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

IF 1.8 3区 工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY
Afshin Anssari-Benam, Giuseppe Saccomandi
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引用次数: 0

Abstract

The comprehensive incompressible strain energy function devised in a preceding contribution (J. Elast. 153:219–244, 2023) is extended in this work for application to the finite deformation of isotropic compressible rubber-like materials. Based on the two established approaches in the literature for constructing a compressible strain energy function \(W\) from the incompressible counterpart, two models are developed and presented: one model is developed on using a \(J\left (= \lambda _{1} \thinspace \lambda _{2} \thinspace \lambda _{3} \right )\) term added to the general functional form of the incompressible model; and the second model on using the isochoric, or modified, principal stretches \(\left (\bar{\lambda }_{a}\right )\), \(a = 1,2,3\), in the functional form of the incompressible model, to account for the deviatoric contribution \(W_{dev}\). The volumetric input \(W_{vol}\) is considred as an additive part. Each model is then simultaneously fitted to extant multi-axial experimental datasets, and the favourable correlation between the models’ predictions and the experimental data is demonstrated. Exemplar challenging individual datasets including a shear-softening behaviour exhibited by an elastomeric foam are also considered, whereby the excellent predictions of the said behaviours by the models will be illustrated. The compatibility of both models with the kinematics of slight compressibility will also be discussed and presented.

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来源期刊
Journal of Elasticity
Journal of Elasticity 工程技术-材料科学:综合
CiteScore
3.70
自引率
15.00%
发文量
74
审稿时长
>12 weeks
期刊介绍: The Journal of Elasticity was founded in 1971 by Marvin Stippes (1922-1979), with its main purpose being to report original and significant discoveries in elasticity. The Journal has broadened in scope over the years to include original contributions in the physical and mathematical science of solids. The areas of rational mechanics, mechanics of materials, including theories of soft materials, biomechanics, and engineering sciences that contribute to fundamental advancements in understanding and predicting the complex behavior of solids are particularly welcomed. The role of elasticity in all such behavior is well recognized and reporting significant discoveries in elasticity remains important to the Journal, as is its relation to thermal and mass transport, electromagnetism, and chemical reactions. Fundamental research that applies the concepts of physics and elements of applied mathematical science is of particular interest. Original research contributions will appear as either full research papers or research notes. Well-documented historical essays and reviews also are welcomed. Materials that will prove effective in teaching will appear as classroom notes. Computational and/or experimental investigations that emphasize relationships to the modeling of the novel physical behavior of solids at all scales are of interest. Guidance principles for content are to be found in the current interests of the Editorial Board.
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