Coexistence of wrinkles and blisters in supported graphene

Blisters induced by gas trapped in the interstitial space between supported graphene and the substrate are commonly observed. These blisters are often quasi-spherical with a circular rim, but polygonal blisters are also common and coexist with wrinkles emanating from their vertices. Here, we show that these different blister morphologies can be understood mechanically in terms of free energy minimization of the supported graphene sheet for a given mass of trapped gas and for a given lateral strain. Using a nonlinear continuum model for supported graphene closely reproducing experimental images of blisters, we build a morphological diagram as a function of strain and trapped mass. We show that the transition from quasi-spherical to polygonal of blisters as compressive strain is increased is a process of stretching energy relaxation and focusing, as many other crumpling events in thin sheets. Furthermore, to characterize this transition, we theoretically examine the onset of nucleation of short wrinkles in the periphery of a quasi-spherical blister. Our results are experimentally testable and provide a framework to control complex out-of-plane motifs in supported graphene combining blisters and wrinkles for strain engineering of graphene.Peer ReviewedPostprint (published version

Hydraulic fracturing in cells and tissues: fracking meets cell biology

The animal body is fundamentally made of water. A small fraction of this water is freely flowing in blood and lymph, but most of it is trapped in hydrogels such as the extracellular matrix (ECM), the cytoskeleton, and chromatin. Besides providing a medium for biological molecules to diffuse, water trapped in hydrogels plays a fundamental mechanical role. This role is well captured by the theory of poroelasticity, which explains how any deformation applied to a hydrogel causes pressure gradients and water flows, much like compressing a sponge squeezes water out of it. Here we review recent evidence that poroelastic pressures and flows can fracture essential biological barriers such as the nuclear envelope, the cellular cortex, and epithelial layers. This type of fracture is known in engineering literature as hydraulic fracturing or "fracking"Peer ReviewedPostprint (author's final draft

An atomistic-based foliation model for multilayer graphene materials and nanotubes

We present a three-dimensional continuum model for layered crystalline materials made out of weakly interacting two-dimensional crystalline sheets. We specialize the model to multilayer graphene materials, including multi-walled carbon nanotubes (MWCNTs). We view the material as a foliation, partitioning of space into a continuous stack of leaves, thus loosing track of the location of the individual graphene layers. The constitutive model for the bulk is derived from the atomistic interactions by appropriate kinematic assumptions, adapted to the foliation structure and mechanics. In particular, the elastic energy along the leaves of the foliation results from the bonded interactions, while the interaction energy between the walls, resulting from van der Waals forces, is parametrized with a stretch transversal to the foliation. The resulting theory is distinct from conventional anisotropic models, and can be readily discretized with finite elements. The discretization is not tied to the individual walls and allows us to coarse-grain the system in all directions. Furthermore, the evaluation of the non-bonded interactions becomes local. We test the accuracy of the foliation model against a previously proposed atomistic-based continuum model that explicitly describes each and every wall. We find that the new model is very efficient and accurate. Furthermore, it allows us to rationalize the rippling deformation modes characteristic of thick MWCNTs, highlighting the role of the van der Waals forces and the sliding between the walls. By exercising the model with very large systems of hollow MWCNTs and suspended multilayer graphene, containing up to 109 atoms, we find new complex post-buckling deformation patterns.Peer ReviewedPostprint (author's final draft

Rippling and a phase-transforming mesoscopic model for multiwalled carbon nanotubes

We propose to model thick multiwalled carbon nanotubes as beams with non-convex curvature energy. Such models develop stressed phase mixtures composed of smoothly bent sections and rippled sections. This model is motivated by experimental observations and large-scale atomistic-based simulations. The model is analyzed, validated against large-scale simulations, and exercised in examples of interest. It is shown that modelling MWCNTs as linear elastic beams can result in poor approximations that overestimate the elastic restoring force considerably, particularly for thick tubes. In contrast, the proposed model produces very accurate predictions both of the restoring force and of the phase pattern. The size effect in the bending response of MWCNTs is also discussed.Peer ReviewedPostprint (author’s final draft

Out-of-equilibrium mechanochemistry and self-organization of fluid membranes interacting with curved proteins

The function of biological membranes is controlled by the interaction of the fluid lipid bilayer with various proteins, some of which induce or react to curvature. These proteins can preferentially bind or diffuse towards curved regions of the membrane, induce or stabilize membrane curvature and sequester membrane area into protein-rich curved domains. The resulting tight interplay between mechanics and chemistry is thought to control organelle morphogenesis and dynamics, including traffic, membrane mechanotransduction, or membrane area regulation and tension buffering. Despite all these processes are fundamentally dynamical, previous work has largely focused on equilibrium and a self-consistent theoretical treatment of the dynamics of curvature sensing and generation has been lacking. Here, we develop a general theoretical and computational framework based on a nonlinear Onsager’s formalism of irreversible thermodynamics for the dynamics of curved proteins and membranes. We develop variants of the model, one of which accounts for membrane curving by asymmetric crowding of bulky off-membrane protein domains. As illustrated by a selection of test cases, the resulting governing equations and numerical simulations provide a foundation to understand the dynamics of curvature sensing, curvature generation, and more generally membrane curvature mechano-chemistry.Peer ReviewedPostprint (author's final draft

Surface tension controls the hydraulic fracture of adhesive interfaces bridged by molecular bonds

