Homogeneous Hyperelastic Materials Research Articles

Effect of the apron in the mechanical characterisation of hyperelastic materials by means of biaxial testing: A new method to improve accuracy

Biological soft tissues and polymers used in biomedical applications (e.g. in the cardiovascular area) are hyperelastic incompressible materials that commonly operate under multi-axial large deformation fields. Their characterisation requires biaxial tensile testing. Due to the typically small sample size, the gripping of the specimens commonly relies on rakes or sutures, where the specimen is punctured at the edges of the gauge area. This approach necessitates of an apron, excess of material around the gauge region.This work analyses the apron influence on the estimated mechanical response of biaxial tests performed by using a rakes gripping system, with the aim of verifying the test accuracy and propose improved solutions.In order to isolate the effect of the apron, avoiding the influence of anisotropy and inhomogeneity typical of most soft tissues, homogeneous and isotropic hyperplastic samples made from a uniform sheet of casted silicone were tested. The stress-strain response of specimens with different apron sizes/shapes was measured experimentally by means of biaxial testing and digital image correlation. Tests were replicated numerically, to interpret the experimental findings.The apron surrounding the gauge area acts as an additional annular constraint which stiffens the system, resulting in a significant overestimate in the stress values. This error can be avoided by introducing specific cuts in the apron.The study quantifies, for the first time, the correlation between the apron size/shape and the experimental stress overestimation, proposing a research protocol which, although identified on homogeneous hyperelastic materials, can be useful in providing more accurate characterisation of both, synthetic polymers and soft tissues.

Symmetry properties of two-dimensional Ciarlet–Mooney–Rivlin constitutive models in nonlinear elastodynamics

Nonlinear dynamic equations for isotropic homogeneous hyperelastic materials are considered in the Lagrangian formulation. An explicit criterion of existence of a natural state for a given constitutive law is presented, and is used to derive natural state conditions for some common constitutive relations.For two-dimensional planar motions of Ciarlet–Mooney–Rivlin solids, equivalence transformations are computed that lead to a reduction of the number parameters in the constitutive law. Point symmetries are classified in a general dynamical setting and in traveling wave coordinates. A special value of traveling wave speed is found for which the nonlinear Ciarlet–Mooney–Rivlin equations admit an additional infinite set of point symmetries. A family of essentially two-dimensional traveling wave solutions is derived for that case.

Analyzing the interplay between single cell rheology and force generation through large deformation finite element models

In this study, experimental results of single cell spreading between two parallel microplates are exploited through finite element modeling. Axisymmetric computations at finite strains are performed to extract the mechanical properties of the cell which can account for cell shape evolution and traction force generation. Our model includes two distinct components representing the cortex associated with the bilayer membrane on the one hand, and the rest of the cell on the other hand. The former is modeled as a homogeneous hyperelastic material described by a slightly compressible Gent strain energy function, while the latter is idealized either as a quasi-incompressible Newtonian fluid or as another homogeneous hyperelastic material. The kinetics of spreading is ensured by a stapling procedure defined from experimental observations. Material parameters are then optimized to match the simulation closely with the experimental data. In particular, the elastic modulus of the cortex is estimated at about 1,000Pa in both models, while the cell interior is characterized by a viscosity of 1,000Pa.s in the biphasic model, or by an elastic modulus of about 100Pa in the hyperelastic one. These results are in good agreement with G(') and G('') measurements carried out previously in the same parallel plates setup and estimated at the typical rate of cell straining. Moreover, stresses are found to concentrate at the edge of the cell-substrate contact area. These observations allow explaining the relationship between cell spreading and force increase since spreading and the consequent straining of the cell mechanical structure could be the source of the force applied by the cell on its substrate. They could also explain, in a very simple manner, why force-sensitive focal contacts concentrate at the cell edges.

On an Incompressible Nonlinearly Elastic Half-Space under a Compressive Point Load

The problem of determining the deformation produced in an elastic half space due to a point force normal to the undeformed boundary has been a subject of considerable interest in the linear theory of elas-ticity and in a variety of engineering and geotechnical applications for well over a century. Recently, this inherently nonlinear problem has been posed within the framework of the nonlinear theory of elasticity for tensile point loads and results stemming from the exact governing equations have been obtained aymptotically In this paper, we consider a compressive point load and address this core problem within the context of incompressible finite elasticity. An asymptotic analysis of the exact governing equations is carried out, and asymptotic tests providing a simple way to determine if an isotropic homogeneous hyperelastic material is capable of sustaining a compressive point load are developed. The results are then applied to several particular constitutive models for incompressible nonlinearly elastic materials, and contrasts with the tensile load problem are made.

The Green's and the Eshelby's identities in generalised continua and in dielectrics

In 1973, A. E. Green pointed out several interesting formulae, which hold true in finite elasticity [1]. One of them (formula (2.10), p.75) is repeatedly quoted in the literature as the Green identity. This remarkable identity has been successfully employed in several contexte. We only mention here its central role in theorems on uniqueness in elastostatics [2,3]. A deeper insight to the Green identity shows in evidence an intimate link of this formula with the Eshelby tensor and with the material balance law of equilibrium [4,5]. In homogeneous hyperelastic materials, this law turns out to an identity, the Eshelby identity, and one can easily prove that the Green identity stems straightforwardly from the Eshelby identity. These identities possibly extend to generalized continua, such as continua with microstructure and elastic dielectrics. Hereafter, the validity of the Eshelby identity is discussed for these materials. Basing on the novel extended Eshelby-like identity, the corresponding extended Green-like identity can be also established, under specifie assumptions. In the case of dielectrics, two equivalent forms for the Eshelby tensor emerge from the treatment, both satisfying the Eshelby identity. One of them is more appropriate for deriving the desired Green-like identity. The second one, which is a reduced form of the first one, represents the physical Eshelby tensor in dielectrics [4-5].

Contribution of the nucleus to the mechanical properties of endothelial cells

The cell nucleus plays a central role in the response of the endothelium to mechanical forces, possibly by deforming during cellular adaptation. The goal of this work was to precisely quantify the mechanical properties of the nucleus. Individual endothelial cells were subjected to compression between glass microplates. This technique allows measurement of the uniaxial force applied to the cell and the resulting deformation. Measurements were made on round and spread cells to rule out the influence of cell morphology on the nucleus mechanical properties. Tests were also carried out with nuclei isolated from cell cultures by a chemical treatment. The non-linear force–deformation curves indicate that round cells deform at lower forces than spread cells and nuclei. Finite-element models were also built with geometries adapted to actual morphometric measurements of round cells, spread cells and isolated nuclei. The nucleus and the cytoplasm were modeled as separate homogeneous hyperelastic materials. The models simulate the compression and yield the force–deformation curve for a given set of elastic moduli. These parameters are varied to obtain a best fit between the theoretical and experimental data. The elastic modulus of the cytoplasm is found to be on the order of 500 N/m 2 for spread and round cells. The elastic modulus of the endothelial nucleus is on the order of 5000 N/m 2 for nuclei in the cell and on the order of 8000 N/m 2 for isolated nuclei. These results represent an unambiguous measurement of the nucleus mechanical properties and will be important in understanding how cells perceive mechanical forces and respond to them.