Application of transversely isotropic materials to multi-layer shell elements undergoing finite rotations and large strains

Lürding, Daniela; Başar, Yavuz; Hanskötter, Ulrike

doi:10.1016/s0020-7683(01)00134-2

Cited by 6 publications

(1 citation statement)

References 19 publications

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“…Owing to symmetries, only one quarter of the structure is illustrated in Figure 19 together with data and boundary conditions considered in the computation. The analysis is performed for two di erent material models, the St. Venant model and a hyperelastic model [22] where the material constants are selected so as to describe a transversely isotropic material with reinforcements placed in circumferential direction. To consider this e ect the circumferential sti ness is assumed to be twice the sti ness of the isotropic material while the sti ness normal to the reinforcement is reduced to half the corresponding value of the isotropy.…”

Section: Non-linear Bending Deformations Of a Pinched Cylindermentioning

confidence: 99%

A general high‐order finite element formulation for shells at large strains and finite rotations

Başar

Hanskötter

Schwab

2003

Numerical Meth Engineering

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SUMMARYFor hyperelastic shells with ÿnite rotations and large strains a p-ÿnite element formulation is presented accommodating general kinematic assumptions, interpolation polynomials and particularly general threedimensional hyperelastic constitutive laws. This goal is achieved by hierarchical, high-order shell models. The tangent sti ness matrices for the hierarchical shell models are derived by computer algebra. Both non-hierarchical, nodal as well as hierarchical element shape functions are admissible. Numerical experiments show the high-order formulation to be less prone to locking e ects.

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Section: Non-linear Bending Deformations Of a Pinched Cylindermentioning

confidence: 99%

A general high‐order finite element formulation for shells at large strains and finite rotations

Başar

Hanskötter

Schwab

2003

Numerical Meth Engineering

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Hyperelastic Energy Densities for Soft Biological Tissues: A Review

Chagnon

Rebouah

Favier

2014

J Elast

232

136

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International audienceMany soft tissues are naturally made of a matrix and fibres that present some privileged directions. They are known to support large reversible deformations. The mechanical behaviour of these tissues highlights different phenomena as hysteresis, stress softening or relaxation. A hyperelastic constitutive equation is typically the basis of the model that describes the behaviour of the material. The hyperelastic constitutive equation can be isotropic or anisotropic, it is generally expressed by means of strain components or strain invariants. This paper proposes a review of these constitutive equations

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Hyperelasticity Modeling for Incompressible Passive Biological Tissues

Chagnon

Ohayon

Martiel

et al. 2017

Biomechanics of Living Organs

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Soft tissues are mainly composed of organised biological media giving them an anisotropic mechanical behavior. Soft tissues also have the ability to undergo large elastic reversible deformations. Many constitutive models were developed to describe these phenomena. In this chapter, we discuss several varying models and their constitutive equations which are defined by means of strain components or strain invariants. The notion of tangent moduli will be plotted for two well-known constitutive equations, and, we will illustrate how to implement explicitly a structural kinematics constraint in a constitutive law to derive the resulting Cauchy stress tensor.

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Application of transversely isotropic materials to multi-layer shell elements undergoing finite rotations and large strains

Cited by 6 publications

References 19 publications

A general high‐order finite element formulation for shells at large strains and finite rotations

A general high‐order finite element formulation for shells at large strains and finite rotations

Hyperelastic Energy Densities for Soft Biological Tissues: A Review

Hyperelasticity Modeling for Incompressible Passive Biological Tissues

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