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Modeling the folding and crumpling of microfilms
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Resumo(s)
Elastic films exhibit complex morphological transitions, such as folding, wrinkling, and crumpling, when subjected to external forces or confinement. In biological contexts, these forces are often generated by adherent cells, which actively apply traction forces on their substrate, creating a dynamic feedback loop. Understanding how such localized, internal stresses drive the evolution of a sheet’s three-dimensional shape is important for fields such as tissue engineering to the design of programmable materials. In this thesis we develop a computational model to study the crumpling and folding of elastic films. We employ molecular dynamics on a discrete bead-spring network, which captures the stretching and bending stiffness of a two-dimensional material. Cells are modeled as central force-generating units connected to the microfilm through Hookean springs, mimicking the transmission of contractile forces through focal adhesions. Our results demonstrate that cell-generated stresses can efficiently crumple microfilms, with the dynamics following an exponential decay. We identify a crucial mechanical regime for out-of-plane deformation, where the balance between stretching and bending stiffness allows the film to escape into the third dimension. Softer sheets crumple more easily, while stiffer films resist deformation. Furthermore we show that the collective orientation of cells is a key determinant of the final morphology: disordered forces lead to isotropic crumpling, while aligned cells generate anisotropic, tubular structures, and also single-folded states. By strategically introducing regions of reduced bending rigidity, we demonstrate that cellular forces can be channeled to guide folding along predetermined pathways, enabling controlled folding. This work establishes a computational framework for studying cell-substrate coupling and reveals how cellular activity reshapes its microenvironment. Our findings bridge the gap between cell-scale force generation and tissue-scale deformation, with implications for bioengineering.
Descrição
Tese de Mestrado, Física e Astrofísica, 2026, Universidade de Lisboa, Faculdade de Ciências
Palavras-chave
Microfilms Föppl-von Kármán Number Bead-Spring Model Folding Crumpling