On Cavitation in Rubberlike Materials

2016 ◽  
Vol 83 (4) ◽  
Author(s):  
Yoav Lev ◽  
Konstantin Y. Volokh
Keyword(s):  
Present Note ◽  
Constitutive Models ◽  
Material Model ◽  
Constitutive Laws ◽  
Constitutive Law ◽  
Cavity Expansion ◽  
Hydrostatic Tension ◽  
Hyperelastic Models ◽  
Rubberlike Materials ◽  
Energy Limiters

Microscopic voids can irreversibly grow into the macroscopic ones under hydrostatic tension. To explain this phenomenon, it was suggested in the literature to use the asymptotic value of the hydrostatic tension in the plateau yieldlike region on the stress–stretch curve obtained for the neo-Hookean model. Such an explanation has two limitations: (a) it relies on analysis of only one material model and (b) the hyperelasticity theory is used for the explanation of the failure phenomenon. In view of the mentioned limitations, the objective of the present note is twofold. First, we simulate the cavity expansion in rubber by using various experimentally calibrated hyperelastic models in order to check whether the stress–stretch curves have the plateau yieldlike regions independently of the constitutive law. Second, we repeat simulations via these same models enhanced with a failure description. We find (and that was not reported in the literature) that the process of cavity expansion simulated via hyperelastic constitutive models exhibiting stiffening, due to unfolding of long molecules, is completely stable and there are no plateau yieldlike regions on the stress–stretch curves associated with cavitation. In addition, we find that the instability in the form of yielding observed in experiments does appear in all simulations when the constitutive laws incorporate failure description with energy limiters.

Effect of Material Model on Finite Element Modeling of Aerospace Alloys

2013 ◽  
Vol 554-557 ◽  
pp. 151-156 ◽  
Author(s):  
Mehdi Saboori ◽  
Javad Gholipour ◽  
Henri Champliaud ◽  
Augustin Gakwaya ◽  
Jean Savoie ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Material Model ◽  
Constitutive Laws ◽  
Material Behavior ◽  
Constitutive Law ◽  
Expansion Process ◽  
Free Expansion ◽  
Element Modeling ◽  
Bulge Height

Increasing acceptance and use of hydroforming technology within the aerospace industry requires a comprehensive understanding of critical issues such as the material characteristics, friction condition and hydroformability of the material. Moreover, the cost of experiments that can be reduced by accurate finite element modeling (FEM), which entails the application of adapted constitutive laws for reproducing with confidence the material behavior. In this paper, the effect of different constitutive laws on FEM of tubular shapes is presented. The free expansion process was considered for developing the FEM. Bulge height, thickness reduction and strains were determined at the maximum bulge height using different constitutive models, including Hollomon, Ludwik, Swift, Voce, Ludwigson. In order to minimize the effect of friction, the free expansion experiments were performed with no end feeding. The simulation results were compared with the experimental data to find the appropriate constitutive law for the free expansion process.

CAVITATION INSTABILITY IN RUBBER

2011 ◽  
Vol 03 (02) ◽  
pp. 299-311 ◽  
Author(s):  
K. Y. VOLOKH
Keyword(s):  
Tensile Deformation ◽  
Biaxial Tension ◽  
Constitutive Models ◽  
Maximum Energy ◽  
Hydrostatic Tension ◽  
Cavitation Instability ◽  
Material Volume ◽  
Static Instability ◽  
Styrene Butadiene ◽  
Energy Limiters

Rubber materials and structures can fracture because tensile deformation and growth of small pre-existing voids become unstable, leading to failure localization and crack propagation. Thus, it is important to predict the onset of static instability of the growing voids. We consider two typical cases of interest: the instability of 3D voids under the remote hydrostatic tension in the bulk and the instability of 2D voids under the remote biaxial tension in the membrane. For the purpose of analysis, we use constitutive models of natural and styrene-butadiene rubbers with the failure description enforced by energy limiters. The limiters provide the saturation value for the strain energy which indicates the maximum energy that can be stored and dissipated by an infinitesimal material volume. We find that the unstable growth of a 3D bulk void can start when the remote hydrostatic tension reaches the value of ~2 ÷ 3 MPa and the unstable growth of a 2D membrane void can start when the remote biaxial tension reaches the value of ~50 ÷ 60 MPa.

