•The mechanical properties of the human cervical spinal cord were investigated.•The spinal cord of 24 male cadavers was excised and subjected to the mechanical loading.•Results showed the elastic ...modulus and failure stress of 40.12 and 62.26kPa, respectively.•The Yeoh, Ogden, and Mooney-Rivlin nonlinear models have also been employed.•The results have implications for investigating the trauma injury thru the numerical simulations.
The spinal cord as the most complex and critical part of the human body is responsible for the transmission of both motor and sensory impulses between the body and the brain. Due to its pivotal role any types of physical injury in that disrupts its function following by shortfalls, including the minor motor and sensory malfunctions as well as complicate quadriplegia and lifelong ventilator dependency. In order to shed light on the injuries to the spinal cord, the application of the computational models to simulate the trauma impact loading to that are deemed required. Nonetheless, it has not been fulfilled since there is a paucity of knowledge about the mechanical properties of the spinal cord, especially the cervical one, under the compressive loading on the grounds of the difficulty in obtaining this tissue from the human body. This study was aimed at experimentally measuring the mechanical properties of the human cervical spinal cord of 24 isolated fresh samples under the unconfined compressive loading at a relatively low strain rate. The stress-strain data revealed the elastic modulus and maximum/failure stress of 40.12±6.90 and 62.26±5.02kPa, respectively. Owing to the nonlinear response of the spinal cord, the Yeoh, Ogden, and Mooney-Rivlin hyperelastic material models have also been employed. The results may have implications not only for understanding the linear elastic and nonlinear hyperelastic mechanical properties of the cervical spinal cord under the compressive loading, but also for providing a raw data for investigating the injury as a result of the trauma thru the numerical simulations.
This work proposes a displacement-based finite element model for large strain analysis of isotropic compressible and nearly-incompressible hyperelastic materials. Constitutive law is written in terms ...of invariants of the right Cauchy-Green tensor; coupled and decoupled formulations of strain energy functions are presented, whereas a penalty function is used to impose an incompressibility constraint. Based on a total Lagrangian formulation, the nonlinear governing equations are thus obtained by employing the principle of virtual displacements. Analytic expression of both internal forces vector and tangent matrix of linear and high-order hexahedral finite elements are derived by adopting a three-dimensional formalism based on the Carrera Unified Formulation. Popular benchmark problems in hyperelasticity are analyzed to establish the capabilities of the present implementation of fully-nonlinear solid elements in the case of compressible and nearly-incompressible beams, cylindrical shells, and curved structures.
Millions of women around the globe have been affected by inadequately assessed gynaecological surgeries and urogynaecology mesh implantations. The unavailability of vaginal tissues could be the ...primary reason for such failed surgeries, which inhibit experimental practice and mesh implantation before real-time surgery. A tissue surrogate with realistic biomechanical properties of vaginal tissue would be anticipated to imitate the surgical suturing practice during traumatic child deliveries (e.g. Caesarean) and hysterectomy. Vaginal tissue surrogates, which simulate different conditions such as vaginal tissue stiffening, would also be highly beneficial in evaluating tissue changes under different scenarios (e.g. prolapse of tissue). The present study reported the development of low-cost elastomer-based vaginal tissue surrogates that simulate the mechanical properties of the human vaginal tissue. The composition of the elastomer material was arbitrarily varied to fabricate the candidate samples for the uniaxial tensile testing. The non-linear mechanical behaviour of the developed vaginal tissue simulants was characterised using the hyperelastic curve fitting formulations. The novel vaginal tissue surrogates with precisely characterised biomechanical properties would be indispensable for surgical training (e.g. gynaecological) and making medical models for educational purposes.
