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This work considers the application of a displacement-based virtual element method to plane hyperelasticity problems with a novel approach to the selection of stabilization parameters. The method is applied to a range of numerical examples and well known strain energy functions, including neo-Hookean, Mooney-Rivlin and Ogden material models. For each of the strain energy functions the performance of the method under varying degrees of compressibility, including near-incompressibility, is investigated. Through these examples the convergence behaviour of the virtual element method is demonstrated. Furthermore, the method is found to be robust and locking free for a variety of element geometries, including elements with a high degree of concavity. • A virtual element method for large deformations was formulated and implemented. • A novel approach to the selection of stabilization parameters is investigated. • A variety of well-known isotropic strain energy functions were considered. • A variety of element geometries, including highly concave elements were considered. • Through a range of examples the VEM is found to be robust and locking free. [ABSTRACT FROM AUTHOR]

Dielectric elastomers have attracted considerable attention both from academia and industry alike over the last two decades due to their superior mechanical properties. In parallel, research on the mechanical properties of dielectrics has been steadily advancing, including the theoretical, experimental, and numerical aspects. It has been recognized that the electromechanical coupling property of dielectric materials can be utilized to drive deformations in functional devices in a more controllable and intelligent manner. This paper reviews recent advances in the theory of dielectrics, with specific attention focused on the theory proposed by Dorfmann and Ogden. Additionally, we provide examples illustrating the application of this theory to analyze the electromechanical deformations and the associated bifurcations in soft dielectrics. We compared the bifurcations in elastic and dielectric materials and found that only compressive bifurcation modes exist in elastic structures, whereas both compressive and tensile modes coexist in dielectric structures. We summarize two proposed ways to suppress and prevent the tensile bifurcations in dielectric materials. We hope that this literature survey will foster further advancements in the field of the electroelastic theory of soft dielectrics. [ABSTRACT FROM AUTHOR]

In this paper, we develop several limited chain extensible (LCE) models using fractional powers of certain forms. The fractional powers provide an alternative functional framework similar to the logarithmic function. The present models exhibit limited extensibility when the arbitrary exponent is less than unity, and reduce to well-posed parent models when the exponent is unity or the stiffening parameter tends to infinity. When the exponent approaches zero, the proposed model reduces to the logarithm-based existing LCE models. Using these arbitrary fractional powers, we construct suitable strain energy functions based on (a) I 1 , (b) both I 1 and I 2 , (c) principal stretches as well as for transversely isotropic materials. The developed functions also generalizes existing limited chain extensible models. We also further modify the Ogden model to deduce a pair of limited extensible models which reduce to existing models as the exponents approach zero. We next apply various inequalities of solid mechanics, viz. (a) Baker–Ericksen inequality, (b) strong ellipticity, (c) polyconvexity, (d) Hill's constitutive inequality to the proposed models. We observe that sufficient conditions for satisfying the above inequalities match exactly with the condition for exhibiting limiting stretchable behavior. We further employ the models for investigating homogeneous and inhomogeneous deformation characteristics. In the sphere inflation characteristics, we observe that these models display a wider range of strain-stiffening and stability patterns. While the critical stiffening parameter is a constant for the Gent model, it can assume any positive value for the present model depending on the exponent. As a result, the proposed models can exhibit stable inflation or an inflation-jump instability in the sphere for any given maximum stretch limit, or the stiffening parameter. The critical values of maximum allowable stretch or stiffening parameters can assume any value in the present framework to fit the experimental results. Since the stability characteristics depend completely on stiffening parameter it is diversified using the present model. We observe inflation-jump instability for a stiffening parameter as low as 2.30. Since the present models involve arbitrary exponents and exhibit limited elasticity, they nicely exhibit the real deformation characteristics of spheres. As a result, they adequately capture the mechanical response of inflating rubber-like spheres. We demonstrate excellent agreements of these theoretical models with the experimental responses of inflation of monkey bladder and rubber balloon. [ABSTRACT FROM AUTHOR]

Open in new tab Download slide OBJECTIVES This study aims to characterize the material properties of ascending thoracic aortic aneurysmal tissue, using regional biomechanical assessment of both tensile and dissection propagation peel strength. METHODS Thirty-four aneurysm specimens (proximal thoracic aorta) were harvested en-bloc from patients undergoing surgery for aneurysm replacement. Specimens were processed into regional samples of similar shapes covering the whole aneurysm isosurface, according to a structured protocol, in both orientations (longitudinal and circumferential). Thickness mapping, uniaxial tensile and peel tests were conducted, enabling calculation of the following parameters: true stress/strain, tangential modulus, tensile strength, peeling force and dissection energy. Two constitutive material models were used (hyperelastic models of Delfino and Ogden) to fit the data. A circumferential strip of tissue was also obtained for computational histology [regional quantification of (i) elastin, (ii) collagen and (iii) smooth muscle cells]. RESULTS The aortic wall was thinner on the outer curve (2.21, standard deviation (SD) 0.4 mm vs inner curve 2.50, SD 0.12 mm). Advanced patient age and higher pulse wave velocity (externally measured) were predictors of increased aortic wall thickness. Tensile strength was higher in the circumferential versus longitudinal direction when analysed according to anatomical regions. Both peel force (35.5, 22 N/m) and dissection energy (88.5, 69 J/m2) were on average lowest at the outer curve of the aneurysm in the longitudinal orientation. Delfino and Ogden model constants varied throughout anatomical regions, with the outer curve being associated a higher ɑ constant (Delfino) and lower µ1 constant (Ogden) (P  < 0.05) indicating increased stiffness. Histologically, collagen abundance was significantly related to circumferential and longitudinal strength (P = 0.010), whilst smooth muscle cell count had no relation with any mechanical property (P > 0.05). CONCLUSIONS Our results suggest that the outer aortic curve is more prone to dissection propagation and perhaps less prone to rupture than the inner aortic curve. This strengthens the notion of disease heterogeneity in ascending thoracic aortic aneurysms and has implications for the pathogenesis of aortic dissection. [ABSTRACT FROM AUTHOR]

Herein, an artificial neural network (ANN)-based approach for the efficient automated modeling and simulation of isotropic hyperelastic solids is presented. Starting from a large data set comprising deformations and corresponding stresses, a simple, physically based reduction of the problem's dimensionality is performed in a data processing step. More specifically, three deformation type invariants serve as the input instead of the deformation tensor itself. In the same way, three corresponding stress coefficients replace the stress tensor in the output layer. These initially unknown values are calculated from a linear least square optimization problem for each data tuple. Using the reduced data set, an ANN-based constitutive model is trained by using standard machine learning methods. Furthermore, in order to ensure thermodynamic consistency, the previously trained network is modified by constructing a pseudo-potential within an integration step and a subsequent derivation which leads to a further ANN-based model. In the second part of this work, the proposed method is exemplarily used for the description of a highly nonlinear Ogden type material. Thereby, the necessary data set is collected from virtual experiments of discs with holes in pure plane stress modes, where influences of different loading types and specimen geometries on the resulting data sets are investigated. Afterwards, the collected data are used for the ANN training within the reduced data space, whereby an excellent approximation quality could be achieved with only one hidden layer comprising a low number of neurons. Finally, the application of the trained constitutive ANN for the simulation of two three-dimensional samples is shown. Thereby, a rather high accuracy could be achieved, although the occurring stresses are fully three-dimensional whereas the training data are taken from pure two-dimensional plane stress states. [ABSTRACT FROM AUTHOR]