Matches in SemOpenAlex for { <https://semopenalex.org/work/W2772087755> ?p ?o ?g. }
- W2772087755 endingPage "158" @default.
- W2772087755 startingPage "147" @default.
- W2772087755 abstract "The logarithmic strain measures $lVertlog UrVert^2$, where $log U$ is the principal matrix logarithm of the stretch tensor $U=sqrt{F^TF}$ corresponding to the deformation gradient $F$ and $lVert,.,rVert$ denotes the Frobenius matrix norm, arises naturally via the geodesic distance of $F$ to the special orthogonal group $operatorname{SO}(n)$. This purely geometric characterization of this strain measure suggests that a viable constitutive law of nonlinear elasticity may be derived from an elastic energy potential which depends solely on this intrinsic property of the deformation, i.e. that an energy function $Wcolonoperatorname{GL^+}(n)tomathbb{R}$ of the form begin{equation} W(F)=Psi(lVertlog UrVert^2) tag{1} end{equation} with a suitable function $Psicolon[0,infty)tomathbb{R}$ should be used to describe finite elastic deformations. However, while such energy functions enjoy a number of favorable properties, we show that it is not possible to find a strictly monotone function $Psi$ such that $W$ of the form (1) is Legendre-Hadamard elliptic. Similarly, we consider the related isochoric strain measure $lVertoperatorname{dev}_nlog UrVert^2$, where $operatorname{dev}_n log U$ is the deviatoric part of $log U$. Although a polyconvex energy function in terms of this strain measure has recently been constructed in the planar case $n=2$, we show that for $ngeq3$, no strictly monotone function $Psicolon[0,infty)tomathbb{R}$ exists such that $Fmapsto Psi(lVertoperatorname{dev}_nlog UrVert^2)$ is polyconvex or even rank-one convex. Moreover, a volumetric-isochorically decoupled energy of the form $Fmapsto Psi(lVertoperatorname{dev}_nlog UrVert^2) + W_{mathrm{vol}}(det F)$ cannot be rank-one convex for any function $W_{mathrm{vol}}colon(0,infty)tomathbb{R}$ if $Psi$ is strictly monotone." @default.
- W2772087755 created "2017-12-22" @default.
- W2772087755 creator A5046930021 @default.
- W2772087755 creator A5059390379 @default.
- W2772087755 creator A5077215828 @default.
- W2772087755 date "2018-06-01" @default.
- W2772087755 modified "2023-10-18" @default.
- W2772087755 title "A non-ellipticity result, or the impossible taming of the logarithmic strain measure" @default.
- W2772087755 cites W1588906972 @default.
- W2772087755 cites W1589640616 @default.
- W2772087755 cites W1778809502 @default.
- W2772087755 cites W1868760746 @default.
- W2772087755 cites W1965424663 @default.
- W2772087755 cites W1971804748 @default.
- W2772087755 cites W1973558132 @default.
- W2772087755 cites W1981631252 @default.
- W2772087755 cites W1989937126 @default.
- W2772087755 cites W2000342819 @default.
- W2772087755 cites W2010769900 @default.
- W2772087755 cites W2023209784 @default.
- W2772087755 cites W2028323374 @default.
- W2772087755 cites W2034161819 @default.
- W2772087755 cites W2034771336 @default.
- W2772087755 cites W2039652752 @default.
- W2772087755 cites W2046312530 @default.
- W2772087755 cites W2051841050 @default.
- W2772087755 cites W2053387058 @default.
- W2772087755 cites W2057047523 @default.
- W2772087755 cites W2057991022 @default.
- W2772087755 cites W2059189991 @default.
- W2772087755 cites W2061880266 @default.
- W2772087755 cites W2078723585 @default.
- W2772087755 cites W2090674257 @default.
- W2772087755 cites W2093551812 @default.
- W2772087755 cites W2117756873 @default.
- W2772087755 cites W2118161967 @default.
- W2772087755 cites W2119618818 @default.
- W2772087755 cites W2131131708 @default.
- W2772087755 cites W2144571142 @default.
- W2772087755 cites W2266240621 @default.
- W2772087755 cites W2323263964 @default.
- W2772087755 cites W2514661951 @default.
- W2772087755 cites W2963440685 @default.
- W2772087755 cites W2963760081 @default.
- W2772087755 cites W2963858514 @default.
- W2772087755 cites W2964015381 @default.
- W2772087755 cites W3103833310 @default.
- W2772087755 cites W3184201526 @default.
- W2772087755 cites W4205876119 @default.
- W2772087755 doi "https://doi.org/10.1016/j.ijnonlinmec.2018.02.011" @default.
- W2772087755 hasPublicationYear "2018" @default.
- W2772087755 type Work @default.
- W2772087755 sameAs 2772087755 @default.
- W2772087755 citedByCount "11" @default.
- W2772087755 countsByYear W27720877552017 @default.
- W2772087755 countsByYear W27720877552019 @default.
- W2772087755 countsByYear W27720877552020 @default.
- W2772087755 countsByYear W27720877552021 @default.
- W2772087755 countsByYear W27720877552022 @default.
- W2772087755 countsByYear W27720877552023 @default.
- W2772087755 crossrefType "journal-article" @default.
- W2772087755 hasAuthorship W2772087755A5046930021 @default.
- W2772087755 hasAuthorship W2772087755A5059390379 @default.
- W2772087755 hasAuthorship W2772087755A5077215828 @default.
- W2772087755 hasBestOaLocation W27720877552 @default.
- W2772087755 hasConcept C114614502 @default.
- W2772087755 hasConcept C121332964 @default.
- W2772087755 hasConcept C134306372 @default.
- W2772087755 hasConcept C135628077 @default.
- W2772087755 hasConcept C14036430 @default.
- W2772087755 hasConcept C186370098 @default.
- W2772087755 hasConcept C199201527 @default.
- W2772087755 hasConcept C2524010 @default.
- W2772087755 hasConcept C2780009758 @default.
- W2772087755 hasConcept C2834757 @default.
- W2772087755 hasConcept C33923547 @default.
- W2772087755 hasConcept C37914503 @default.
- W2772087755 hasConcept C39927690 @default.
- W2772087755 hasConcept C41008148 @default.
- W2772087755 hasConcept C44280652 @default.
- W2772087755 hasConcept C62520636 @default.
- W2772087755 hasConcept C77088390 @default.
- W2772087755 hasConcept C78458016 @default.
- W2772087755 hasConcept C85523063 @default.
- W2772087755 hasConcept C86803240 @default.
- W2772087755 hasConcept C97355855 @default.
- W2772087755 hasConceptScore W2772087755C114614502 @default.
- W2772087755 hasConceptScore W2772087755C121332964 @default.
- W2772087755 hasConceptScore W2772087755C134306372 @default.
- W2772087755 hasConceptScore W2772087755C135628077 @default.
- W2772087755 hasConceptScore W2772087755C14036430 @default.
- W2772087755 hasConceptScore W2772087755C186370098 @default.
- W2772087755 hasConceptScore W2772087755C199201527 @default.
- W2772087755 hasConceptScore W2772087755C2524010 @default.
- W2772087755 hasConceptScore W2772087755C2780009758 @default.
- W2772087755 hasConceptScore W2772087755C2834757 @default.
- W2772087755 hasConceptScore W2772087755C33923547 @default.
- W2772087755 hasConceptScore W2772087755C37914503 @default.