henki
Mechanical
- Jun 27, 2011
- 22
Hi,
I am interested in explicit dynamics (crash and impact problems). If I would want to create my own explicit FE solver (hydrocode), which formulation would be optimal for speed: total or updated Lagrangian? As far as I know, nearly all commercial software are in updated Lagrangian (for example ABAQUS/Explicit). This would imply that updated Lagrangian is optimal, but this article made me think about the subject:
In the article a total Lagrangian explicit dynamics algorithm for soft tissue deformation is presented. It uses hyperelastic material model. According to the article, this algorithm "requires approximately 35% fewer floating-point operations per element, per time step than the updated Lagrangian explicit algorithm using the same elements".
I was wondering if the same results could be obtained by creating a total Lagrangian explicit dynamics algorithm for metal plasticity, using the multiplicative decomposition of the deformation gradient. The rotations needed in updated Lagrangian formulation would not be needed in total Lagrangian, thus computational time is saved.
I read many articles and browsed through the books "Computational Inelasticity" and "Nonlinear Finite Elements for Continua and Structures". The hyperelastic-plastic material model was presented in both books and in many articles and I got the impression that the hyperelastic-plastic model fixes some defects of the hypoelastic-plastic material models. But nowhere could I find a clear statement of which formulation is the fastest: total Lagrangian with hyperelastic-plastic model OR updated Lagrangian with hypoelastic-plastic model? Or maybe something else? Or is it just that obvious that a hydrocode should use updated Lagrangian formulation, that nobody even bothers to say it clearly?
I sure would appreciate if someone could give any answer, as I just can't help thinking of this. It may be that this is very obvious, but I am not very experienced in this field yet.
-henki
I am interested in explicit dynamics (crash and impact problems). If I would want to create my own explicit FE solver (hydrocode), which formulation would be optimal for speed: total or updated Lagrangian? As far as I know, nearly all commercial software are in updated Lagrangian (for example ABAQUS/Explicit). This would imply that updated Lagrangian is optimal, but this article made me think about the subject:
In the article a total Lagrangian explicit dynamics algorithm for soft tissue deformation is presented. It uses hyperelastic material model. According to the article, this algorithm "requires approximately 35% fewer floating-point operations per element, per time step than the updated Lagrangian explicit algorithm using the same elements".
I was wondering if the same results could be obtained by creating a total Lagrangian explicit dynamics algorithm for metal plasticity, using the multiplicative decomposition of the deformation gradient. The rotations needed in updated Lagrangian formulation would not be needed in total Lagrangian, thus computational time is saved.
I read many articles and browsed through the books "Computational Inelasticity" and "Nonlinear Finite Elements for Continua and Structures". The hyperelastic-plastic material model was presented in both books and in many articles and I got the impression that the hyperelastic-plastic model fixes some defects of the hypoelastic-plastic material models. But nowhere could I find a clear statement of which formulation is the fastest: total Lagrangian with hyperelastic-plastic model OR updated Lagrangian with hypoelastic-plastic model? Or maybe something else? Or is it just that obvious that a hydrocode should use updated Lagrangian formulation, that nobody even bothers to say it clearly?
I sure would appreciate if someone could give any answer, as I just can't help thinking of this. It may be that this is very obvious, but I am not very experienced in this field yet.
-henki
