An improved EAS brick element for finite deformation

Korelc, Jože; Šolinc, Urša; Wriggers, Peter

doi:10.1007/s00466-010-0506-0

Cited by 76 publications

(104 citation statements)

References 24 publications

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“…Such models can be used for isotropic and near-incompressible rubber-like materials. The mathematical expressions of these models are [21,22,24]:…”

Section: Hyperelastic Constitutive Lawsmentioning

confidence: 99%

“…Similarly to [9], as the equilibrium condition (24) gives rise to a nonlinear system of equations, the Newton-Raphson iterative technique is employed to achieve the solution. In order to apply this technique, the following equations are used: (27) where r is the residual force vector, also called out-of-balance force vector; and H is the Hessian matrix.…”

Section: Equilibriummentioning

confidence: 99%

“…The computer code is developed in FORTRAN language. The integrals (24) and (26) are evaluated via a full integration scheme, with neither hourglass stabilization nor enhanced strain modes. In order to do so, the Gaussian quadratures given in [32][33][34] are used.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…This numerical example is a benchmark shell problem often studied in the scientific literature (see, for example, [31], [26], [36], [37] and [24]). This problem is used to identify shear locking in the thin-shell limit for bending dominated situations.…”

Section: Thin Plate Ringmentioning

confidence: 99%

“…Further details can be found in [17], [18] and [19], for instance. The modeling of finite strains is performed here by means of nonlinear isotropic hyperelastic laws, often used to describe the response of homogeneous rubber-like materials (see, for example, [3,[20][21][22][23][24]). …”

Section: Introductionmentioning

confidence: 99%

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A shell finite element formulation to analyze highly deformable rubber-like materials

Pascon

Coda

2013

Lat. Am. j. solids struct.

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In this paper, a shell finite element formulation to analyze highly deformable shell structures composed of homogeneous rubberlike materials is presented. The element is a triangular shell of anyorder with seven nodal parameters. The shell kinematics is based on geometrically exact Lagrangian description and on the ReissnerMindlin hypothesis. The finite element can represent thickness stretch and, due to the seventh nodal parameter, linear strain through the thickness direction, which avoids Poisson locking. Other types of locking are eliminated via high-order approximations and mesh refinement. To deal with high-order approximations, a numerical strategy is developed to automatically calculate the shape functions. In the present study, the positional version of the Finite Element Method (FEM) is employed. In this case, nodal positions and unconstrained vectors are the current kinematic variables, instead of displacements and rotations. To model near-incompressible materials under finite elastic strains, which is the case of rubber-like materials, three nonlinear and isotropic hyperelastic laws are adopted. In order to validate the proposed finite element formulation, some benchmark problems with materials under large deformations have been numerically analyzed, as the Cook's membrane, the spherical shell and the pinched cylinder. The results show that the mesh refinement increases the accuracy of solutions, high-order Lagrangian interpolation functions mitigate general locking problems, and the seventh nodal parameter must be used in bending-dominated problems in order to avoid Poisson locking.Keywo rds large deformation analysis; homogeneous rubber-like materials; shell finite elements.

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“…Such models can be used for isotropic and near-incompressible rubber-like materials. The mathematical expressions of these models are [21,22,24]:…”

Section: Hyperelastic Constitutive Lawsmentioning

confidence: 99%

Section: Equilibriummentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

Section: Thin Plate Ringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A shell finite element formulation to analyze highly deformable rubber-like materials

Pascon

Coda

2013

Lat. Am. j. solids struct.

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A 3D Cosserat point element (CPE) for nonlinear orthotropic solids: Generalization for an initially distorted mesh and an arbitrary orientation of material orthotropy

Jabareen

Mtanes

2015

Numerical Meth Engineering

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Summary The objective of the present paper is to develop a Cosserat point element (CPE) formulation for the numerical solution of three‐dimensional problems of general hyperelastic orthotropic materials under finite deformations with initially distorted element shapes. Generally speaking, the accuracy of the CPE depends on the constitutive coefficients of the strain energy function that controls the inhomogeneous deformations. In the present study, a new methodology for the determination of the constitutive coefficients is presented, which allows the CPE to model any elastic material including isotropic, orthotropic, and anisotropic materials and with initially distorted element geometry. A number of example problems are considered, which verify and compare the performance of the developed CPE with other 3D brick elements that exist in the commercial finite element package ABAQUS. These examples demonstrate that the developed CPE is accurate, robust, free of hourglass instabilities, and can be used for modeling both 3D and thin structures that undergo large deformations. Copyright © 2015 John Wiley & Sons, Ltd.

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Different approaches for mixed LSFEMs in hyperelasticity: Application of logarithmic deformation measures

Schwarz

Steeger

Igelbüscher

et al. 2018

Numerical Meth Engineering

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Summary We present geometrically nonlinear formulations based on a mixed least‐squares finite element method. The L2‐norm minimization of the residuals of the given first‐order system of differential equations leads to a functional, which is a two‐field formulation dependent on displacements and stresses. Based thereon, we discuss and investigate two mixed formulations. Both approaches make use of the fact that the stress symmetry condition is not fulfilled a priori due to the row‐wise stress approximation with vector‐valued functions belonging to a Raviart‐Thomas space, which guarantees a conforming discretization of H(div). In general, the advantages of using the least‐squares finite element method lie, for example, in an a posteriori error estimator without additional costs or in the fact that the choice of the polynomial interpolation order is not restricted by the Ladyzhenskaya‐Babuška‐Brezzi condition (inf‐sup condition). We apply a hyperelastic material model with logarithmic deformation measures and investigate various benchmark problems, adaptive mesh refinement, computational costs, and accuracy.

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An improved EAS brick element for finite deformation

Cited by 76 publications

References 24 publications

A shell finite element formulation to analyze highly deformable rubber-like materials

A shell finite element formulation to analyze highly deformable rubber-like materials

A 3D Cosserat point element (CPE) for nonlinear orthotropic solids: Generalization for an initially distorted mesh and an arbitrary orientation of material orthotropy

Different approaches for mixed LSFEMs in hyperelasticity: Application of logarithmic deformation measures

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