Mesoscopic continuum hyperelastic models for open-cell solids subject to large elastic deformations are derived from the architecture of the cellular body and the microscopic responses of the cell walls. These models are valid for general structures, with randomly oriented cell walls, made from an arbitrary isotropic nonlinear hyperelastic material, and subject to finite triaxial stretches. Their analyses provide global descriptors of the cellular structure, such as nonlinear stretch and shear moduli, and Poisson's ratio. Comparisons with numerical simulations show that the mesoscopic models capture well the mechanical responses under large strain deformations of three-dimensional periodic structures and of two-dimensional honeycombs made from a neo-Hookean material.

Motivated by the need to quantify uncertainties in the mechanical behaviour of solid materials, we perform simple uniaxial tensile tests on a manufactured rubber-like material that provide critical information regarding the variability in the constitutive responses between different specimens. Based on the experimental data, we construct stochastic homogeneous hyperelastic models where the parameters are described by spatially independent probability density functions at a macroscopic level. As more than one parametrised model is capable of capturing the observed material behaviour, we apply Bayes' theorem to select the model that is most likely to reproduce the data. Our analysis is fully tractable mathematically and builds directly on knowledge from deterministic finite elasticity. The proposed stochastic calibration and Bayesian model selection are generally applicable to more complex tests and materials. Keywords Stochastic elasticity • Finite strain analysis • Hyperelastic material • Bayes' factor • Experiments • Probabilities "This task is made more difficult than it otherwise would be by the fact that some of the test-pieces used have to be moulded individually, and it is difficult to make two rubber specimens having identical properties even if nominally identical procedures are followed in preparing them."-R.S. Rivlin and D.W. Saunders [55]

For cellular bodies involving large elastic deformations, mesoscopic continuum models that take into account the interplay between the geometry and the microstructural responses of the constituents are developed, analysed and compared with finite-element simulations of cellular structures with different architecture. For these models, constitutive restrictions for the physical plausibility of the material responses are established, and global descriptors such as nonlinear elastic and shear moduli and Poisson’s ratio are obtained from the material characteristics of the constituents. Numerical results show that these models capture well the mechanical responses of finite-element simulations for three-dimensional periodic structures of neo-Hookean material with closed cells under large tension. In particular, the mesoscopic models predict the macroscopic stiffening of the structure when the stiffness of the cell-core increases.

For cellular bodies with uniform cell size, wall thickness, and shape, an important question is whether the same volume of material has the same effect when arranged as many small cells or as fewer large cells. To answer this question, for finite element models of periodic structures of Mooney-type material with different structural geometry and subject to large strain deformations, we identify a nonlinear elastic modulus as the ratio between the mean effective stress and the mean effective strain in the solid cell walls, and show that this modulus increases when the thickness of the walls increases, as well as when the number of cells increases while the volume of solid material remains fixed. Since, under the specified conditions, this nonlinear elastic modulus increases also as the corresponding mean stress increases, either the mean modulus or the mean stress can be employed as indicator when the optimum wall thickness or number of cells is sought.

Electrosurgical vessel sealing has been demonstrated to have benefits for both patients and practitioners, but significant variation in the strength of the seal continues to be a concern. This study aims to examine the variation in electrosurgical seal quality along the length of a porcine common carotid artery and explore the relationships between seal quality, vessel size and morphology. Additionally, the study aimed to investigate the minimum safety threshold for successful seals and the influence of vessel characteristics on meeting this requirement. A total of 35 porcine carotid arteries were sealed using the PlasmaKinetic Open Seal device (Gyrus). Each seal was burst pressure tested and a sample taken for staining with elastin van Gieson’s stain, with morphological quantification using image processing software ImageJ. With increasing distance from the bifurcation, there was an increase in seal strength and a reduction in both elastin content and vessel outer diameter. A significant correlation was found between burst pressure with both outer diameter (p < 0.0001) and elastin content (p = 0.001). When considering the safe limits of operation, vessels of less than 5 mm in outer diameter were shown to consistently produce a seal of a sufficient strength (burst pressure > 360 mmHg) irrespective of vessel morphology.