Transient stability analysis of composite hydrogel structures based on a minimization-type variational formulation
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| Format: | Preprint |
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2021
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| author | Sriram, Siddharth Polukhov, Elten Keip, Marc-Andre |
| author_facet | Sriram, Siddharth Polukhov, Elten Keip, Marc-Andre |
| contents | We employ a canonical variational framework for the predictive characterization of structural instabilities that develop during the diffusion-driven transient swelling of hydrogels under geometrical constraints. The variational formulation of finite elasticity coupled with Fickian diffusion has a two-field minimization structure, wherein the deformation map and the fluid-volume flux are obtained as minimizers of a time-discrete potential involving internal and external energetic contributions. Following spatial discretization, the minimization principle is implemented using a conforming Q$_1$RT$_0$ finite-element design, making use of the lowest-order Raviart-Thomas-type interpolations for the fluid-volume flux. To analyze the structural stability of a certain equilibrium state of the gel satisfying the minimization principle, we apply the local stability criterion on the incremental potential, which is based on the idea that a stable equilibrium state has the lowest potential energy among all possible states within an infinitesimal neighborhood. Using this criterion, it is understood that bifurcation-type structural instabilities are activated when the coupled global finite-element stiffness matrix loses its positive definiteness. This concept is then applied to determine the onset and nature of wrinkling instabilities occurring in a pair of representative film-substrate hydrogel systems. In particular, we analyze the dependencies of the critical buckling load and mode shape on the system geometry and material parameters. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2103_14971 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Transient stability analysis of composite hydrogel structures based on a minimization-type variational formulation Sriram, Siddharth Polukhov, Elten Keip, Marc-Andre Numerical Analysis Soft Condensed Matter We employ a canonical variational framework for the predictive characterization of structural instabilities that develop during the diffusion-driven transient swelling of hydrogels under geometrical constraints. The variational formulation of finite elasticity coupled with Fickian diffusion has a two-field minimization structure, wherein the deformation map and the fluid-volume flux are obtained as minimizers of a time-discrete potential involving internal and external energetic contributions. Following spatial discretization, the minimization principle is implemented using a conforming Q$_1$RT$_0$ finite-element design, making use of the lowest-order Raviart-Thomas-type interpolations for the fluid-volume flux. To analyze the structural stability of a certain equilibrium state of the gel satisfying the minimization principle, we apply the local stability criterion on the incremental potential, which is based on the idea that a stable equilibrium state has the lowest potential energy among all possible states within an infinitesimal neighborhood. Using this criterion, it is understood that bifurcation-type structural instabilities are activated when the coupled global finite-element stiffness matrix loses its positive definiteness. This concept is then applied to determine the onset and nature of wrinkling instabilities occurring in a pair of representative film-substrate hydrogel systems. In particular, we analyze the dependencies of the critical buckling load and mode shape on the system geometry and material parameters. |
| title | Transient stability analysis of composite hydrogel structures based on a minimization-type variational formulation |
| topic | Numerical Analysis Soft Condensed Matter |
| url | https://arxiv.org/abs/2103.14971 |