| 1. |
- Aiki, Toyohiko, et al.
(author)
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A macro-micro elasticity-diffusion system modeling absorption-induced swelling in rubber foams : Proof of the strong solvability
- 2021
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In: Quarterly of Applied Mathematics. - : American Mathematical Society (AMS). - 0033-569X .- 1552-4485. ; 79:3, s. 545-579
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Journal article (peer-reviewed)abstract
- In this article, we propose a macro-micro (two-scale) mathematical model for describing the macroscopic swelling of a rubber foam caused by the microscopic absorption of some liquid. In our modeling approach, we suppose that the material occupies a one-dimensional domain which swells as described by the standard beam equation including an additional term determined by the liquid pressure. As special feature of our model, the absorption takes place inside the rubber foam via a lower length scale, which is assumed to be inherently present in such a structured material. The liquid's absorption and transport inside the material is modeled by means of a nonlinear parabolic equation derived from Darcy's law posed in a non-cylindrical domain defined by the macroscopic deformation (which is a solution of the beam equation). Under suitable assumptions, we establish the existence and uniqueness of a suitable class of solutions to our evolution system coupling the nonlinear parabolic equation posed on the microscopic non-cylindrical domain with the beam equation posed on the macroscopic cylindrical domain. In order to guarantee the regularity of the non-cylindrical domain, we impose a singularity to the elastic response function appearing in the beam equation.
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| 2. |
- Kronberg, Vi C. E., et al.
(author)
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Numerical explorations of solvent borne adhesives : A lattice-based approach to morphology formation
- 2023
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In: Modelling and Simulation in Materials Science and Engineering. - : Institute of Physics (IOP). - 0965-0393 .- 1361-651X. ; 31:7
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Journal article (peer-reviewed)abstract
- The internal structure of adhesive tapes determines the effective mechanicalproperties. This holds true especially for blended systems, here consisting ofacrylate and rubber phases. In this note, we propose a lattice-based modelto study numerically the formation of internal morphologies within a fourcomponent mixture (of discrete particles) where the solvent components evaporate. Mimicking numerically the interaction between rubber, acrylate, andtwo different types of solvents, relevant for the technology of adhesive tapes,we aim to obtain realistic distributions of rubber ball-shaped morphologies—they play a key role in the overall functionality of those special adhesives.Our model incorporates the evaporation of both solvents and allows for tuningthe strength of two essentially different solvent–solute interactions and of thetemperature of the system.
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