Preface

The main goal of the article is to compare a computational efficiency of different implementation of a hyperelastic material model in the ABAQUS/Standard v. 6.14 [1]. The software offers basically two ways to proceed, namely UMAT and UHYPER user subroutines [2]. The procedures are employed to implement an isotropic, compressible neo-Hookean material model [3]. Corresponding stored-energy function, constitutive equations and the consistent tangent operator are presented. These are essential to program the subroutines. Some theoretical and numerical aspects of different implementation approaches are discussed. As examples, a tube under axial compression and a contact problem of disc are considered. On the basis of obtained results, selected aspects of computational efficiency and quality of solutions are compared.

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“…A general form of the constitutive equation based on (7) in material and spatial description respectively reads as…”

Section: A Simple Compressible Materials Modelmentioning

confidence: 99%

An efficiency comparison of numerical implementation approaches of hyperelastic constitutive model in ABAQUS/Standard

Franus

Kowalewski

2018

MATEC Web Conf.

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“…Parameter zn E may be interpreted as the initial Young's modulus of n-th fiber family. Among others in works [10,12,13] the special case of SE function, which corresponds to the Ciarlet model for incompressible materials discussed in [6]:…”

Section: Poly-convex Stored Energy Functionsmentioning

confidence: 99%

“…Here we are proceeding analogically as shown in [10][11][12][13]. The model presented in section 4 was programmed as the UMAT procedure, which requires the formulation of constitutive relations (5) in incremental form.…”

Section: Umat Proceduresmentioning

confidence: 99%

“…Within these classes, a simplified model of hyper-elastic materials with isotropic matrix reinforced with fibre families was proposed. In particular, the proposed SE functions are simplifications of the SE functions applied in our earlier works [10,12,13]. These models do not lead to non-realistic results, as shown in [21], where the transversally isotropic material models available in the ABAQUS program [9] were used.…”

Section: Final Remarksmentioning

confidence: 99%

“…The simplest possible examples of poly-convex SE functions and related constitutive relationships are given altogether with presentation of the basic equations needed for implementation in FEM software ABAQUS/Standard [7][8][9]. The issues presented here may be treated as a continuation and generalization of concepts presented by authors in papers [10][11][12][13] related to modelling of fibre reinforced materials.…”

Section: Introductionmentioning

confidence: 99%

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Constitutive modelling of fibre reinforced nonhomogenous hyperelastic materials

Jemioło

Gajewski

2017

MATEC Web Conf.

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Abstract. In the paper two classes of poly-convex stored energy functions for transversally isotropic hyper-elastic materials have been proposed. Within these classes, a simplified model of hyper-elastic materials with an isotropic matrix reinforced with fibre family was derived and implemented in finite element software ABAQUS/Standard. The two numerical examples proving correctness of the implementation and showing its positive physical features are presented.

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Numerical implementation of the Murnaghan material model in ABAQUS/Standard

Jemioło

Franus

2018

MATEC Web Conf.

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The paper presents a numerical implementation of the Murnaghan material model (M) [1] in the finite element method software ABAQUS / Standard v. 6.14 [2]. The UHYPER user subroutine is employed, which is suitable for the class of isotropic hyperelastic models [3]. As a special case of the M model, the Saint Venant-Kirchhoff (SVK) model is considered [4]. Formal verification on the basis of elementary tests is performed. Among others, a special attention is paid to a simple shear deformation. In all tested types of deformation, analytical values confirms results based on the finite element procedure within assumed numerical precision and accuracy. It should be noted that the stored-energy function of the M and SVK models do not meet any requirements of the mathematical theory of non-linear elasticity [4, 5]. Therefore, these models are suitable for relatively small deformations, while there are no restrictions on finite rotations. As an example of applications, a tube under axial compression is considered in two cases. Various starting parameters for the Riks procedure [6, 7] are adopted to obtain different solutions of corresponding boundary value problem. Material parameters of steel are considered according to Lurie [8].

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Preface

Cited by 4 publications

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An efficiency comparison of numerical implementation approaches of hyperelastic constitutive model in ABAQUS/Standard

An efficiency comparison of numerical implementation approaches of hyperelastic constitutive model in ABAQUS/Standard

Constitutive modelling of fibre reinforced nonhomogenous hyperelastic materials

Numerical implementation of the Murnaghan material model in ABAQUS/Standard

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