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The exponentiated Hencky energy: anisotropic extension and case studies

Jörg Schröder, Markus von Hoegen, Patrizio Neff
2017 Computational Mechanics  
In this paper we propose an anisotropic extension of the isotropic exponentiated Hencky energy, based on logarithmic strain invariants.  ...  Unlike other elastic formulations, the isotropic exponentiated Hencky elastic energy has been derived solely on differential geometric grounds, involving the geodesic distance of the deformation gradient  ...  for highly nonlinear and anisotropic elastic arterial wall models in 3D" (SCHR 570/15-2) under the D-A-CH agreement, section 4.3-5.  ... 
doi:10.1007/s00466-017-1466-4 fatcat:wgesn7hvnbbszlvddoivkyk2zm

The exponentiated Hencky-logarithmic strain energy. Part I: Constitutive issues and rank-one convexity [article]

Patrizio Neff and Ionel-Dumitrel Ghiba and Johannes Lankeit
2014 arXiv   pre-print
We investigate a family of isotropic volumetric-isochoric decoupled strain energies F W__ eH(F):=W__ eH(U):={< a r r a y >. based on the Hencky-logarithmic (true, natural) strain tensor U, where μ>0 is  ...  For small elastic strains, W__ eH approximates the classical quadratic Hencky strain energy F W__ H(F):=W__ H(U):=μ dev_n U^2+κ/2 [ tr( U)]^2, which is not everywhere rank-one convex.  ...  Rank-one convexity of the isochoric exponentiated Hencky energy in plane elastostatics In this subsection we consider a variant of the exponentiated Hencky energy in plane strain, with isochoric part W  ... 
arXiv:1403.3843v2 fatcat:xrm6p6azbvgcded4vevhilzeca

The Exponentiated Hencky-Logarithmic Strain Energy. Part I: Constitutive Issues and Rank-One Convexity

Patrizio Neff, Ionel-Dumitrel Ghiba, Johannes Lankeit
2015 Journal of elasticity  
We investigate a family of isotropic volumetric-isochoric decoupled strain energies F → W eH (F ) := W eH (U ) :=   1 Corresponding author: Patrizio Neff, Head of Lehrstuhl für Nichtlineare Analysis  ...  Rank-one convexity of the isochoric exponentiated Hencky energy in plane elastostatics In this subsection we consider a variant of the exponentiated Hencky energy in plane strain, with isochoric part W  ...  Hencky energy W eH and the classical Hencky energy W H for uniaxial deformation.  ... 
doi:10.1007/s10659-015-9524-7 fatcat:iyouvpetwzahlmmdbd6p4nzk4e

A finite element implementation of the isotropic exponentiated Hencky-logarithmic model and simulation of the eversion of elastic tubes [article]

Boumediene Nedjar, Herbert Baaser, Robert J. Martin, Patrizio Neff
2017 arXiv   pre-print
We investigate a finite element formulation of the exponentiated Hencky-logarithmic model whose strain energy function is given by W_eH(F) = μk e^ k dev_n U^2 + κ2 k̂ e^k̂ [tr (U)]^2 , where μ>0 is the  ...  to the deformation gradient F, denotes the principal matrix logarithm on the set of positive definite symmetric matrices, dev_n X = X-trX/n1 and X = √(trX^TX) are the deviatoric part and the Frobenius  ...  In [42] , the exponentiated Hencky energy has also been formally generalized to the anisotropic setting.  ... 
arXiv:1705.08381v1 fatcat:twfcwgvbf5fcrgqyvrpav527ue

A finite element implementation of the isotropic exponentiated Hencky-logarithmic model and simulation of the eversion of elastic tubes

Boumediene Nedjar, Herbert Baaser, Robert J. Martin, Patrizio Neff
2017 Computational Mechanics  
In [44] , the exponentiated Hencky energy has also been formally generalized to the anisotropic setting.  ...  Application to the exponentiated Hencky strain energy To use the relations developed so far for the tangent moduli, we first have to express the strain-energy function (1) in terms of the principal logarithmic  ... 
doi:10.1007/s00466-017-1518-9 fatcat:54mprr3yefcmhhi3eeublwirje

A linearized and incompressible constitutive model for arteries

Y. Liu, W. Zhang, C. Wang, G.S. Kassab
2011 Journal of Theoretical Biology  
The advantages and limitations of this model are discussed.  ...  Thus, the relationships between model parameters due to the incompressibility constraint are easy to analyze and interpret.  ...  Acknowledgments This research was supported in part by the National Institute of Health-National Heart, Lung, and Blood Institute Grant 1 R01 HL087235-01 and 2 R01 HL055554-12.  ... 
doi:10.1016/j.jtbi.2011.05.005 pmid:21605567 pmcid:PMC3164528 fatcat:msmxnztmfrdafjut5qb43eqs7q

An anisotropic viscoelastic fibre–matrix model at finite strains: Continuum formulation and computational aspects

B. Nedjar
2007 Computer Methods in Applied Mechanics and Engineering  
The deformation gradient and its multiplicative decomposition apply to all the continua linking them implicitly. The global anisotropic response is obtained by an assembly of all the contributions.  ...  This paper presents a fully three-dimensional constitutive model for anisotropic viscoelasticity suitable for the macroscopic description of fibre reinforced composites that experience finite strains.  ...  Recently, a considerable effort has been devoted into the extension of isotropic finite strain inelastic models to the anisotropic case from the theoretical and the numerical points of view.  ... 
doi:10.1016/j.cma.2006.09.009 fatcat:ip5g2ip5zrcl5i5dotwr3doqni

