A finite element method for non-linear hyperelasticity applied for the simulation of octopus arm motions

Vasileios Vavourakis, Asimina Kazakidi, Dimitrios P. Tsakiris, John A. Ekaterinaris

Research output: Contribution to conferencePaper

3 Citations (Scopus)

Abstract

An implicit non-linear finite element (FE) numerical procedure for the simulation of biological muscular tissues is presented. The method has been developed for studying the motion of muscular hydrostats, such as squid and octopus arms and its general framework is applicable to other muscular tissues. The FE framework considered is suitable for the dynamic numerical simulations of three-dimensional non-linear nearly incompressible hyperelastic materials that undergo large displacements and deformations. Human and animal muscles, consisting of fibers and connective tissues, belong to this class of materials. The stress distribution inside the muscular FE model is considered as the superposition of stresses along the muscular fibers and the connective tissues. The stresses along the fibers are modeled as the sum of active and passive stresses, according to the muscular model of Van Leeuwen and Kier (1997) Philos. Trans. R. Soc. London, 352: 551-571. Passive stress distribution is an experimentally-defined function of fibers' deformation; while active stress distribution is the product of an activation level time function, a force-stretch function and a force-stretch ratio function. The mechanical behavior of the surrounding tissues is determined adopting a Mooney-Rivlin constitutive model. The incompressibility criterion is met by enforcing large bulk modulus and by introducing modified deformation measures. Due to the non-linear nature of the problem approximate determination of the Jacobian matrix is performed, in order to utilize the full Newton-Raphson iterative procedure within each time-step. In addition, time discretization is performed via the implicit Newmark method. We developed an open-source finite element code that is capable of simulating large deflection maneuvers of muscular hydrostats. The proposed methodology is validated by comparing the numerical results with existing measurements for the squid arm extension. The efficiency and robustness of the proposed numerical method is demonstrated through a series of octopus arm maneuvers, such as extension, compression and bending.

Conference

Conference4th International Conference on Computational Methods for Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2011
CountryGreece
CityKos
Period20/06/1122/06/11

Fingerprint

Hyperelasticity
Stress Distribution
Finite Element Method
Fiber
Tissue
Finite element method
SQUID
Motion
Stress concentration
Stretch
Fibers
Simulation
Newmark Method
Finite Element
Hyperelastic Material
Bulk Modulus
Large Deflection
Large Displacements
Incompressibility
Newton-Raphson

Keywords

  • FEM
  • muscular hydrostats
  • sceletal muscles
  • coupled circuits
  • collagen
  • computational methods
  • deformation
  • arm motions
  • elasticity
  • fibers
  • finite element method
  • histology
  • Jacobian matrices

Cite this

Vavourakis, V., Kazakidi, A., Tsakiris, D. P., & Ekaterinaris, J. A. (2011). A finite element method for non-linear hyperelasticity applied for the simulation of octopus arm motions. 147-159. Paper presented at 4th International Conference on Computational Methods for Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2011, Kos, Greece.
Vavourakis, Vasileios ; Kazakidi, Asimina ; Tsakiris, Dimitrios P. ; Ekaterinaris, John A. / A finite element method for non-linear hyperelasticity applied for the simulation of octopus arm motions. Paper presented at 4th International Conference on Computational Methods for Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2011, Kos, Greece.13 p.
@conference{6fc4976f8264456a966dd2581facb62d,
title = "A finite element method for non-linear hyperelasticity applied for the simulation of octopus arm motions",
abstract = "An implicit non-linear finite element (FE) numerical procedure for the simulation of biological muscular tissues is presented. The method has been developed for studying the motion of muscular hydrostats, such as squid and octopus arms and its general framework is applicable to other muscular tissues. The FE framework considered is suitable for the dynamic numerical simulations of three-dimensional non-linear nearly incompressible hyperelastic materials that undergo large displacements and deformations. Human and animal muscles, consisting of fibers and connective tissues, belong to this class of materials. The stress distribution inside the muscular FE model is considered as the superposition of stresses along the muscular fibers and the connective tissues. The stresses along the fibers are modeled as the sum of active and passive stresses, according to the muscular model of Van Leeuwen and Kier (1997) Philos. Trans. R. Soc. London, 352: 551-571. Passive stress distribution is an experimentally-defined function of fibers' deformation; while active stress distribution is the product of an activation level time function, a force-stretch function and a force-stretch ratio function. The mechanical behavior of the surrounding tissues is determined adopting a Mooney-Rivlin constitutive model. The incompressibility criterion is met by enforcing large bulk modulus and by introducing modified deformation measures. Due to the non-linear nature of the problem approximate determination of the Jacobian matrix is performed, in order to utilize the full Newton-Raphson iterative procedure within each time-step. In addition, time discretization is performed via the implicit Newmark method. We developed an open-source finite element code that is capable of simulating large deflection maneuvers of muscular hydrostats. The proposed methodology is validated by comparing the numerical results with existing measurements for the squid arm extension. The efficiency and robustness of the proposed numerical method is demonstrated through a series of octopus arm maneuvers, such as extension, compression and bending.",
keywords = "FEM, muscular hydrostats, sceletal muscles, coupled circuits, collagen , computational methods, deformation, arm motions, elasticity, fibers, finite element method, histology, Jacobian matrices",
author = "Vasileios Vavourakis and Asimina Kazakidi and Tsakiris, {Dimitrios P.} and Ekaterinaris, {John A.}",
year = "2011",
month = "6",
day = "22",
language = "English",
pages = "147--159",
note = "4th International Conference on Computational Methods for Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2011 ; Conference date: 20-06-2011 Through 22-06-2011",

}

Vavourakis, V, Kazakidi, A, Tsakiris, DP & Ekaterinaris, JA 2011, 'A finite element method for non-linear hyperelasticity applied for the simulation of octopus arm motions' Paper presented at 4th International Conference on Computational Methods for Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2011, Kos, Greece, 20/06/11 - 22/06/11, pp. 147-159.

