting a soft rock tunnel

“…(34) -(36) with the generalized Hooke's law of the plane strain problem [15], it is seen that the elastic solution of a plane strain problem is the same as Laplace transforms of the viscoelastic solution for the same problem. Thus by applying inverse Laplace transforms to the elastic solution of a plane strain problem, the corresponding viscoelastic solution can be obtained.…”

“…Utilizing the Poynting -Thomson model [15] in the region of non-anchor-grouting surrounding rock, as shown in Fig. 2, the constitutive equation is given as…”

Tensorial generalization of a phenomenological material law for shape memory alloys

“…In classical plasticity (see Slater [6] for example), a yield function is defined in order to determine the onset of the plastic flow for tensorial (or three-dimensional) stress states. In a yield criterion, the deviatoric stress must be used because it filters the hydrostatic part that is inactive in the yielding process.…”

“…The second invariant I'2 ofthe deviatoric stress tensor is calculated as follows: (1), (4) and (5), we obtain K1 = . The expression ofthe equivalent stress based on the von Mises criterion is finally given by equation (6). Ifthe equivalent stress exceeds the yield stress S, plastic deformations are assumed to be generated in the material.…”