Dear Jean-Paul Why we must calculate reaction forces at a boundary which has external force? When we apply external load (load control solution) so we control the load level at that boundaries and reaction forces must be equal to applied load level (residual is zero) at each time step at these BCs due to equilibrium condition. But we usually calculate reaction forces at BCs with prescribed displacement which it is better to calculate them from residual vector (which equal to [-1.0 * internal forces] at these BCs). You aslo explained same method as:
"In general (for a linear/nonlinear hyperelastic/dissipative material), to compute the total force acting on the surface of a domain one should integrate the tractions acting on that surface. As the body is in equilibrium, they are balanced by the stresses generated by the material." As the body is in equilibrium, they are balanced by the stresses generated by the material = internal forces So when we calculate internal forces why computation is performed again for integral over BCs? I think this method is used in advance FEM software. Please, did you test the attached code for a plastic material model? Best Regards Pasha On Sunday, February 26, 2017 at 3:06:25 PM UTC+3:30, Jean-Paul Pelteret wrote: > > Dear Amir (and Hamed), > > >> Integration stress on external faces is correct when the material >> constitutive model is linear (for example elastic material model in which >> behavior is not history dependent). It is better to extract residual forces >> at the boundary from the system residual vector. >> > > I disagree and consider both statements that you've made to be incorrect. > For starters, in a nonlinear problem one uses a nonlinear solution scheme > to drive the residual (a consequence of equilibrium imbalance) down to > zero. So not only does the residual not represent any measure of external > force, but also one expects this vector to be zero in for a balanced system! > > In general (for a linear/nonlinear hyperelastic/dissipative material), to > compute the total force acting on the surface of a domain one should > integrate the tractions acting on that surface. As the body is in > equilibrium, they are balanced by the stresses generated by the material. > Using Cauchy's theorum > <https://en.wikipedia.org/wiki/Cauchy_stress_tensor#Cauchy.E2.80.99s_stress_theorem.E2.80.94stress_tensor> > > one can re-express this traction in terms of the internal stresses and > compute the forces developed on any arbitrary cut-plane in the material > domain. > > To demonstrate, I've attached an example for one-field elasticity that > shows the computation of the reaction forces on either side of a cube under > uniaxial stress conditions. All of the computations are done in the > post-processing step (Solid<dim>::output_results). Since this cube has flat > faces, computing the nodal reaction forces (which, by the way, are > outputted so that you can visualise them as well) and then summing them is > equivalent to directly integrating the contributions over the surface. > > I hope that this helps provide you with some clarification on the point > that you made. > > Regards, > Jean-Paul > > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. For more options, visit https://groups.google.com/d/optout.
