A note on Padé approximants of tensor logarithm with application to Hencky-type hyperelasticity

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10438136" target="_blank" >RIV/00216208:11320/21:10438136 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=NlCzUpIGXq" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=NlCzUpIGXq</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00466-020-01915-0" target="_blank" >10.1007/s00466-020-01915-0</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A note on Padé approximants of tensor logarithm with application to Hencky-type hyperelasticity

Popis výsledku v původním jazyce

We show that the logarithmic (Hencky) strain and its derivatives can be approximated, in a straightforward manner and with a high accuracy, using Padé approximants of the tensor (matrix) logarithm. Accuracy and computational efficiency of the Padé approximants are favourably compared to an alternative approximation method employing the truncated Taylor series. As an application, Hencky-type hyperelasticity models are considered, in which the elastic strain energy is expressed in terms of the Hencky strain, and of our particular interest is the anisotropic energy quadratic in the Hencky strain. Finite-element computations are carried out to examine performance of the Padé approximants of tensor logarithm in Hencky-type hyperelasticity problems. A discussion is also provided on computation of the stress tensor conjugate to the Hencky strain in a general anisotropic case.

Název v anglickém jazyce

A note on Padé approximants of tensor logarithm with application to Hencky-type hyperelasticity

Popis výsledku anglicky

We show that the logarithmic (Hencky) strain and its derivatives can be approximated, in a straightforward manner and with a high accuracy, using Padé approximants of the tensor (matrix) logarithm. Accuracy and computational efficiency of the Padé approximants are favourably compared to an alternative approximation method employing the truncated Taylor series. As an application, Hencky-type hyperelasticity models are considered, in which the elastic strain energy is expressed in terms of the Hencky strain, and of our particular interest is the anisotropic energy quadratic in the Hencky strain. Finite-element computations are carried out to examine performance of the Padé approximants of tensor logarithm in Hencky-type hyperelasticity problems. A discussion is also provided on computation of the stress tensor conjugate to the Hencky strain in a general anisotropic case.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA18-12719S" target="_blank" >GA18-12719S: Thermodynamická a matematická analýza proudění strukturovaných tekutin</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Computational Mechanics

ISSN

0178-7675

e-ISSN

—

Svazek periodika

68

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

14

Strana od-do

619-632

Kód UT WoS článku

000566065900001

EID výsledku v databázi Scopus

2-s2.0-85090141964