An ALE approach for large-deformation thermoplasticity with application to friction welding

Hamed, M. M. O.; McBride, Andrew; Reddy, B. D.

doi:10.1007/s00466-023-02303-0

Cited by 4 publications

(2 citation statements)

References 31 publications

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“…In the standard ALE solid formulation, 19,36 the physical deformation gradient is generally computed based upon the referential gradient of the respective geometries, mathematically defined as

\boldsymbol{F}=\left(\frac{\partial \boldsymbol{\Phi}}{\partial \boldsymbol{\chi}}\right){\left(\frac{\partial \boldsymbol{\Psi}}{\partial \boldsymbol{\chi}}\right)}^{-1}

. This implies that the accuracy of the physical deformation gradient tensor relies heavily on the resolution of the respective referential gradient computations.…”

Section: Ale First Order Conservation Equations For Solidsmentioning

confidence: 99%

“…One attractive feature of the presented ALE formulation is its possibility to degenerate into three different mixed‐based sets of conservation equations, namely Total Lagrangian formulation, 26–29 Eulerian formulation 30 and Updated Reference Lagrangian formulation 31 . This paper sets the foundations of a robust ALE computational framework capable of handling path‐dependent constitutive models 32–34 (such as large strain elasto‐visco‐plasticity 35 ), along with the consideration of thermal effects 36 induced through strong thermo‐mechanical coupling due to shocks. This will be the focus of our next publication on the topic.…”

Section: Introductionmentioning

confidence: 99%

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A first‐order hyperbolic arbitrary Lagrangian Eulerian conservation formulation for non‐linear solid dynamics

Di Giusto,

Lee,

Gil

et al. 2024

Numerical Meth Engineering

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SummaryThe paper introduces a computational framework using a novel Arbitrary Lagrangian Eulerian (ALE) formalism in the form of a system of first‐order conservation laws. In addition to the usual material and spatial configurations, an additional referential (intrinsic) configuration is introduced in order to disassociate material particles from mesh positions. Using isothermal hyperelasticity as a starting point, mass, linear momentum and total energy conservation equations are written and solved with respect to the reference configuration. In addition, with the purpose of guaranteeing equal order of convergence of strains/stresses and velocities/displacements, the computation of the standard deformation gradient tensor (measured from material to spatial configuration) is obtained via its multiplicative decomposition into two auxiliary deformation gradient tensors, both computed via additional first‐order conservation laws. Crucially, the new ALE conservative formulation will be shown to degenerate elegantly into alternative mixed systems of conservation laws such as Total Lagrangian, Eulerian and Updated Reference Lagrangian. Hyperbolicity of the system of conservation laws will be shown and the accurate wave speed bounds will be presented, the latter critical to ensure stability of explicit time integrators. For spatial discretisation, a vertex‐based Finite Volume method is employed and suitably adapted. To guarantee stability from both the continuum and the semi‐discretisation standpoints, an appropriate numerical interface flux (by means of the Rankine–Hugoniot jump conditions) is carefully designed and presented. Stability is demonstrated via the use of the time variation of the Hamiltonian of the system, seeking to ensure the positive production of numerical entropy. A range of three dimensional benchmark problems will be presented in order to demonstrate the robustness and reliability of the framework. Examples will be restricted to the case of isothermal reversible elasticity to demonstrate the potential of the new formulation.

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“…In the standard ALE solid formulation, 19,36 the physical deformation gradient is generally computed based upon the referential gradient of the respective geometries, mathematically defined as

\boldsymbol{F}=\left(\frac{\partial \boldsymbol{\Phi}}{\partial \boldsymbol{\chi}}\right){\left(\frac{\partial \boldsymbol{\Psi}}{\partial \boldsymbol{\chi}}\right)}^{-1}

. This implies that the accuracy of the physical deformation gradient tensor relies heavily on the resolution of the respective referential gradient computations.…”