We investigate the Poisson ratio ν of fluid lipid bilayers, i.e. , the question how area strains compare to the changes in membrane thickness (or, equivalently, volume) that accompany them. We first examine existing experimental results on the area- and volume compressibility of lipid membranes. Analyzing them within the framework of linear elasticity theory for homogeneous thin fluid sheets leads us to conclude that lipid membrane deformations are to a very good approximation volume-preserving, with a Poisson ratio that is likely about 3% smaller than the common soft matter limit . These results are fully consistent with atomistic simulations of a DOPC membrane at varying amount of applied lateral stress, for which we instead deduce ν by directly comparing area- and volume strains. To assess the problematic assumption of transverse homogeneity, we also define a depth-resolved Poisson ratio ν ( z ) and determine it through a refined analysis of the same set of simulations. We find that throughout the membrane's thickness, ν ( z ) is close to the value derived assuming homogeneity, with only minor variations of borderline statistical significance.
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Investigation of temperature induced mechanical changes in supported bilayers by variants of tapping mode atomic force microscopy: Investigation of mechanical changes in bilayers
- Award ID(s):
- 1054211
- PAR ID:
- 10018308
- Date Published:
- Journal Name:
- Scanning
- Volume:
- 37
- Issue:
- 1
- ISSN:
- 0161-0457
- Page Range / eLocation ID:
- 23 to 35
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Mechanical metamaterials are usually designed to show desired responses to prescribed forces. In some applications, the desired force–response relationship is hard to specify exactly, but examples of forces and desired responses are easily available. Here, we propose a framework for supervised learning in thin, creased sheets that learn the desired force–response behavior by physically experiencing training examples and then, crucially, respond correctly (generalize) to previously unseen test forces. During training, we fold the sheet using training forces, prompting local crease stiffnesses to change in proportion to their experienced strain. We find that this learning process reshapes nonlinearities inherent in folding a sheet so as to show the correct response for previously unseen test forces. We show the relationship between training error, test error, and sheet size (model complexity) in learning sheets and compare them to counterparts in machine-learning algorithms. Our framework shows how the rugged energy landscape of disordered mechanical materials can be sculpted to show desired force–response behaviors by a local physical learning process.
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1002/sca.21175