Determination of a Rubber-Like Material Model as an Inverse Problem

2011 ◽  
Vol 70 ◽  
pp. 225-230 ◽  
Author(s):  
Agnieszka Derewonko ◽  
Andrzej Kiczko
Keyword(s):  
Selection Process ◽  
Axial Stress ◽  
Constitutive Models ◽  
Material Model ◽  
Polyester Fabric ◽  
Point Of View ◽  
Air Cushion ◽  
Ill Conditioning ◽  
Stress States

The purpose of this paper is to describe the selection process of a rubber-like material model useful for simulation behaviour of an inflatable air cushion under multi-axial stress states. The air cushion is a part of a single segment of a pontoon bridge. The air cushion is constructed of a polyester fabric reinforced membrane such as Hypalon®. From a numerical point of view such a composite type poses a challenge since numerical ill-conditioning can occur due to stiffness differences between rubber and fabric. Due to the analysis of the large deformation dynamic response of the structure, the LS-Dyna code is used. Since LS-Dyna contains more than two-hundred constitutive models the inverse method is used to determine parameters characterizing the material on the base of results of the experimental test.

scholarly journals Application of the Generalized Nonlinear Constitutive Law in 2D Shear Flexible Beam Structures

2021 ◽  
Author(s):  
Damian Mrówczyński ◽  
Tomasz Gajewski ◽  
Tomasz Garbowski
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Reference Model ◽  
Constitutive Models ◽  
Constitutive Law ◽  
Flexible Beam ◽  
Beam Model ◽  
Beam Structures ◽  
Nodal Displacements ◽  
Nonlinear Constitutive Law

The paper presents a modified finite element method for nonlinear analysis of 2D beam structures. To take into account the influence of the shear flexibility, a Timoshenko beam element was adopted. The algorithm proposed enables using complex material laws without the need of implementing advanced constitutive models in finite element routines. The method is easy to implement in commonly available CAE software for linear analysis of beam structures. It allows to extend the functionality of these programs with material nonlinearities. By using the structure deformations, computed from the nodal displacements, and the presented here generalized nonlinear constitutive law, it is possible to iteratively reduce the bending, tensile and shear stiffnesses of the structures. By applying a beam model with a multi layered cross-section and generalized stresses and strains to obtain a representative constitutive law, it is easy to model not only the complex multi-material cross-sections, but also the advanced nonlinear constitutive laws (e.g. material softening in tension). The proposed method was implemented in the MATLAB environment, its performance was shown on the several numerical examples. The cross-sections such us a steel I-beam and a steel I-beam with a concrete encasement for different slenderness ratios were considered here. To verify the accuracy of the computations, all results are compared with the ones received from a commercial CAE software. The comparison reveals a good correlation between the reference model and the method proposed.

Application of a Smooth Approximation of the Schmid’s Law to a Single Crystal Gas Turbine Blade: Part 1—Theory and Governing Equations

2012 ◽  
Author(s):  
Alessandro D. Ramaglia
Keyword(s):  
Single Crystal ◽  
Constitutive Models ◽  
Material Model ◽  
Research Literature ◽  
Elastic Behaviour ◽  
Full Potential ◽  
Smooth Approximation ◽  
Suitable Material ◽  
Von Mises ◽  
Term Creep

In industrial practice, the choice of the most suitable material model does not solely rely on the ability of the model in describing the intended phenomena. Most of the choice is often based on a trade-off between a great variety of factors. Robustness, cost and time for the minimum testing campaign necessary to identify the model and pre-existing standard practices are only a few of them. This is particularly true in the case of nonlinear structural analyses because of their intrinsic difficulties and the higher level of skills needed to carefully exploit their full potential. So, despite the great progress in this field, in certain cases it is desirable to use plasticity models that are rate-independent and possess very simple hardening terms. This is for example the case in which long term creep can be an issue or when the designer may want to treat separately different phenomena contributing to inelastic deformation. If the material to be modelled is isotropic, commercial FE packages are able to deal with such problems in almost every case. On the contrary for anisotropic materials like Ni-based super-alloys cast as single crystals, the choice of the designer is more limited and despite the large amount of research literature on the subject, single crystal constitutive models remain quite difficult to handle, to implement into FE codes, to calibrate and to validate. Such difficulties, coupled with the unavoidable approximations introduced by any model, often force the practice of using oversimplifications of the material behaviour. In what follows this problem is addressed by showing how single crystal plasticity modelling can be reduced to the adoption of an anisotropic elastic behaviour with a sort of von Mises yield surface.

Development of a Biofidelic Material Model for Brain Tissue

2011 ◽  
Author(s):  
Sandeep Kulathu ◽  
David L. Littlefield
Keyword(s):  
Brain Tissue ◽  
Grey Matter ◽  
Mechanical Response ◽  
Constitutive Models ◽  
Material Model ◽  
Small Sample ◽  
Material Models ◽  
Computational Mesh ◽  
Injury Mechanisms ◽  
The Brain

Computational simulations of brain injury mechanisms have advanced to a level of sophistication where in addition to capturing different anatomic regions, the computational mesh is capable of distinguishing white and grey matter in the brain. Brain tissue is typically modeled as an isotropic, viscoelastic material. Experiments have shown that the mechanical response of brain tissue to an external load varies depending on the location from which the tissue is harvested and also the direction of loading. Some researchers have developed anisotropic constitutive models by appealing to the composite material case wherein cylindrical axon fibers are immersed in a cellular matrix. Though such material models have been developed over a small sample, they have not been applied over the entire brain for simulation purposes.

scholarly journals A Review on Recent Advances in the Constitutive Modeling of Bone Tissue

