A three-parameter structurally motivated robust constitutive model for isotropic incompressible unfilled and filled rubber-like materials

Anssari-Benam, Afshin; Horgan, Cornelius O.

doi:10.1016/j.euromechsol.2022.104605

Cited by 28 publications

(15 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It was demonstrated by Anssari-Benam and Horgan [17] that model ( 4) is indeed the parent to the celebrated Gent model, reducing to the Gent model in the limit n → ∞. Moreover, the functional form of the model (4) proved rich enough to provide favourable fits to the deformation of both unfilled and filled rubbers, as demonstrated in [17], making this model one of the very few available models in literature with such a capability, next to the model by Lopez-Pamies [12,34]. Models (3) and ( 4) are within Rivlin's representation form in terms of the principal invariant(s).…”

Section: Theoretical Backgroundmentioning

confidence: 84%

“…Indeed, the only two models that have been successfully applied to this dataset in the literature are that of Lopez-Pamies [12] and the invariant form of the proposed model, Eq. ( 4), employed by Anssari-Benam and Horgan [17]. Figure 2 illustrates the favourable application of the proposed model (1) to this dataset.…”

Section: Correlation With the Experimental Datamentioning

confidence: 99%

“…1−nN . While both N and n in the original derivation of the models (3) and ( 4) were constrained to be integers, Anssari-Benam and Horgan [16,17] later showed that phenomenologically there is no reason for such a restriction, and generalised those constraints to: n, N ∈ R + . Subject to this new constraint, and that in (4), the ln ( ) function remains well defined.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…The performance of most, if not all, models in the literature encounters further problems when the models are applied to datasets from different types of rubber-like specimens which exhibit discernible mechanical behaviours. For example, as recently studied by Anssari-Benam and Horgan [16,17], even some of the most celebrated models cannot suitably capture the mechanical behaviour of both unfilled and filled rubbers. This shortcoming implies, then, that the application of most of the existing models in the literature is at best limited to only a specific type of rubber-like materials.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Large Isotropic Elastic Deformations: On a Comprehensive Model to Correlate the Theory and Experiments for Incompressible Rubber-Like Materials

Anssari-Benam

2023

J Elast

Self Cite

View full text Add to dashboard Cite

A comprehensive model, i.e., a model that: (i) suitably captures the mechanical behaviour of various types of rubber-like materials; (ii) describes the constitutive behaviour of a subject rubber-like specimen under different deformation modes via a single set of model parameter values, and (iii) is parent to many of the existing models of distinct types, is presented in this paper for application to the finite deformation of incompressible isotropic rubber-like materials. The model breaks away from Rivlin’s principal invariants $I_{i}$ I i and Valanis-Landel’s separable function of principal stretches $\lambda _{i}$ λ i representations, and instead adopts a general non-separable functional form $W( \lambda _{1}, \lambda _{2}, \lambda _{3} )$ W ( λ 1 , λ 2 , λ 3 ) , subject to the incompressibility constraint. By way of example, the application of the model to extant datasets from four types of rubber-like materials that exhibit discernible mechanical behaviours, namely natural unfilled and filled rubbers, hydrogels and (extremely) soft tissue specimens, will be considered. The favourable correlation between the model predictions and the considered experimental datasets, obtained via simultaneous fitting of the model to the data of various deformations, will be demonstrated. It will be shown that most of the landmark models in the literature including the $W( I_{1}, I_{2} )$ W ( I 1 , I 2 ) form Mooney-Rivlin, the Gent-like limiting chain extensibility, the nonaffine tube and the separable principal stretches-based type Ogden models are all a special sub-set of the presented parent model, and are all recovered from this model. An important implication of the non-separable functional form of the model will be conferred, through a specific dataset, where the predictions of the separable functions prove inherently inadequate. The consequences of these improvements for a more accurate modelling of the finite deformation of incompressible isotropic rubber-like materials will also be discussed.

show abstract

Section: Theoretical Backgroundmentioning

confidence: 84%

Section: Correlation With the Experimental Datamentioning

confidence: 99%

Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Large Isotropic Elastic Deformations: On a Comprehensive Model to Correlate the Theory and Experiments for Incompressible Rubber-Like Materials

Anssari-Benam

2023

J Elast

Self Cite

View full text Add to dashboard Cite

show abstract

“…However, the adjustment of the analytical pressuredeflection relation based on the fitting of numerical solutions was carried out considering incompressible materials. Incompressibility is a well-established assumption for rubbers and rubber-like materials [41,42]. However, this hypothesis may result inappropriate for some class of materials able to experience large deformations [43][44][45].…”

Section: Compressible Materialsmentioning

confidence: 99%

Analytical pressure–deflection curves for the inflation of pre-stretched circular membranes

Sirotti

Pelliciari

Aloisio

et al. 2023

European Journal of Mechanics - A/Solids

View full text Add to dashboard Cite

A constitutive modeling approach to simulate time‐dependent phenomena in rubber‐like materials

Landgraf,

Ihlemann

2023

Proc Appl Math and Mech

View full text Add to dashboard Cite

Industrial rubber materials and similar rubber‐like materials exhibit complex mechanical behavior including nonlinear stress‐strain behavior up to large strains, hysteresis, Mullins effect, permanent set, as well as time‐dependent effects, like relaxation and rate dependency. The modeling of all these phenomena is a challenging task. One constitutive model that is capable to capture many effects in the large strain regime is the so‐called model of rubber phenomenology (MORPH). However, it is not able to capture any of the mentioned time‐dependent phenomena. Thus, this contribution deals with the extension of this model to simulate relaxation and rate dependency of rubber‐like materials. Thereby, a basic modeling approach is proposed, where only a slight change in the original system of tensorial equations is necessary. This approach is further extended by applying not only a constant relaxation time, but also loading history‐depended relaxation properties. For numerical simulations, a time discretization has to be applied to the constitutive equations, which is briefly shown. Finally, the extended MORPH model is applied to two different materials: an industrial rubber material and a polyurethane based adhesive. In both cases, the extended MORPH model is adjusted to uniaxial tension test data by parameter identification procedures. It will be shown that basic time‐dependent phenomena of rubber‐like materials can be captured well with the proposed extensions.

show abstract

A three-parameter structurally motivated robust constitutive model for isotropic incompressible unfilled and filled rubber-like materials

Cited by 28 publications

References 43 publications

Large Isotropic Elastic Deformations: On a Comprehensive Model to Correlate the Theory and Experiments for Incompressible Rubber-Like Materials

Large Isotropic Elastic Deformations: On a Comprehensive Model to Correlate the Theory and Experiments for Incompressible Rubber-Like Materials

Analytical pressure–deflection curves for the inflation of pre-stretched circular membranes

A constitutive modeling approach to simulate time‐dependent phenomena in rubber‐like materials

Contact Info

Product

Resources

About