Retrospective Evaluation and Framework Development of Bone Anisotropic Material Behavior Compared with Elastic, Elastic-Plastic, and Hyper-Elastic Properties

The main motivation for studying damage in bone tissue is to better understand how damage develops in the bone tissue and how it progresses. Such knowledge may help in the surgical aspects of joint replacement, fracture fixation or establishing the fracture tolerance of bones to prevent injury. Currently, there are no standards that create a realistic bone model with anisotropic material properties, although several protocols have been suggested. This study seeks to retrospectively evaluate the damage of bone tissue with respect to patient demography including age, gender, race, body mass index (BMI), height, and weight, and their role in causing fracture. Investigators believe that properties derived from CT imaging data to estimate the material properties of bone tissue provides more realistic models. Quantifying and associating damage with in vivo conditions will provide the required information to develop mathematical equations and procedures to predict the premature failure and potentially mitigate problems before they begin. Creating a realistic model for bone tissue can predict the premature failure(s), provide preliminary results before getting the surgery, and optimize the design of orthopaedic implants. A comparison was performed between the proposed model and previous efforts, where they used elastic, hyper- elastic, or elastic-plastic properties. Results showed that there was a significant difference between the anisotropic material properties of bone when compared with unrealistic previous methods. The results showed that the density is 50% higher in male subjects than female subjects. Additionally, the results showed that the density is 47.91% higher in Black subjects than Mixed subjects, 53.27% higher than Caucasian subjects and 57.41% higher than Asian. In general, race should be considered during modeling implants or suggesting therapeutic techniques.

Microfluidic device integrating a network of hyper-elastic valves for automated glucose stimulation and insulin secretion collection from a single pancreatic islet

Advances in microphysiological systems have prompted the need for robust and reliable cell culture devices. While microfluidic technology has made significant progress, devices often lack user-friendliness and are not designed to be industrialized on a large scale. Pancreatic islets are often being studied using microfluidic platforms in which the monitoring of fluxes is generally very limited, especially because the integration of valves to direct the flow is difficult to achieve. Considering these constraints, we present a thermoplastic manufactured microfluidic chip with an automated control of fluxes for the stimulation and secretion collection of pancreatic islet. The islet was directed toward precise locations through passive hydrodynamic trapping and both dynamic glucose stimulation and insulin harvesting were done automatically via a network of large deformation valves, directing the reagents and the pancreatic islet toward different pathways. This device we developed enables monitoring of insulin secretion from a single islet and can be adapted for the study of a wide variety of biological tissues and secretomes.

An Immersed Boundary–Lattice Boltzmann Approach to Study Deformation and Fluid–Structure Interaction of Hollow Sealing Strip

A combined immersed boundary–lattice Boltzmann approach is used to simulate the dynamics of the fluid–structure interaction of a hollow sealing strip under the action of pressure difference. Firstly, the multiple relaxation times LBM model, hyper-elastic material model and immersed boundary method were deduced. According to the strain characteristics of hyper-elastic materials and the specific situation of friction between the elastic boundary and solid boundary, the internal force and the external force on the immersed boundary were discussed and deduced, respectively. Then, a 2D calculation model of the actual hollow sealing strip system was established, during which technical problems such as the equivalent wall thickness of the sealing strip and the correction of the stiffness of the contact corner were solved. The reliability of the model was verified by comparing results of FEM simulation of quasi-static deformation. Following this, the simulation results of three typical cases of sealing strips were presented. The results show that when the sealing strip fails, there will be a strong coupling phenomenon between the flow field and the sealing strip, resulting in the oscillation of the flow field and the sealing strip at the same frequency.

Characterisation and Modelling of an Artificial Lens Capsule Mimicking Accommodation of Human Eyes

A synthetic material of silicone rubber was used to construct an artificial lens capsule (ALC) in order to replicate the biomechanical behaviour of human lens capsule. The silicone rubber was characterised by monotonic and cyclic mechanical tests to reveal its hyper-elastic behaviour under uniaxial tension and simple shear as well as the rate independence. A hyper-elastic constitutive model was calibrated by the testing data and incorporated into finite element analysis (FEA). An experimental setup to simulate eye focusing (accommodation) of ALC was performed to validate the FEA model by evaluating the shape change and reaction force. The characterisation and modelling approach provided an insight into the intrinsic behaviour of materials, addressing the inflating pressure and effective stretch of ALC under the focusing process. The proposed methodology offers a virtual testing environment mimicking human capsules for the variability of dimension and stiffness, which will facilitate the verification of new ophthalmic prototype such as accommodating intraocular lenses (AIOLs).

Random Stiffness Tensor of Particulate Composites with Hyper-Elastic Matrix and Imperfect Interface

