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1. Dynamic competition of inflation and delamination in the finite deformation of thin membranes

   https://doi.org/10.1039/C9SM00988D  

   Benet, Eduard ; Vernerey, Franck J. ( August 2019 , Soft Matter)

   The mechanics of blister delamination and growth plays a major role in a diversity of areas including medicine (skin pathology and mechanics of cell membranes), materials (adhesive and fracture) or soft robotics (actuation and morphing). The behavior of a blister in this context is typically difficult to grasp as it arises from the interplay of two highly nonlinear and time-dependent processes: membrane attachment and decohesion from a substrate. In the present work, we device a simplified approach, based on experimental systems, to predict the deformation path of a blister under various conditions. For this, we consider the problem of a growing blister made of a rubber-like membrane adhered on a rigid substrate, and develop a theoretical and experimental framework to study its stability and growth. We start by constructing a theoretical model of viscoelastic blister growth which we later validate with an experimental setup. We show that blister growth is controlled by the competition between two instabilities: one inherent to the rubber, and a second one pertaining to the adhesion with the substrate. Using these concepts, we show that a “targeted” stable blister shape can be achieved by controlling two parameters: the thickness of the film and the inflation rate. 

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2. The Mathematics of Thin Structures

   Babadjian, J.-F. ; Di Fratta, G. ; Fonseca, I. ; Francfort, G. ; Lewicka, M. ; Muratov, C. B. ( January 2023 , Quarterly of applied mathematics)

   This articles offers various mathematical contributions to the behavior of thin films. The common thread is to view thin film behavior as the variational limit of a three-dimensional domain with a related behavior when the thickness of that domain vanishes. After a short review in Section 1 of the various regimes that can arise when such an asymptotic process is performed in the classical elastic case, giving rise to various well-known model in plate theory (membrane, bending, Von Karmann, etc...), the other sections address various extensions of those initial results. Section 2 adds brittleness and delamination and investigates the brittle membrane regime. Sections 4 and 5 focus on micro-magnetics, rather than elasticity, this once again in the membrane regime and discuss magnetic skyrmions and domain walls, respectively. Finally, Section 3 revisits the classical setting in a non-Euclidean setting induced by the presence of a pre-strain in the model. 

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3. Formation of rolls from liquid crystal elastomer bistrips

   https://doi.org/10.1039/d1sm01830b  

   Chen, Yuzhen ; Kuenstler, Alexa S. ; Hayward, Ryan C. ; Jin, Lihua ( June 2022 , Soft Matter)

   Formation of desired three-dimensional (3D) shapes from flat thin sheets with programmed non-uniform deformation profiles is an effective strategy to create functional 3D structures. Liquid crystal elastomers (LCEs) are of particular use in programmable shape morphing due to their ability to undergo large, reversible, and anisotropic deformation in response to a stimulus. Here we consider a rectangular monodomain LCE thin sheet divided into one high- and one low-temperature strip, which we dub a ‘bistrip’. Upon activation, a discontinuously patterned, anisotropic in-plane stretch profile is generated, and induces buckling of the bistrip into a rolled shape with a transitional bottle neck. Based on the non-Euclidean plate theory, we derive an analytical model to quantitatively capture the formation of the rolled shapes from a flat bistrip with finite thickness by minimizing the total elastic energy involving both stretching and bending energies. Using this analytical model, we identify the critical thickness at which the transition from the unbuckled to buckled configuration occurs. We further study the influence of the anisotropy of the stretch profile on the rolled shapes by first converting prescribed metric tensors with different anisotropy to a unified metric tensor embedded in a bistrip of modified geometry, and then investigating the effect of each parameter in this unified metric tensor on the rolled shapes. Our analysis sheds light on designing shape morphing of LCE thin sheets, and provides quantitative predictions on the 3D shapes that programmed LCE sheets can form upon activation for various applications. 

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4. The mathematics of thin structures

   https://doi.org/10.1090/qam/1628  

   Babadjian, Jean-François ; Di Fratta, Giovanni ; Fonseca, Irene ; Francfort, Gilles ; Lewicka, Marta ; Muratov, Cyrill ( March 2023 , Quarterly of Applied Mathematics)

   This article offers various mathematical contributions to the behavior of thin films. The common thread is to view thin film behavior as the variational limit of a three-dimensional domain with a related behavior when the thickness of that domain vanishes. After a short review in Section 1 of the various regimes that can arise when such an asymptotic process is performed in the classical elastic case, giving rise to various well-known models in plate theory (membrane, bending, Von Karmann, etc…), the other sections address various extensions of those initial results. Section 2 adds brittleness and delamination and investigates the brittle membrane regime. Sections 4 and 5 focus on micromagnetics, rather than elasticity, this once again in the membrane regime and discuss magnetic skyrmions and domain walls, respectively. Finally, Section 3 revisits the classical setting in a non-Euclidean setting induced by the presence of a pre-strain in the model. 

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5. Large Enhancement in Thermal Conductivity of Solvent−Cast Expanded Graphite/Polyetherimide Composites

   https://doi.org/10.3390/nano12111877  

   Tarannum, Fatema ; Danayat, Swapneel S. ; Nayal, Avinash ; Muthaiah, Rajmohan ; Annam, Roshan Sameer ; Garg, Jivtesh ( June 2022 , Nanomaterials)

   We demonstrate in this work that expanded graphite (EG) can lead to a very large enhancement in thermal conductivity of polyetherimide−graphene and epoxy−graphene nanocomposites prepared via solvent casting technique. A k value of 6.6 W⋅m−1⋅K−1 is achieved for 10 wt% composition sample, representing an enhancement of ~2770% over pristine polyetherimide (k~0.23 W⋅m−1⋅K−1). This extraordinary enhancement in thermal conductivity is shown to be due to a network of continuous graphene sheets over long−length scales, resulting in low thermal contact resistance at bends/turns due to the graphene sheets being covalently bonded at such junctions. Solvent casting offers the advantage of preserving the porous structure of expanded graphite in the composite, resulting in the above highly thermally conductive interpenetrating network of graphene and polymer. Solvent casting also does not break down the expanded graphite particles due to minimal forces involved, allowing for efficient heat transfer over long−length scales, further enhancing overall composite thermal conductivity. Comparisons with a recently introduced effective medium model show a very high value of predicted particle–particle interfacial conductance, providing evidence for efficient interfacial thermal transport in expanded graphite composites. Field emission environmental scanning electron microscopy (FE−ESEM) is used to provide a detailed understanding of the interpenetrating graphene−polymer structure in the expanded graphite composite. These results open up novel avenues for achieving high thermal conductivity polymer composites. 

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