A damage directional constitutive model for Mullins effect with permanent set and induced anisotropy

Diani, Julie; Brieu, Mathias; Vacherand, J.-M.

doi:10.1016/j.euromechsol.2005.09.011

Cited by 136 publications

(110 citation statements)

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“…However, subsequent experimental studies mainly focused on proportional loadings and the induced anisotropy was not investigated further for several decades. Only recently, several studies (Laraba-Abbes et al, 2003;Hanson et al, 2005;Diani et al, 2006;Itskov et al, 2006;Dargazany and Itskov, 2009;Machado, 2011;Merckel et al, 2012) brought to light Mullins softening induced anisotropy by application of successive non-proportional loadings.…”

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confidence: 99%

Constitutive modeling of the anisotropic behavior of Mullins softened filled rubbers

Merckel

Diani

Brieu

et al. 2013

Mechanics of Materials

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. Original constitutive modeling is proposed for filled rubber materials in order to capture the anisotropic softened behavior induced by general non-proportional pre-loading histories. The hyperelastic framework is grounded on a thorough analysis of cyclic experimental data. The strain energy density is based on a directional approach. The model leans on the strain amplification factor concept applied over material directions according to the Mullins softening evolution. In order to provide a model versatile that applies for a wide range of materials, the proposed framework does not require to postulate the mathematical forms of the elementary directional strain energy density and of the Mullins softening evolution rule. A computational procedure is defined to build both functions incrementally from experimental data obtained during cyclic uniaxial tensile tests. Successful comparisons between the model and the experiments demonstrate the model abilities. Moreover, the model is shown to accurately predict the non-proportional uniaxial stress-stretch responses for uniaxially and biaxially pre-stretched samples. Finally, the model is efficiently tested on several materials and proves to provide a quantitative estimate of the anisotropy induced by the Mullins softening for a wide range of filled rubbers.

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Constitutive modeling of the anisotropic behavior of Mullins softened filled rubbers

Merckel

Diani

Brieu

et al. 2013

Mechanics of Materials

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“…Mullins' effect tests were initially developed for rubber testing but were implemented for other types of polymers such as thermoplastic elastomers and semi-crystalline thermoplastic polymers [24][25][26]. Three main material characteristics are distinguishable for such tests: hysteresis of energy, strain softening and strain hardening [27][28][29].…”

Section: Mullins' Effect Testsmentioning

confidence: 99%

Viscoplastic Behaviour of Polyamides

Dan-Andrei¹

2016

Viscoelastic and Viscoplastic Materials

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In this study, the viscoplastic behaviour of a polyamide-based thermoplastic polymer was investigated by performing a number of tests that highlighted the influence of time and temperature on the mechanical behaviour: strain-rate-and temperature-dependency tests, creep tests, dynamic mechanical analysis (DMA) tests, Mullins' effect tests, and low-cycle fatigue tests. The results are discussed and explanations are proposed regarding the particularities the investigated material exhibits during deformation.

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“…Results in this respect have been given based either on phenomenological models with damage-like variables or micro-mechanical models with macromolecular mechanisms. Representatives in these respects may be found, e.g., earlier in [3] and later in [4][5][6][7][8][9][10][11][12][13][14] for phenomenological models, and in [15][16][17][18][19][20][21][22][23][24][25] for micro-mechanical models. On the other side, the modeling of the shape memory effect for SMPs is relatively recent.…”

Section: Motivation and Introductionmentioning

confidence: 99%

An Explicit Approach Toward Modeling Thermo-Coupled Deformation Behaviors of SMPs

Ding

Yin

et al. 2017

Applied Sciences

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Abstract:A new elastoplastic J 2 -flow models with thermal effects is proposed toward simulating thermo-coupled finite deformation behaviors of shape memory polymers. In this new model, an elastic potential evolving with development of plastic flow is incorporated to characterize the stress-softening effect at unloading and, moreover, thermo-induced plastic flow is introduced to represent the strain recovery effect at heating. It is shown that any given test data for both effects may be accurately simulated by means of direct and explicit procedures. Numerical examples for model predictions compare well with test data in literature.Keywords: shape memory polymers; thermo-coupled effects; finite deformations; stress softening; elastoplasticity models; explicit simulation Motivation and IntroductionIn recent years, much attention has been directed to smart materials such as shape memory alloys (SMAs) and shape memory polymers (SMPs) (cf., e.g., [1,2]). It is of great interest to simulate thermo-coupled deformation behaviors of such materials under both loading and heating. Unlike deformation behavior of SMAs with very small elastic deformations, however, SMPs exhibit complicated thermo-mechanical deformation effects coupled with both temperature and large recoverable deformations. Typical representatives of such effects are the stress softening effect at unloading in the isothermal case and the strain recovery effect at pure heating. The former is characteristic of all kinds of polymers and associated with a number of unloading stress-strain curves of complex shapes that differ from one another and result in different permanent sets, while the latter is unique to SMPs and related to the recovery of a large pre-strain at heating. Usually, recoverable strains of SMPs both at unloading and at heating may be several hundred percents. As such, large thermo-coupled inelastic deformations incorporating large recoverable deformations should be treated toward modeling thermo-mechanical behavior of SMPs, in particular, in simulating both the stress-softening effect at unloading and the large strain recovery effect at heating (i.e., the shape memory effect).Many efforts have been made to establish constitutive models for the purpose of incorporating the above two effects. As a typical isothermal deformation feature for various kinds of polymers, the stress softening effect at unloading was observed earlier and has been simulated for some time. Results in this respect have been given based either on phenomenological models with damage-like variables or micro-mechanical models with macromolecular mechanisms. Representatives in these respects may be found, e.g., earlier in [3] and later in [4][5][6][7][8][9][10][11][12][13][14] for phenomenological models, and in [15][16][17][18][19][20][21][22][23][24][25] for micro-mechanical models. On the other side, the modeling of the shape memory effect for SMPs is relatively recent. Results in this respect and, generally, in the thermo-mechanical behavior of SMPs may be found, e.g., in ...

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A damage directional constitutive model for Mullins effect with permanent set and induced anisotropy

Cited by 136 publications

References 31 publications

Constitutive modeling of the anisotropic behavior of Mullins softened filled rubbers

Constitutive modeling of the anisotropic behavior of Mullins softened filled rubbers

Viscoplastic Behaviour of Polyamides

An Explicit Approach Toward Modeling Thermo-Coupled Deformation Behaviors of SMPs

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