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Nonlinear multiscale simulation of instabilities due to growth of an elastic film on a microstructured substrate

Valizadeh, Iman ; Weeger, Oliver (2021):
Nonlinear multiscale simulation of instabilities due to growth of an elastic film on a microstructured substrate. (Publisher's Version)
In: Archive of Applied Mechanics, 90 (11), pp. 2397-2412. Springer, ISSN 0939-1533, e-ISSN 1432-0681,
DOI: 10.26083/tuprints-00019869,
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Item Type: Article
Origin: Secondary publication service
Status: Publisher's Version
Title: Nonlinear multiscale simulation of instabilities due to growth of an elastic film on a microstructured substrate
Language: English
Abstract:

The objective of this contribution is the numerical investigation of growth-induced instabilities of an elastic film on a microstructured soft substrate. A nonlinear multiscale simulation framework is developed based on the FE2 method, and numerical results are compared against simplified analytical approaches, which are also derived. Living tissues like brain, skin, and airways are often bilayered structures, consisting of a growing film on a substrate. Their modeling is of particular interest in understanding biological phenomena such as brain development and dysfunction. While in similar studies the substrate is assumed as a homogeneous material, this contribution considers the heterogeneity of the substrate and studies the effect of microstructure on the instabilities of a growing film. The computational approach is based on the mechanical modeling of finite deformation growth using a multiplicative decomposition of the deformation gradient into elastic and growth parts. Within the nonlinear, concurrent multiscale finite element framework, on the macroscale a nonlinear eigenvalue analysis is utilized to capture the occurrence of instabilities and corresponding folding patterns. The microstructure of the substrate is considered within the large deformation regime, and various unit cell topologies and parameters are studied to investigate the influence of the microstructure of the substrate on the macroscopic instabilities. Furthermore, an analytical approach is developed based on Airy’s stress function and Hashin–Shtrikman bounds. The wavelengths and critical growth factors from the analytical solution are compared with numerical results. In addition, the folding patterns are examined for two-phase microstructures and the influence of the parameters of the unit cell on the folding pattern is studied.

Journal or Publication Title: Archive of Applied Mechanics
Journal volume: 90
Issue Number: 11
Publisher: Springer
Classification DDC: 600 Technik, Medizin, angewandte Wissenschaften > 600 Technik
600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften
Divisions: 16 Department of Mechanical Engineering > Cyber-Physical Simulation (CPS)
Date Deposited: 14 Dec 2021 10:12
Last Modified: 14 Dec 2021 10:12
DOI: 10.26083/tuprints-00019869
Corresponding Links:
URN: urn:nbn:de:tuda-tuprints-198694
Additional Information:

Growth-induced instabilities, Microstructures, Concurrent multiscale simulation, Finite element squared method

URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/19869
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