Rate-dependent evolution of wrinkling films due to growth on semi-infinite planar viscoelastic substrates

Zavodnik, Jan (author), Košmrlj, Andrej (author), Brojan, Miha (author)

A mechanistic understanding of morphogenesis in biology, the fabrication of advanced meta surfaces with specific functionalities and structures with enhanced energy dissipation often have in common that the combined effects of energy dissipation due to viscoelasticity and a loss of stability govern both their mechanical response and their final forms. In this paper we show that the interplay between viscoelasticity and multistability crucially influences the evolution of deformations in viscoelastic structures undergoing large deformations. The influence is studied on a prototypical system of a uniaxially growing film on a semi-infinite planar viscoelastic substrate, where it is shown that during the evolution of deformation the choice of multiple developing modes is greatly affected by this interplay. For the analysis of the underlying mechanics of the mode competition in the post-buckling regime, when the system undergoes large deformations, a 3D general finite-strain visco-hyperelastic theory is built. It includes kinematic and material nonlinearities in the film and in the substrate. For the case of ramp-loading time functions the phase space of the solutions is characterized and the evolution of a deformation pattern is analyzed. We find that the interaction between multistability and viscoelasticity greatly increases the evolution time of the system and that the growth rate and viscoelastic stress-relaxation rate influence the choice of the final equilibrium deformation state of the structure. This shows that viscoelastic structures can evolve into (meta)stable equilibrium states that are unattainable using purely elastic structures. The nonlinear problem is solved numerically with the use of the finite-element method. In parallel, we develop analytical solutions for a simplified problem that is based on Föppl–von Karman plate kinematics to describe the mechanics of the film and substrate that is modeled as a 2D linear-viscoelastic continuum. A remarkably good match between the analytical and the numerical results was obtained.

• Language: English
• Keywords: thin films, visco-hyperelasticity, dissipation, pattern evolution, stability
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Year: 2022
• Number of pages: 18 str.
• Numbering: Vol. 173, art. 105219
• PID: 20.500.12556/RUL-144059
• UDC: 539.3
• ISSN on article: 1873-4782
• DOI: 10.1016/j.jmps.2023.105219
• COBISS.SI-ID: 139863811
• Publication date in RUL: 30.01.2023

Record is a part of a journal

• Title: Journal of the mechanics and physics of solids
• Publisher: Elsevier
• ISSN: 1873-4782
• COBISS.SI-ID: 23271685

Secondary language

• Language: Slovenian
• Keywords: tanki filmi, visko-hiperelastičnost, disipacija, razvoj vzorcev, stabilnost

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: J2-9223
• Name: Kristalografija nagubanih elastičnih površin

• Funder: ARRS - Slovenian Research Agency
• Project number: J2-2499
• Name: Razvoj kvazi-periodičnih deformacijskih vzorcev v viskoelastičnih strukturah