variable_friction#

Description#

This behavior 1this behavior is Z-set specific, and therefore does not apply for Z-mat for other codes is used to specify a variable friction in certain contact models (see the command ***contact **zone *variable_friction in the Z-set user manual). The behavior specifies a friction coefficient \(\mu\) that may depend on the current total relative sliding \(u_s\) of the contact surfaces, and/or the cumulative relative sliding \(u_{cum}\). This is analogous to the role played by the current inelastic deformation and the cumulative plastic deformation in isotropic and kinematic hardening in conventional material models. The analogy is as follows: the total friction coefficient \(\mu\) is written as \(\mu = \mu_0 + \mu_R(u_{cum}) + \mu_X(u_{cum},u_s)\), where \(\mu_0\) plays the role analogous to the elastic limit, \(\mu_R\) to the isotropic hardening and \(\mu_X\) to the kinematic hardening.

Syntax#

***behavior variable_friction \(~\,~\,\) *isotropic constant | linear | nonlinear \(~\,~\,~\,~\,\) fric1 \(\mu_0\) \(~\,~\,~\,\) [ fric3 \(Q\) ] \(~\,~\,~\,\) [ b1 \(b_1\) ] \(~\,~\,~\,\) [ betai \(\beta_i\) ] \(~\,~\,~\,\) [ *kinematic linear | nonlinear ] \(~\,~\,~\,\) [ fric2 \(C\) ] \(~\,~\,~\,\) [ b \(b\) ] \(~\,~\,~\,\) [ betak \(\beta_k\) ]

Possible choices are:

*isotropic constant

takes one parameter \(\mu_0\).

*isotropic linear

takes two parameters \(\mu_0\) and \(Q\) to give \(\mu_R = Q u_{cum}\).

*isotropic nonlinear

takes four parameters \(\mu_0\), \(Q\), \(b_1\) and \(\beta_i\) to give \(\mu_R = Q \left( 1. - \mbox{exp}[ -( b_1 u_{cum})^{\beta_i} ]\right)\).

*kinematic linear

takes one parameter \(C\) to give \(\mu_X = C \vert u_s \vert\).

*kinematic nonlinear

takes three parameters \(C\), \(b\) and \(\beta_k\), to give \(\mu_X = C \left( 1. - \mbox{exp}[ -( b u_{cum})^{\beta_k} ]\right)\frac{\vert u_s \vert}{u_{max}}\). Here \(u_{max}\) is…

Currently,the behavior parameters cannot depend on any external parameter (such as temperature). Also note that not all contact models support a variable friction coefficient. If so, it is indicated in the description of each contact model.

Example#

***behavior variable_friction
  *kinematic nonlinear
  fric2 3.
  b 4.e-2
  betak 1.8
  *isotropic nonlinear
  fric1 0.18
  fric3 3.
  b1 5.e-2
***return