Nonlinear elasticity
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Fibrous nonlinear elasticity enables positive mechanical feedback between cells and ECMs Open
Significance Mechanical interactions between cells and the ECM critically regulate cell function, including growth and migration. By measuring forces exerted by breast tumor cells embedded within collagen matrices, we reveal a positive mec…
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Strain-enhanced stress relaxation impacts nonlinear elasticity in collagen gels Open
Significance The extracellular matrix is a complex assembly of structural proteins that provides physical support and biochemical signaling to cells within our tissues. One of the key structural components of the extracellular matrix is co…
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Stable Neo-Hookean Flesh Simulation Open
Nonlinear hyperelastic energies play a key role in capturing the fleshy appearance of virtual characters. Real-world, volume-preserving biological tissues have Poisson’s ratios near 1/2, but numerical simulation within this regime is notor…
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Mathematical and computational modelling of skin biophysics: a review Open
The objective of this paper is to provide a review on some aspects of the mathematical and computational modelling of skin biophysics, with special focus on constitutive theories based on nonlinear continuum mechanics from elasticity, thro…
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High-precision acoustic measurements of the nonlinear dilatational elasticity of phospholipid coated monodisperse microbubbles Open
We present a novel experimental method to measure at high precision the nonlinear viscoelastic properties of micron sized phospholipid-coated bubbles as a function of their surface dilatation.
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Fluid-structure interaction between an incompressible, viscous 3D fluid and an elastic shell with nonlinear Koiter membrane energy Open
The long-time existence of a weak solution is proved for a nonlinear, fluid-structure interaction (FSI) problem between an incompressible, viscous fluid and a semilinear cylindrical Koiter membrane shell with inertia. No axial symmetry is …
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An introduction to the Ogden model in biomechanics: benefits, implementation tools and limitations Open
Constitutive models are important to biomechanics for two key reasons. First, constitutive modelling is an essential component of characterizing tissues’ mechanical properties for informing theoretical and computational models of biomechan…
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Geometric Frustration and Solid-Solid Transitions in Model 2D Tissue Open
We study the mechanical behavior of two-dimensional cellular tissues by formulating the continuum limit of discrete vertex models based on an energy that penalizes departures from a target area A_{0} and a target perimeter P_{0} for the co…
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A Hybrid High-Order Method for Nonlinear Elasticity Open
International audience
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Nonlinear elasticity with limiting small strain for cracks subject to non-penetration Open
A major drawback of the study of cracks within the context of the linearized theory of elasticity is the inconsistency that one obtains with regard to the strain at a crack tip, namely it becoming infinite. In this paper we consider the pr…
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Aspects of interface elasticity theory Open
Interfaces significantly influence the overall material response especially when the area-to-volume ratio is large, for instance in nanocrystalline solids. A well-established and frequently applied framework suitable for modeling interface…
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Inverse method based on 3D nonlinear physically constrained minimisation in the framework of traction force microscopy Open
We present a new inverse and physically-consistent traction force microscopy method developed and implemented in the context of 3D nonlinear elasticity. We prove its enhanced accuracy applying it to real cases of cells cultured in a 3D hyd…
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Nonlinear elasticity of incompatible surface growth Open
Surface growth is a crucial component of many natural and artificial processes, from cell proliferation to additive manufacturing. In elastic systems surface growth is usually accompanied by the development of geometrical incompatibility, …
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Biopolymers: life's mechanical scaffolds Open
The cells and tissues that make up our body juggle contradictory mechanical demands. It is crucial for their survival to be able to withstand large mechanical loads, but it is equally crucial for them to produce forces and actively change …
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Geometric charges and nonlinear elasticity of two-dimensional elastic metamaterials Open
Problems of flexible mechanical metamaterials, and highly deformable porous solids in general, are rich and complex due to their nonlinear mechanics and the presence of nontrivial geometrical effects. While numeric approaches are successfu…
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The Ogden model of rubber mechanics: 50 years of impact on nonlinear elasticity Open