The main aim of this study is determination of the basic probabilistic characteristics of the effective stiffness for inelastic particulate composites with spherical reinforcement and an uncertain Gaussian volume fraction of the interphase defects. This is determined using a homogenization method with a cubic single-particle representative volume element (RVE) of such a composite and the finite element method solution. A reinforcing particle is spherical, located centrally in the RVE, surrounded by the thin interphase of constant thickness, and remains in an elastic reversible regime opposite to the matrix, which is hyper-elastic. The interphase defects are represented as semi-spherical voids, which are placed on the outer surface of this particle. The interphase is modeled as hyper-elastic and isotropic, whose effective stiffness is calculated by the spatial averaging of hyper-elastic parameters of the matrix and of the defects. A constitutive relation of the matrix is recovered experimentally by its uniaxial stretch. The 3D homogenization problem solution is based upon a numerical determination of strain energy density in the given RVE under specific uniaxial and biaxial stretches as well as under shear deformations. The analytical relation of the effective composite stiffness to the input uncertain parameter is recovered via the response function method, using a polynomial basis and an optimized order. Probabilistic calculations are completed using three concurrent approaches, namely the iterative stochastic finite element method (SFEM), Monte Carlo simulation and by the semi-analytical method. Previous papers consider the composite fully elastic, which limits the applicability of the resulting effective stiffness tensor computed therein. The current study voids this assumption and defines the composite as fully hyper-elastic, thus extending applicability of this tensor to strains up to 0.25. The most important research finding is that (1) the effective stiffness tensor is sensitive to random interface defects in its hyper-elastic range, (2) its resulting randomness is not close to Gaussian, (3) the semi-analytical method is not perfectly suited to stochastic calculations in this region of strains, as opposed to the linear elastic region, and (4) that the increase in random dispersion of defects volume fraction has a much higher effect on the stochastic characteristics of this stiffness tensor than fluctuation of the strain.

Spectral solution to a problem on the axisymmetric nonlinear deformation of a cylindrical membrane shell due to pressure and edges convergence

A geometrically and physically nonlinear model of a membrane cylindrical shell, which has been built and tested, describes the behavior of a airbag made of fabric material. Based on the geometrically accurate relations of "strain-displacement", it has been shown that the equilibrium equations of the shell, written in terms of Biot stresses, together with boundary conditions acquire a natural physical meaning and are the consequences of the principle of virtual work. The physical properties of the shell were described by Fung’s hyper-elastic biological material because its behavior is similar to that of textiles. For comparison, simpler hyper-elastic non-compressible Varga and Neo-Hookean materials, the zero-, first-, and second-order materials were also considered. The shell was loaded with internal pressure and convergence of edges. The approximate solution was constructed by an spectral method; the exponential convergence and high accuracy of the equilibrium equations inherent in this method have been demonstrated. Since the error does not exceed 1 % when keeping ten terms in the approximations of displacement functions, the solution can be considered almost accurate. Similar calculations were performed using a finite element method implemented in ANSYS WB in order to verify the results. Differences in determining the displacements have been shown to not exceed 0.2 %, stresses – 4 %. The study result has established that the use of Fung, Varga, Neo-Hookean materials, as well as a zero-order material, lead to similar values of displacements and stresses, from which displacements of shells from the materials of the first and second orders significantly differ. This finding makes it possible, instead of the Fung material whose setting requires a significant amount of experimental data, to use simpler ones – a zero-order material and the Varga material

Matrix Description of Non-Linear Properties of Materials or Structural Components—Idea and Application Examples

Numerical methods are widely used in structural analysis problems. In the cases of the most complex and practical problems, they are often the only way to obtain solutions, as analytical methods prove ineffective. The motivation for this paper was the desire to extend the scope of numerical methods to cover the problems of creating constitutive models of structural materials. The aim of this research was to develop a matrix or numerical discrete constitutive model of materials. It presents the general assumptions of the developed method for modeling the physical properties of materials. The matrix model is only useful with an appropriate numerical algorithm. Such an algorithm was created and described in this paper. Based on its findings, computer software was developed to perform numerical simulations. Presented calculation examples confirmed the effectiveness of the developed method to create constitutive matrix models of various typical materials, such as steel, but also, e.g., hyper-elastic materials. It also presents the usefulness of constitutive matrix models for simulations of simple stress states and analyses of structural elements such as reinforced concrete. All presented examples involved the physical nonlinearity of the materials. It is proved that the developed matrix constitutive model of materials is efficient and quite versatile. In complex analyses of structures made of nonlinear materials, it can be used as an effective alternative to classical constitutive or analytical models based on elementary mathematical functions.

Reversal modeling and optimal design of hyper-elastic diaphragm in space fuel tanks

Diaphragm tanks are a common type of pressurized tanks in which the diaphragm is used to separate the fuel part from the high-pressure part, compress the fuel in the tank, and reduce free space to avoid liquid fuel sloshing. The main purpose of the application of the diaphragm tanks is to ensure the continuous flow of pure fuel without the gas bubble into the spacecraft engine. In space mission, diaphragm tanks will experience a wide range of acceleration at different levels of filling. These conditions change the state of equilibrium between the volume of the gas and the fluid and move the diaphragm toward the discharge portion of the tank. As a result of this movement, the diaphragm curvature is changed and the structure collapses at rest, which is called folding. When large nonlinear folding occurs, there is potential for diaphragm damage through wear, rubbing, and excessive stress. Predicting diaphragm behavior in order to calculate a diaphragm’s susceptibility to corrosion, rupture, and surface strain is one of the major design challenges. In this study, new method is provided to analyze deformation of diaphragm tanks by using numerical techniques. Also, the investigation method is verified by using experimental methods. In this process, first a 3D numerical model is developed to investigate the inverse behavior of a hyper-elastic diaphragm by using ANSYS software and the results of the simulations are compared with the results of experimental tests in the same situation. After validation, a second case study is performed to survey the effect of reducing diaphragm thickness according to the strain energy and natural frequency behavior of the diaphragm in different fill levels. The results of this study showed that numerical simulations are capable of reconstructing diaphragm inversion properties with good accuracy. In addition, the numerical model can detect the proper thickness for the diaphragm. In the last section, algorithm and software for optimal automatic modeling of diaphragm tanks are proposed.