Biological function requires cell-cell adhesions to tune their cohesiveness; for instance, during the opening of new fluid-filled cavities under hydraulic pressure. To understand the physical mechanisms supporting this adaptability, we develop a stochastic model for the hydraulic fracture of adhesive interfaces bridged by molecular bonds. We find that surface tension strongly enhances the stability of these interfaces by controlling flaw sensitivity, lifetime, and optimal architecture in terms of bond clustering. We also show that bond mobility embrittles adhesions and changes the mechanism of decohesion. Our study provides a mechanistic background to understand the biological regulation of cell-cell cohesion and fracture.Peer ReviewedPostprint (author's final draft

Mechanics of tubular meshes formed by elastic helical fibers

© 2023 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/Tubular structures made of elastic helical fibers are widely found in nature and in technology. The complex and highly nonlinear mechanical properties of such assemblies have been understood either through minimal models or through complex simulations describing each individual fiber and their interactions. Here, inspired by Chebyshev’s geometric model of nets, we propose and experimentally validate a modeling framework that treats tubular braided meshes as continuum surfaces corresponding to the virtual envelope defined by the fibers. The key idea is to relate surface geometry and fiber kinematics, enabling us to follow large deformations. This theory is amenable to efficient computations and, in axisymmetric cases, the problem reduces to finding two scalar fields defined over 1D segments. We validate our model against experiments of axial compression, revealing the existence of a plateau with vanishing stiffness in the axial force–displacement curve, a feature that could prove particularly useful in applications where an applied compressive force needs to be held constant even against settlements of the compressed object.We thank G. Noselli for useful discussions on the plateau in the response under compression of braided tubular meshes, and for his help in manufacturing supports for the mesh. J.Q. and A.D.S. acknowledge the support of the Italian Ministry of University and Research (PRIN2020PFCXPE) and of the European Union Horizon 2020 Research and Innovation Programme (I-Seed, Grant Agreement No101017940, MAPWORMS, Grant Agreement No101046846); M.A. acknowledges the support of the Generalitat de Catalunya (AGAUR: 2017-SGR-1278 and ‘‘ICREA Academia’’ award to M.A.), the European Research Council (CoG-681434 to M.A.). IBEC and CIMNE are recipients of a Severo Ochoa Award of Excellence from the MINECO. A.D.S is a member of the INDAM research group GNFM.Peer ReviewedPostprint (published version

Onsager’s variational principle in soft matter : introduction and application to the dynamics of adsorption of proteins onto fluid membranes

This book is the first collection of lipid-membrane research conducted by leading mechanicians and experts in continuum mechanics. It brings the overall intellectual framework afforded by modern continuum mechanics to bear on a host of challenging problems in lipid membrane physics. These include unique and authoritative treatments of differential geometry, shape elasticity, surface flow and diffusion, interleaf membrane friction, phase transitions, electroelasticity and flexoelectricity, and computational modelling. [Chapter] Lipid bilayers are unique soft materials operating in general in the low Reynolds limit. While their shape is predominantly dominated by curvature elasticity as in a solid shell, their in-plane behavior is that of a largely inextensible viscous fluid. Furthermore, lipid membranes are extremely responsive to chemical stimuli. Because in their biological context they are continuously brought out-of-equilibrium mechanically or chemically, it is important to understand their dynamics. Here, we introduce Onsager’s variational principle as a general and transparent modeling tool for lipid bilayer dynamics. We introduce this principle with elementary examples, and then use it to study the sorption of curved proteins on lipid membranes.Peer ReviewedPostprint (author's final draft

Phase-field modeling and simulation of fracture in brittle materials with strongly anisotropic surface energy

Crack propagation in brittle materials with anisotropic surface energy is important in applications involving single crystals, extruded polymers, or geological and organic materials. Furthermore, when this anisotropy is strong, the phenomenology of crack propagation becomes very rich, with forbidden crack propagation directions or complex sawtooth crack patterns. This problem interrogates fundamental issues in fracture mechanics, including the principles behind the selection of crack direction. Here, we propose a variational phase-field model for strongly anisotropic fracture, which resorts to the extended Cahn-Hilliard framework proposed in the context of crystal growth. Previous phase-field models for anisotropic fracture were formulated in a framework only allowing for weak anisotropy. We implement numerically our higher-order phase-field model with smooth local maximum entropy approximants in a direct Galerkin method. The numerical results exhibit all the features of strongly anisotropic fracture and reproduce strikingly well recent experimental observations.Peer ReviewedPostprint (author’s final draft

Smart helical structures inspired by the pellicle of euglenids

This paper deals with a concept for a reconfigurable structure bio-inspired by the cell wall architecture of euglenids, a family of unicellular protists, and based on the relative sliding of adjacent strips. Uniform sliding turns a cylinder resulting from the assembly of straight and parallel strips into a cylinder of smaller height and larger radius, in which the strips are deformed into a family of parallel helices. We examine the mechanics of this cylindrical assembly, in which the interlocking strips are allowed to slide freely at their junctions, and compute the external forces (axial force and axial torque at the two ends, or pressure on the lateral surface) necessary to drive and control the shape changes of the composite structure. Despite the simplicity of the structure, we find a remarkably complex mechanical behaviour that can be tuned by the spontaneous curvature or twist of the strips