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

Abstract

Forming of tires during production is a challenging process for Lagrangian solid mechanics due to large changes in the geometry and material properties of the rubber layers. This paper extends the Arbitrary Lagrangian–Eulerian (ALE) formulation to thermomechanical inelastic material models with special consideration of rubber. The ALE approach based on tracking the material and spatial meshes is used, and an operator-split is employed which splits up the solution within a time step into a mesh smoothing step, a history remapping step and a Lagrangian step. Mesh distortion is reduced in the smoothing step by solving a boundary value problem. History variables are subsequently remapped to the new mesh with a particle tracking scheme. Within the Lagrangian steps, a fully coupled thermomechanical problem is solved. An advanced two-phase rubber model is incorporated into the ALE approach, which can describe green rubber, cured rubber and the transition process. Several numerical examples demonstrate the superior behavior of the developed formulation in comparison to purely Lagrangian finite elements.

Transient response of pavement structures under moving wheel loads using the ALE methodology

“…It has been demonstrated that the response of pavements can be obtained efficiently using the Arbitrary Lagrangian Eulerian (ALE) methodology [1][2][3]. Typically, ALE formulations are used in adaptive meshing strategies [4][5][6][7] or fluid mechanics [8][9][10]. However, the ALE formulation has been adapted to be capable of simulating the quasi-static response of tire structures [11].…”

Simulation of the Frequency Response Analysis of Gas Diffusion in Zeolites by Means of Computational Fluid Dynamics

“…Several smoothing methods are available, each with varying complexity and computational costs. Three commonly used methods include [34][35][36][37][38]: (i) elliptic mesh generation smoothing, such as the Laplacian smoothing [35,[39][40][41][42][43][44][45]; (ii) forced-based smoothing, using spring-like methods [34,46]; (iii) smoothing methods based on structural mechanics, such as elastic smoothing [36,37,47] (sometimes with the combination of the FEM Jacobian-based stiffening [48,49]) or hyperelastic smoothing [50][51][52].…”