We place the Ogden model of rubber elasticity, published in Proceedings of the Royal Society 50 years ago, in the wider context of the theory of nonlinear elasticity. We then follow with a short interview of Ray Ogden FRS and introduce the…
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Wrinkles and creases in the bending, unbending and eversion of soft sectors Open
We study what is clearly one of the most common modes of deformation found in nature, science and engineering, namely the large elastic bending of curved structures, as well as its inverse, unbending, which can be brought beyond complete s…
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Nonlinear finite element analysis within strain gradient elasticity: Reissner-Mindlin plate theory versus three-dimensional theory Open
Nonlinear plate bending within Mindlin's strain gradient elasticity theory (SGT) is investigated by employing somewhat non-standard finite element methods. The main goal is to compare the bending results provided by the geometrically nonli…
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Effect of directed aging on nonlinear elasticity and memory formation in a material Open
Disordered solids often change their elastic response as they slowly age. Using experiments and simulations, we study how aging disordered planar networks under an applied stress affects their nonlinear elastic response. We are able to mod…
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Nonlinear Elasticity Assessment with Optical Coherence Elastography for High-Selectivity Differentiation of Breast Cancer Tissues Open
Soft biological tissues, breast cancer tissues in particular, often manifest pronounced nonlinear elasticity, i.e., strong dependence of their Young’s modulus on the applied stress. We showed that compression optical coherence elastography…
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Inverse mechanical-swelling coupling of a highly deformed double-network gel Open
Mechanical behaviors of a polymer gel are coupled with its swelling behavior. It has been known that typical hydrogels display extension-induced swelling and drying-induced stiffening, called normal mechanical-swelling coupling. In this st…
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Breakdown of nonlinear elasticity in amorphous solids at finite temperatures Open
It is known [H. G. E. Hentschel et al., Phys. Rev. E 83, 061101 (2011)PLEEE81539-375510.1103/PhysRevE.83.061101] that amorphous solids at zero temperature do not possess a nonlinear elasticity theory: besides the shear modulus, which exist…
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Strain Hardening in Highly Acetylated Chitosan Gels Open
Strain hardening has recently emerged as a near-universal response of biological tissues to mechanical stimulation as well as a powerful regulator of cell fate. Understanding the mechanistic basis for this nonlinear elasticity is crucial f…
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A one-dimensional model for elasto-capillary necking Open
We derive a nonlinear one-dimensional (1d) strain gradient model predicting the necking of soft elastic cylinders driven by surface tension, starting from three-dimensional (3d) finite-strain elasticity. It is asymptotically correct: the m…
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Hyperelastic bodies under homogeneous Cauchy stress induced by non-homogeneous finite deformations Open
We discuss whether homogeneous Cauchy stress implies homogeneous strain in isotropic nonlinear elasticity. While for linear elasticity the positive answer is clear, we exhibit, through detailed calculations, an example with inhomogeneous c…
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Variational-hemivariational inverse problems for unilateral frictional contact Open
The paper investigates inverse problems for a class of nonlinear elliptic variational-hemivariational inequalities. We prove results on the well posedness of a variational-hemivariational inequality and on the existence of solution to inve…
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A framework for data‐driven structural analysis in general elasticity based on nonlinear optimization: The dynamic case Open
Summary In this article, we present an extension of the formulation recently developed by the authors to the structural dynamics setting. Inspired by a structure‐preserving family of variational integrators, our new formulation relies on a…
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Derivation of a refined six-parameter shell model: descent from the three-dimensional Cosserat elasticity using a method of classical shell theory Open
Starting from the three-dimensional Cosserat elasticity, we derive a two-dimensional model for isotropic elastic shells. For the dimensional reduction, we employ a derivation method similar to that used in classical shell theory, as presen…
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Nonlinear Focusing in Dynamic Crack Fronts and the Microbranching Transition Open
Cracks in brittle materials produce two types of generic surface structures: facets at low velocities and microbranches at higher ones. Here we observe a transition from faceting to microbranching in polyacrylamide gels that is characteriz…
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Stress-dependent amplification of active forces in nonlinear elastic media Open
Forces generated by molecular motors and contractile cells can be dramatically amplified by the nonlinear elasticity of the surrounding medium.