This paper presents the results of the comparison between a proposed Fourth Order Elastic Constants (FOECs) nonlinear model defined in the sense of Landau's theory, and the two most contrasted ...hyperelastic models in the literature, Mooney-Rivlin, and Ogden models. A mechanical testing protocol is developed to investigate the large-strain response of ex vivo cervical tissue samples in uniaxial tension in its two principal anatomical locations, the epithelial and connective layers. The final aim of this work is to compare the reconstructed shear modulus of the epithelial and connective layers of cervical tissue. According to the obtained results, the nonlinear parameter
from the proposed FOEC model could be an important biomarker in cervical tissue diagnosis. In addition, the calculated shear modulus depended on the anatomical location of the cervical tissue (μepithelial = 1.29 ± 0.15 MPa, and μconnective = 3.60 ± 0.63 MPa).
Likely Cavitation in Stochastic Elasticity Mihai, L. Angela; Fitt, Danielle; Woolley, Thomas E. ...
Journal of elasticity,
10/2019, Letnik:
137, Številka:
1
Journal Article
Recenzirano
Odprti dostop
We revisit the classic problem of elastic cavitation within the framework of stochastic elasticity. For the deterministic elastic problem, involving homogeneous isotropic incompressible hyperelastic ...spheres under radially symmetric tension, there is a critical dead-load traction at which cavitation can occur for some materials. In addition to the well-known case of stable cavitation post-bifurcation at the critical dead load, we show the existence of unstable snap cavitation for some isotropic materials satisfying Baker-Ericksen inequalities. For the stochastic problem, we derive the probability distribution of the deformations after bifurcation. In this case, we find that, due to the probabilistic nature of the material parameters, there is always a competition between the stable and unstable states. Therefore, at a critical load, stable or unstable cavitation occurs with a given probability, and there is also a probability that the cavity may form under smaller or greater loads than the expected critical value. We refer to these phenomena as ‘likely cavitation’. Moreover, we provide examples of homogeneous isotropic incompressible materials exhibiting stable or unstable cavitation together with their stochastic equivalent.
•Ranking different hyperelastic models for pure and simple shear.•Bayesian approach is used for parameters identification and to rank the models.•Pure shear: all models demonstrated excellent ...agreement with the experimental data.•Simple shear: not all models were suitable for describing the available experiments.•The best models. For pure shear Mooney–Rivlin. For simple shear 2-terms Ogden.
Hyperelastic materials are extensively employed in a wide range of applications. Although there are well-established models for describing the mechanical behavior of the hyperelastic materials, relatively few papers have attempted to rank different models. This paper aims to identify parameters of some constitutive models for pure and simple shear of an incompressible isotropic hyperelastic material under large deformations, and also aims to propose a strategy to rank different models. The constitutive models considered in the present analysis are the following: Mooney–Rivlin, Yeoh, Ogden (1 and 2 terms), Lopez-Pamies (1 and 2 terms), and Gent. In the first part of the paper, the Bayesian framework is applied for the identification of the parameters of the models, where experimental data are used to update the prior probabilistic model of the unknown parameters. The Maximum a Posteriori Estimate is obtained, and the error between the model prediction and the experimental data is computed to rank the models. In the second part of the paper, the Bayesian framework is again employed, but now as an strategy for model selection. Instead of ranking the models using the error between the model prediction and the experimental result, more ingredients, such as the Ockham factor, are taken into account for the model selection. The results indicate that all models and experimental results for pure shear are in good agreement, but Mooney–Rivlin, Gent and Yeoh models were not able to well describe the available experimental data from simple shear. The best model for pure shear is Mooney–Rivlin and the best model for simple shear is Ogden (2 terms), considering the available experimental data and the criteria proposed in the present paper.
When an elastic tube reinforced with helical fibres is inflated, its ends rotate. In large deformations, the amount and chirality of rotation is highly non-trivial, as it depends on the choice of ...strain–energy density and the arrangements of the fibres. For anisotropic hyperelastic tubes where the material parameters are single-valued constants, the problem has been satisfactorily addressed. However, in many systems, the material parameters are not precisely known, and it is therefore more appropriate to treat them as random variables. The problem is then to understand chirality in a probabilistic framework. Here, we develop a procedure for examining the elastic responses of a hyperelastic cylindrical tube of stochastic anisotropic material, where the material parameters are spatially-independent random variables defined by probability density functions. The tube is subjected to uniform dead loading consisting of internal pressure, axial tension and torque. Assuming that the tube wall is thin and that the resulting deformation is the combined inflation, extension and torsion from the reference circular cylindrical configuration to a deformed circular cylindrical state, we derive the probabilities of radial expansion or contraction, and of right-handed or left-handed torsion. We refer to these stochastic behaviours as ‘likely inflation’ and ‘likely chirality’, respectively.
