Two stress update algorithms for large strains: accuracy analysis and numerical implementation

Autor: Pierre Pegon, Antonio Huerta, Antonio Rodríguez-Ferran
Přispěvatelé: Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III, Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria
Jazyk: angličtina
Rok vydání: 2020
Předmět:
Nonlinear computational mechanics
Finite element method
Mecànica dels sòlids -- Mètodes numèrics
Engineering
Civil
Constitutive equation
Engineering
Multidisciplinary
Física::Física de l'estat sòlid [Àrees temàtiques de la UPC]
Solids--Mechanical properties
law.invention
Matemàtiques i estadística::Anàlisi numèrica [Àrees temàtiques de la UPC]
law
Cartesian coordinate system
Stress update
Engineering
Ocean
Engineering
Aerospace
Engineering
Biomedical
Mathematics
Large strains
Numerical Analysis
Applied Mathematics
Numerical analysis
General Engineering
Convected frames
Computer Science
Software Engineering
Engineering
Marine
Numerical integration
Simple shear
Engineering
Manufacturing
Engineering
Mechanical
Rate of convergence
Error analysis
Solid mechanics
Engineering
Industrial
Algorithm
Zdroj: Recercat. Dipósit de la Recerca de Catalunya
instname
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
Scipedia Open Access
Scipedia SL
Popis: Two algorithms for the stress update (i.e., time integration of the constitutive equation) in large-strain solid mechanics are compared from an analytical point of view. The order of the truncation error associated to the numerical integration is deduced for each algorithm a priori, using standard numerical analysis. This accuracy analysis has been performed by means of a convected frame formalism, which also allows a unied derivation of both algorithms in spite of their inherent dierences. Then the two algorithms are adapted from convected frames to a xed Cartesian frame and implemented in a small-strain nite element code. The implementation is validated by means of a set of simple deformation paths (simple shear, extension, extension and compression, extension and rotation) and two benchmark tests in non-linear mechanics (the necking of a circular bar and a shell under ring loads). In these numerical tests, the observed order of convergence is in very good agreement with the theoretical order of convergence, thus corroborating the accuracy analysis. ? 1997 John Wiley & Sons, Ltd.
Databáze: OpenAIRE
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