View in EDS

Robust and efficient implementation of finite strain generalized continuum models for material failure: Analytical, numerical, and automatic differentiation with hyper-dual numbers.

Saved in:
Bibliographic Details
Title: Robust and efficient implementation of finite strain generalized continuum models for material failure: Analytical, numerical, and automatic differentiation with hyper-dual numbers.
Authors: Dummer, Alexander1 (AUTHOR) Alexander.Dummer@uibk.ac.at, Neuner, Matthias1 (AUTHOR), Gamnitzer, Peter1 (AUTHOR), Hofstetter, Günter1 (AUTHOR)
Source: Computer Methods in Applied Mechanics & Engineering. Jun2024, Vol. 426, pN.PAG-N.PAG. 1p.
Subjects: Automatic differentiation, Fracture mechanics, Finite element method, Numerical differentiation, Derivatives (Mathematics), Strains & stresses (Mechanics)
Abstract: Generalized continuum models for representing nonlinear material behavior including material failure in the finite strain regime are commonly formulated based on scalar elastic and dissipation potential functions. The evolution of stresses and internal variables, i.e., the material state, is governed by partial derivatives of the potential functions with respect to deformation and stress measures. Furthermore, for application of such models in implicit nonlinear finite element analysis tangent operators, consistent with the numerical integration algorithm, are required. In this work, we study analytical, numerical and automatic differentiation schemes for the implementation of coupled, generalized continuum models considering finite inelastic deformations and fracture. This includes the application of finite difference approximations, complex-step derivative approximations and automatic differentiation based on hyper-dual numbers. For the use of automatic differentiation, a semi-analytical split approach is introduced for increasing the computational efficiency. Based on a comprehensive 2D and 3D finite element study, we demonstrate the superior properties of automatic differentiation compared to numerical differentiation methods with regards to accuracy and robustness. Furthermore, the additional computational cost for automatic differentiation using the proposed split approach becomes negligible for large problems. • Study of techniques for computing derivatives in generalized continuum models. • Implementation details using analytical, numerical, and automatic differentiation. • Proposal of an efficient semi-analytical approach with automatic differentiation. • Evaluation of CPU time in 2D and 3D finite element analysis of experimental tests. • The semi-analytical approach enables fast and robust implementations. [ABSTRACT FROM AUTHOR]
Copyright of Computer Methods in Applied Mechanics & Engineering is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
Description
Abstract:Generalized continuum models for representing nonlinear material behavior including material failure in the finite strain regime are commonly formulated based on scalar elastic and dissipation potential functions. The evolution of stresses and internal variables, i.e., the material state, is governed by partial derivatives of the potential functions with respect to deformation and stress measures. Furthermore, for application of such models in implicit nonlinear finite element analysis tangent operators, consistent with the numerical integration algorithm, are required. In this work, we study analytical, numerical and automatic differentiation schemes for the implementation of coupled, generalized continuum models considering finite inelastic deformations and fracture. This includes the application of finite difference approximations, complex-step derivative approximations and automatic differentiation based on hyper-dual numbers. For the use of automatic differentiation, a semi-analytical split approach is introduced for increasing the computational efficiency. Based on a comprehensive 2D and 3D finite element study, we demonstrate the superior properties of automatic differentiation compared to numerical differentiation methods with regards to accuracy and robustness. Furthermore, the additional computational cost for automatic differentiation using the proposed split approach becomes negligible for large problems. • Study of techniques for computing derivatives in generalized continuum models. • Implementation details using analytical, numerical, and automatic differentiation. • Proposal of an efficient semi-analytical approach with automatic differentiation. • Evaluation of CPU time in 2D and 3D finite element analysis of experimental tests. • The semi-analytical approach enables fast and robust implementations. [ABSTRACT FROM AUTHOR]
ISSN:00457825
DOI:10.1016/j.cma.2024.116987