•Hyperelastic cylindrical tubes of stochastic anisotropic material are treated.•The material parameters are random variables defined by probability densities.•The deformation is the combined inflation, extension and torsion.•The probability of right-handed or left-handed torsion is characterised.•The probability of radial expansion or contraction is also obtained.
In this paper, we consider a monolithic approach to handle coupled fluid–structure interaction problems with different hyperelastic models in an all-at-once manner. We apply Newton’s method in the ...outer iteration dealing with nonlinearities of the coupled system. We discuss preconditioned Krylov sub-space, algebraic multigrid and algebraic multilevel methods for solving the linearized algebraic equations. Finally, we compare the results of the monolithic approach with those of the corresponding partitioned approach that was studied in our previous work.
Recent research studies on industrial cyber-physical systems (ICPSs) have witnessed vast patronage with emphasis on data utility for improved design, maintenance, and high-level decision making. The ...design of proton-exchange membrane fuel cells (PEMFC) is geared towards improving performance and extending life cycles. More often, material selection of PEMFC components contributes a major determining factor for efficiency and durability with the seal/gasket quality being one of the most critical components. Finite element analysis (FEA) offers a simulated alternative to real-life stress analysis of components and has been employed on different rubber-like gasket materials for hydrogen fuel cells for determining an optimal strain energy density function using different hyperelastic models following uniaxial tensile testing. The results show that the Mooney–Rivlin, Ogden, and Yeoh models were the most fitting model with the best stress–strain fit following a weighted error evaluation criteria which returned 18.54%, 19.31%, and 21.96% for 25% displacement, and 22.1%, 21.7%, and 21.17% for 40% displacements, respectively. Further empirical analysis using the multi-metric regression technique for compatibility testing (curve similarity) between the hyperelastic model outputs and the tensile data reveal that the Yeoh model is the most consistent as seen in the marginal error difference amidst increasing displacement while the Arruda–Boyce model is most inconsistent as shown in the high error margin as the displacement increases from 25% to 40%. Lastly, a comparative assessment between different rubber-like materials (RLM) was presented and is expected to contribute to improved decision-making and material selection.
The growing interest in soft robotics has resulted in an increased demand for accurate and reliable material modelling. As soft robots experience high deformations, highly nonlinear behavior is ...possible. Several analytical models that are able to capture this nonlinear behavior have been proposed, however, accurately calibrating them for specific materials and applications can be challenging. Multiple experimental testbeds may be required for material characterization which can be expensive and cumbersome. In this work, we propose an alternative framework for parameter fitting established hyperelastic material models, with the aim of improving their utility in the modelling of soft continuum robots. We define a minimization problem to reduce fitting errors between a soft continuum robot deformed experimentally and its equivalent finite element simulation. The soft material is characterized using four commonly employed hyperelastic material models (Neo Hookean; Mooney-Rivlin; Yeoh; and Ogden). To meet the complexity of the defined problem, we use an evolutionary algorithm to navigate the search space and determine optimal parameters for a selected material model and a specific actuation method, naming this approach as Evolutionary Inverse Material Identification (EIMI). We test the proposed approach with a magnetically actuated soft robot by characterizing two polymers often employed in the field: Dragon Skin™ 10 MEDIUM and Ecoflex™ 00-50. To determine the goodness of the FEM simulation for a specific set of model parameters, we define a function that measures the distance between the mesh of the FEM simulation and the experimental data. Our characterization framework showed an improvement greater than 6% compared to conventional model fitting approaches at different strain ranges based on the benchmark defined. Furthermore, the low variability across the different models obtained using our approach demonstrates reduced dependence on model and strain-range selection, making it well suited to application-specific soft robot modelling.
PDF