2020 ◽  
Vol 18 (6) ◽  
pp. 696-704
Author(s):  
Dieter H. Pahr ◽  
Andreas G. Reisinger
Keyword(s):  
Cortical Bone ◽  
Constitutive Models ◽  
Simulation Models ◽  
Material Model ◽  
Element Analysis ◽  
Physical Mechanisms ◽  
Constitutive Material Model ◽  
Recent Advances ◽  
Osteoporosis Research

Abstract Purpose of Review Image-based finite element analysis (FEA) to predict and understand the biomechanical response has become an essential methodology in musculoskeletal research. An important part of such simulation models is the constitutive material model of which recent advances are summarized in this review. Recent Findings The review shows that existing models from other fields were introduced, such as cohesion zone (cortical bone) or phase-field models (trabecular bone). Some progress has been made in describing cortical bone involving physical mechanisms such as microcracks. Problems with validations at different length scales remain a problem. Summary The improvement of recent constitutive models is partially obscured by uncertainties that affect overall predictions, such as image quality and calibration or boundary conditions. Nevertheless, in vivo CT-based FEA simulations based on a sophisticated constitutive behavior are a very valuable tool for clinical-related osteoporosis research.

On instability of constitutive models for isotropic elastic-perfectly plastic material behaviour at finite deformations

2020 ◽  
pp. 095440622092068
Author(s):  
Marina Trajković-Milenković ◽  
Otto T Bruhns ◽  
Andrija Zorić
Keyword(s):  
Plastic Material ◽  
Constitutive Relations ◽  
Relevant Literature ◽  
Constitutive Models ◽  
Constitutive Law ◽  
Elastoplastic Deformations ◽  
Perfectly Plastic ◽  
User Subroutine ◽  
Shear Problem ◽  
Elastic Perfectly Plastic

The main goal of this work is to test the possibility of a newly introduced constitutive law to model the behaviour of the isotropic elastic-perfectly plastic material which is exposed to large elastoplastic deformations. The proposed constitutive relation is based on the hypo-elastic relation and the inelastic INTERATOM model. The verification of the model is done by its implementation into the commercial software ABAQUS/Standard via the user subroutine UMAT. For that purpose, the large simple shear problem is studied where selected objective corotational rates, i.e. the logarithmic rate, the Jaumann rate and the Green-Naghdi rate, are individually implemented in the aforementioned constitutive relations. The obtained results are compared mutually and with the relevant literature. The proposed constitutive model is also used to test the behaviour of the part of a real engineering structure, i.e. a seismic isolator, in order to obtain the correct input data for further analysis of superstructure behaviour due to seismic excitation.

scholarly journals Extensive CGMD Simulations of Atactic PS Providing Pseudo Experimental Data to Calibrate Nonlinear Inelastic Continuum Mechanical Constitutive Laws

Polymers ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1824 ◽  
Author(s):  
Maximilian Ries ◽  
Gunnar Possart ◽  
Paul Steinmann ◽  
Sebastian Pfaller
Keyword(s):  
Md Simulations ◽  
Multiscale Simulation ◽  
Constitutive Laws ◽  
The Body ◽  
Constitutive Law ◽  
Compression Load ◽  
Body Of Knowledge ◽  
Research Activities ◽  
Tension And Compression ◽  
Atactic Polystyrene

In this contribution, we present a characterization methodology to obtain pseudo experimental deformation data from CG MD simulations of polymers as an inevitable prerequisite to choose and calibrate continuum mechanical constitutive laws. Without restriction of generality, we employ a well established CG model of atactic polystyrene as exemplary model system and simulate its mechanical behavior under various uniaxial tension and compression load cases. To demonstrate the applicability of the obtained data, we exemplarily calibrate a viscoelastic continuum mechanical constitutive law. We conclude our contribution by a thorough discussion of the findings obtained in the numerical pseudo experiments and give an outline of subsequent research activities. Thus, this work contributes to the field of multiscale simulation methods and adds a specific application to the body of knowledge of CG MD simulations.

scholarly journals Inverse Strategies for Identifying the Parameters of Constitutive Laws of Metal Sheets

2016 ◽  
Vol 2016 ◽  
pp. 1-18 ◽  
Author(s):  
P. A. Prates ◽  
A. F. G. Pereira ◽  
N. A. Sakharova ◽  
M. C. Oliveira ◽  
J. V. Fernandes
Keyword(s):  
Finite Element ◽  
Cost Function ◽  
Optimization Algorithm ◽  
Yield Criterion ◽  
Kinematic Hardening ◽  
Constitutive Laws ◽  
Constitutive Law ◽  
Identification Procedure ◽  
Metal Sheets ◽  
The Cost

This article is a review regarding recently developed inverse strategies coupled with finite element simulations for the identification of the parameters of constitutive laws that describe the plastic behaviour of metal sheets. It highlights that the identification procedure is dictated by the loading conditions, the geometry of the sample, the type of experimental results selected for the analysis, the cost function, and optimization algorithm used. Also, the type of constitutive law (isotropic and/or kinematic hardening laws and/or anisotropic yield criterion), whose parameters are intended to be identified, affects the whole identification procedure.

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