On the thermomechanics of solids surrounded by liquid media: balance equations, free energy and nonlinear diffusion

Lion, Alexander; Johlitz, Michael

doi:10.1007/s00161-019-00828-5

Cited by 4 publications

(12 citation statements)

References 34 publications

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“…Within the framework of the thermomechanical theory of binary systems, Lion et al [13] formulated the mass balance, balance of linear momentum, balance of angular momentum, energy balance and entropy balance. Each of them has been formulated for the solid, the fluid as well as for the mixture and set up on the current configuration.…”

Section: Governing Equationsmentioning

confidence: 99%

“…To develop a thermodynamical consistent constitutive theory Lion et al [13] formulated a dissipation inequality for the mixture. That inequality necessitates the non-negativity of the total entropy production for arbitrary thermomechanical processes and has to be satisfied by the constitutive model.…”

Section: Constitutive Relationsmentioning

confidence: 99%

“…That inequality necessitates the non-negativity of the total entropy production for arbitrary thermomechanical processes and has to be satisfied by the constitutive model. In comparison to Lion et al [13], the mechanical volume ratio J M as well as the mechanical isochoric deformation ̂ are taken as process variables instead of the determinant det( S ) and the solid deformation S = S ⋅ T S , which is more useful with respect to modelling mechanically incompressible solids. Consequently, both the stress power and the fourth term of the inequality (24) contain associated mechanical rates.…”

Section: Constitutive Relationsmentioning

confidence: 99%

“…can flow in or out through the system boundary and thus carries a specific amount of mass, momentum, energy as well as entropy. This kind of approach has been followed in the work of Weitsman [18] and has also been further developed among other by Chester and Anand [4] as well as by Lion et al [13]. Achenbach [1] developed a physico-chemical swelling model for implementation within the framework of the finite-element method.…”

Section: Introductionmentioning

confidence: 99%

“…This paper is motivated by the work of Lion et al [13] and shows an implementation and practical application of the theory developed in that publication towards the simulation of non-linear swelling processes adapted to solids made of mechanically incompressible materials. For these reasons, the constitutive modelling will be slightly modified to simplify the parameter identification procedure and allow fast and stable simulations with regard to elastomeric components.…”

Section: Introductionmentioning

confidence: 99%

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A contribution to the chemomechanics of elastomers surrounded by liquid media: continuum mechanical approach for parameter identification using the example of sorption experiments

et al. 2021

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Rubber components are used in almost all areas of industrial applications and are often surrounded by liquid media. Caused by thermodynamical reasons the ambient medium is diffusing into or out of the solid. In consequence, the solid can change in mass, volume and material properties. In this study, the diffusion and swelling behaviour using the example of an application of acrylonitrile-butadiene rubber (NBR) in mesitylene is experimentally investigated. For this purpose, sorption experiments are carried out. Within the framework of continuum mechanical material modelling, a thermodynamically consistent approach is presented, which describes non-linear diffusion of fluids in solids including the swelling phenomenon. Finite strains of the solid as well as an exchange of mass, linear and angular momentum, energy and entropy for open systems are considered. The resulting governing equations of such a multi-field problem are solved using the finite-element method. An optimisation strategy is presented by performing inverse calculations with the numerically converted material model to identify its relevant material parameters. Finally, the swelling of an NBR sealing in mesitylene is simulated.

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Section: Governing Equationsmentioning

confidence: 99%

Section: Constitutive Relationsmentioning

confidence: 99%

Section: Constitutive Relationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A contribution to the chemomechanics of elastomers surrounded by liquid media: continuum mechanical approach for parameter identification using the example of sorption experiments

et al. 2021

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Hydrothermal behavior of pure PA 6 and homogenization of discontinuous long carbon fiber‐reinforced PA 6

Kehrer,

Scheuring,

Blarr

et al. 2024

Proc Appl Math and Mech

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Polymer‐based composites play a crucial role in lightweighting applications by providing resource‐efficient semi‐structural materials. Among these, polyamides, in particular polyamide 6 (PA 6), serve as widely used matrix materials in various technical applications, especially in fiber‐reinforced composites. The mechanical properties and performance of PA 6 are significantly affected by environmental factors such as temperature and humidity. Previous research has investigated the influence of hydrothermal conditions on the mechanical properties of pure PA 6. This study aims to extend the preceding investigations with additional experimental tests. As a preliminary work to later investigate the influence of the fibers on the hydrothermal behavior, discontinuous long carbon fiber‐reinforced PA 6 is considered for micromechanical modeling of the effective behavior. In this context, a mean‐field homogenization approach based on the Hashin–Shtrikman principle is used. By means of a variable reference stiffness, an approach specifically tailored to the material system under consideration can be applied. The simulation data are compared with data from experiments under tension load indicating good agreements for a specific choice of the reference material.

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A numerical study on the physical couplings of a geometrically linear thermo-chemo-mechanical model

Gisy,

Dyck,

Böhlke

2025

International Journal of Solids and Structures

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On the thermomechanics of solids surrounded by liquid media: balance equations, free energy and nonlinear diffusion

Cited by 4 publications

References 34 publications

A contribution to the chemomechanics of elastomers surrounded by liquid media: continuum mechanical approach for parameter identification using the example of sorption experiments

A contribution to the chemomechanics of elastomers surrounded by liquid media: continuum mechanical approach for parameter identification using the example of sorption experiments

Hydrothermal behavior of pure PA 6 and homogenization of discontinuous long carbon fiber‐reinforced PA 6

A numerical study on the physical couplings of a geometrically linear thermo-chemo-mechanical model

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