A finite element method for non-linear hyperelasticity applied for the simulation of octopus arm motions. / Vavourakis, Vasileios; Kazakidi, Asimina; Tsakiris, Dimitrios P.; Ekaterinaris, John A.

2011. 147-159 Paper presented at 4th International Conference on Computational Methods for Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2011, Kos, Greece.

Research output: Contribution to conferencePaper

TY - CONF

T1 - A finite element method for non-linear hyperelasticity applied for the simulation of octopus arm motions

AU - Vavourakis, Vasileios

AU - Kazakidi, Asimina

AU - Tsakiris, Dimitrios P.

AU - Ekaterinaris, John A.

PY - 2011/6/22

Y1 - 2011/6/22

N2 - An implicit non-linear finite element (FE) numerical procedure for the simulation of biological muscular tissues is presented. The method has been developed for studying the motion of muscular hydrostats, such as squid and octopus arms and its general framework is applicable to other muscular tissues. The FE framework considered is suitable for the dynamic numerical simulations of three-dimensional non-linear nearly incompressible hyperelastic materials that undergo large displacements and deformations. Human and animal muscles, consisting of fibers and connective tissues, belong to this class of materials. The stress distribution inside the muscular FE model is considered as the superposition of stresses along the muscular fibers and the connective tissues. The stresses along the fibers are modeled as the sum of active and passive stresses, according to the muscular model of Van Leeuwen and Kier (1997) Philos. Trans. R. Soc. London, 352: 551-571. Passive stress distribution is an experimentally-defined function of fibers' deformation; while active stress distribution is the product of an activation level time function, a force-stretch function and a force-stretch ratio function. The mechanical behavior of the surrounding tissues is determined adopting a Mooney-Rivlin constitutive model. The incompressibility criterion is met by enforcing large bulk modulus and by introducing modified deformation measures. Due to the non-linear nature of the problem approximate determination of the Jacobian matrix is performed, in order to utilize the full Newton-Raphson iterative procedure within each time-step. In addition, time discretization is performed via the implicit Newmark method. We developed an open-source finite element code that is capable of simulating large deflection maneuvers of muscular hydrostats. The proposed methodology is validated by comparing the numerical results with existing measurements for the squid arm extension. The efficiency and robustness of the proposed numerical method is demonstrated through a series of octopus arm maneuvers, such as extension, compression and bending.

AB - An implicit non-linear finite element (FE) numerical procedure for the simulation of biological muscular tissues is presented. The method has been developed for studying the motion of muscular hydrostats, such as squid and octopus arms and its general framework is applicable to other muscular tissues. The FE framework considered is suitable for the dynamic numerical simulations of three-dimensional non-linear nearly incompressible hyperelastic materials that undergo large displacements and deformations. Human and animal muscles, consisting of fibers and connective tissues, belong to this class of materials. The stress distribution inside the muscular FE model is considered as the superposition of stresses along the muscular fibers and the connective tissues. The stresses along the fibers are modeled as the sum of active and passive stresses, according to the muscular model of Van Leeuwen and Kier (1997) Philos. Trans. R. Soc. London, 352: 551-571. Passive stress distribution is an experimentally-defined function of fibers' deformation; while active stress distribution is the product of an activation level time function, a force-stretch function and a force-stretch ratio function. The mechanical behavior of the surrounding tissues is determined adopting a Mooney-Rivlin constitutive model. The incompressibility criterion is met by enforcing large bulk modulus and by introducing modified deformation measures. Due to the non-linear nature of the problem approximate determination of the Jacobian matrix is performed, in order to utilize the full Newton-Raphson iterative procedure within each time-step. In addition, time discretization is performed via the implicit Newmark method. We developed an open-source finite element code that is capable of simulating large deflection maneuvers of muscular hydrostats. The proposed methodology is validated by comparing the numerical results with existing measurements for the squid arm extension. The efficiency and robustness of the proposed numerical method is demonstrated through a series of octopus arm maneuvers, such as extension, compression and bending.

KW - FEM

KW - muscular hydrostats

KW - sceletal muscles

KW - coupled circuits

KW - collagen

KW - computational methods

KW - deformation

KW - arm motions

KW - elasticity

KW - fibers

KW - finite element method

KW - histology

KW - Jacobian matrices

UR - http://www.scopus.com/inward/record.url?scp=84857380162&partnerID=8YFLogxK

M3 - Paper

SP - 147

EP - 159

ER -

Vavourakis V, Kazakidi A, Tsakiris DP, Ekaterinaris JA. A finite element method for non-linear hyperelasticity applied for the simulation of octopus arm motions. 2011. Paper presented at 4th International Conference on Computational Methods for Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2011, Kos, Greece.