A total ALE FE formulation for axisymmetric and torsional problems (including viscoplasticity, thermodynamic coupling and dynamics)

Abstract

SUMMARYThis paper-first-extends a recent 'assumed enhanced deformation gradient' finite ring(segment) element (Int. J. Numer. Methods Eng. 2001; 50:899-918.) to Arbitary Lagrange Euler (ALE) computations, by setting up the assumed tensor on the computational configuration, and-second-shows an elegant way of incorporating dynamics into real ALE computations (no splitting into purely-Lagrange steps and thenremeshing steps), by introducing material mesh velocities and accelerations and spatial mesh velocities and accelerations.

Direct-differentiation-based sensitivity analysis of an axisymmetric finite element formulation including torsion

“…(16) and (17) are similar to the definitions of the respective variations in Eqs. (6) and (7), respectively, with the difference that the former use derivatives of sensitivities of the coordinates, whereas the latter use derivatives of the variations of the displacements. The sensitivity of Eq.…”

“…Finite strain formulations for generalized axisymmetry in solid mechanics have been presented in [5], and later on in various contexts like thermomechanical homogenization [6], mixed or enhanced strain formulations [7][8][9], ALE formulations [6], consolidation analysis [10], or others [11,12]. Contact mechanics in the context of generalized axisymmetry has been treated in [14], for example.…”

ALE formulation for thermomechanical inelastic material models applied to tire forming and curing simulations

“…ALE equations can be solved as a monolithic fully coupled problem as proposed by [3,30] for elasticity and [8,12] for inelasticity. However, the staggered stepwise solution is more common, because it minimizes the computational time for ALE calculations and enables the use of the already available Lagrangian formulation as a substep of the new approach.…”