Large Deformations of a Soft Porous Material

Christopher W. MacMinn, Eric R. Dufresne, John S. Wettlaufer
2016 Physical Review Applied  
This theory has been used extensively in biomechanics to model large elastic deformations in soft tissues, and in geomechanics to model large elastoplastic deformations in soils.  ...  This poromechanical coupling has applications ranging from tissue mechanics to hydrogeology.  ...  Largedeformation poroelasticity has found extensive application over the past few decades in computational biomechanics for the study of soft tissues, which are porous, fluid saturated, and can accommodate  ... 
doi:10.1103/physrevapplied.5.044020 fatcat:j5xequsnfnejtdr3q4ke3ieogq

Theoretical and electrophysiological evidence for axial loading about aortic baroreceptor nerve terminals in rats

Bin Feng, Bai-yan Li, Eric A. Nauman, John H. Schild
2007 American Journal of Physiology. Heart and Circulatory Physiology  
The pressure-dependent discharge of carotid and aortic baroreceptor afferents has been extensively studied.  ...  mediated orthostatic intolerance are discussed. finite element modeling; mechanosensory afferent; orthostatic hypotension; arterial biomechanics; baroreflex  ...  However, to achieve an adequate fit to the sigmoidal-shaped stress-strain relation of arterial tissues, an additional exponential term was added to the strain energy function (23) .  ... 
doi:10.1152/ajpheart.00712.2007 pmid:17951369 fatcat:ritglsoxybcylgwmmiebsthhqm

Invariant formulation for dispersed transverse isotropy in aortic heart valves

Alan D. Freed, Daniel R. Einstein, Ivan Vesely
2005 Biomechanics and Modeling in Mechanobiology  
The invariant theory is derived from a novel closed-form 'splay invariant' that can easily handle 3D fiber populations, and that only requires a single parameter in the 2D case.  ...  Most soft tissues possess an oriented architecture of collagen fiber bundles, conferring both anisotropy and nonlinearity to their elastic behavior.  ...  Todd Doehring at the Cleveland Clinic and Mr. Dimitri Deserranno at the National Center for Microgravity Research for many delightful discussions on this and related topics.  ... 
doi:10.1007/s10237-005-0069-8 pmid:16133588 fatcat:sj724doryja5rcwnbcyn6e7c6q

Geometrical foundations of plasticity yield criteria: A unified theory [article]

J. M. Luque, R. Campoamor-Stursberg
2009 arXiv   pre-print
Its theoretical development involves the analysis of tensor functions and provides a series expansion which allows the functional stress-dependence of plasticity yield criteria to be predicted.  ...  The theoretical framework for the model includes a series of spatial coefficients that provide a more flexible theory for in-depth examination of symmetry and anisotropy in compact solid materials.  ...  the members of the Mechanical Engineering and Materials Research Group of the University of Seville for their support.  ... 
arXiv:0912.0426v1 fatcat:zioqpnc5o5c7recd5ymj5y7oqm

Proceedings of the FEniCS Conference 2017

Jack S. Hale
2017 Figshare  
Proceedings of the FEniCS Conference 2017 that took place 12-14 June 2017 at the University of Luxembourg, Luxembourg.You can cite individual articles in the proceedings using the following bibtex as a  ...  of the FEniCS Conference 2017  ...  We use the SLEPc eigenvalue solver combined with the FEniCS libraries to compute the natural frequencies for each random realisation and schedule and run the MLMC algorithm using the podS library in parallel  ... 
doi:10.6084/m9.figshare.5086369 fatcat:iwajrgqf3nfgzgyloge3f7dz74

Proceedings of the FEniCS Conference 2017

Jack S. Hale
2017 Figshare  
Proceedings of the FEniCS Conference 2017 that took place 12-14 June 2017 at the University of Luxembourg, Luxembourg.You can cite individual articles in the proceedings using the following bibtex as a  ...  of the FEniCS Conference 2017  ...  The FEniCS project has embraced the use of containers for Continuous Integration, and for distribution of pre-configured images for users.  ... 
doi:10.6084/m9.figshare.5086369.v1 fatcat:siyz4enqijbp5byzmdrvi75owm

A physics-based model for wrinkling skin

Darcy Harrison
2015
The layered structure of skin, and the properties of each layer are critical to producing the buckling patterns observed in real life.  ...  Wrinkles convey emotion and expression, provide clues of age and health, and indicate interaction between the skin and external objects.  ...  and efficient approximation to the Hencky strain tensor due to Bažant [5] is given byȞ = 1 2 U −U −1 . (3.21) This approximation will be used extensively in Chapter 4.  ... 
doi:10.14288/1.0166733 fatcat:fgs4d442yzejtd36nul77todlu

Material degradation due to moisture and temperature. Part 1: mathematical model, analysis, and analytical solutions

C. Xu, M. K. Mudunuru, K. B. Nakshatrala
2016 Continuum Mechanics and Thermodynamics  
materials in these applications are often subjected to adverse environments.  ...  We then obtain semi-analytical solutions of several canonical problems to illustrate the nature of the quasi-static and unsteady behaviors of degrading hyperelastic solids.  ...  ACKNOWLEDGMENTS The authors acknowledge the support from the Department of Energy through Nuclear Energy University Programs (NEUP).  ... 
doi:10.1007/s00161-016-0511-4 fatcat:bh4qafeiwjdhxgyed2zzr6abpi
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