Hyperelastic neo-Hookean Material Research Articles

Numerical Investigation of Solitary Wave Attenuation by a Vertical Plate-Type Flexible Breakwater Constructed Using Hyperelastic Neo-Hookean Material

This study conducted numerical investigations on solitary wave attenuation by a vertical plate-type flexible breakwater constructed using hyperelastic neo-Hookean material. The wave attenuation performance and elastic behaviors of the flexible breakwater were discussed systematically by considering the effects of three prominent factors: mass coefficient, stiffness coefficient, and Poisson’s ratio. It is indicated that more compressible and flexible materials are beneficial for enhancing efficiency in mitigating solitary wave energy and protecting the structure from damage. In addition, the performance of the hyperelastic neo-Hookean material model was compared with that of a linear elastic isotropic material model coupled with linear and nonlinear geometry analysis (LGEOM and NLGEOM) by evaluating several key targets: wave reflection coefficient, transmission coefficient, horizontal tip displacement, and wave load. Our findings revealed that the hyperelastic neo-Hookean material model showed almost the same predictions as the linear elastic isotropic material model with NLGEOM, but significantly diverged from that with LGEOM. The linear elastic isotropic material model with LGEOM cannot capture the nonlinear variations in structural geometry and stress–strain relationship, resulting in the underestimation and overestimation of horizontal tip displacement under moderate and extreme wave loads, respectively. Moreover, it underestimates the damage inflicted by solitary waves due to inaccurately predicted wave reflection and transmission.

Topology optimization of soft compressible phononic laminates for widening the mechanically tunable band gaps

Active tuning of frequency bandgaps has received significant attention in the recent past. To this end, soft compressible phononic composites have indicated great promise owing to their capability to undergo large reversible deformations and deformation dependent constitutive properties. In this investigation, we present an optimization framework for arriving at the optimum topology of a two-phase soft compressible phononic composite for maximizing the frequency gap between the first four consecutive frequency bands of longitudinal wave propagation. The laminate is subjected simultaneously to an equal biaxial pre-stretch in the plane perpendicular to the direction of wave propagation and a prestress in the direction of wave propagation. The nonlinear hyperelastic neo-Hookean material model is employed for characterizing the constitutive behavior of the soft compressible laminate phases. The finite element method with Bloch–Floquet theory is employed for finding the band-structure of the infinitely periodic soft laminate. A gradient-based method of moving asymptotes is used to solve the underlying topology optimization problem. In particular, we present the optimum unit cell designs for two separate problems involving maximization of the absolute width of the band gap and that of the relative width of the band gap when compared to that in the un-deformed laminate. Test cases are presented to highlight the effects of the levels of biaxial prestretch and the longitudinal prestress. Our results indicate that a compressional longitudinal prestress and a lateral prestretch have a favorable impact on widening of the frequency band-gaps. The numerical framework and the inferences reported here can find their potential use in the optimal design of soft compressible composites used in acoustic applications.

Stress-based topology optimization of compliant mechanisms using nonlinear mechanics

The present work demonstrates how a light structure can be easily designed through Topology Optimization even including complex analysis and sizing criteria such as hyperelastic Neo-Hookean materials for nonlinear analysis and aggregated stress constraints. The SIMP approach was adopted and two different strategies were analysed using an in house versatile MATLAB code. MMA was used as reference optimizer (in structural optimization) whereas a unified aggregation and relaxation method was adopted to deal with stress constraints. Feasibility was analyzed from the viewpoint of allowable stress verification. Two test cases are then studied: a morphing airfoil (for aeronautical applications) and a geometric inverter (for mechanics and bio-medical applications). For both, a hyperelastic Neo-Hookean material was chosen. Finally a complementary study on the effects of constraints and the input force intensity is also presented.

A phase-field model for fluid–structure interaction

In this paper, we develop a novel phase-field model for fluid–structure interaction (FSI), that is capable to handle very large deformations as well as topology changes like contact of the solid to a wall. The model is based on a fully Eulerian description of the velocity field in both, the fluid and the elastic domain. Viscous and elastic stresses in the Navier–Stokes equations are restricted to the corresponding domains by multiplication with their characteristic functions. The solid is described as a hyperelastic neo-Hookean material and the elastic stress is obtained by solving an additional Oldroyd-B – like equation. Thermodynamically consistent forces are derived by energy variation. The convergence of the derived equations to the traditional sharp interface formulation of fluid–structure interaction is shown by matched asymptotic analysis. The model is evaluated in a challenging benchmark scenario of an elastic body traversing a fluid channel. A comparison to reference values from Arbitrary Lagrangian Eulerian (ALE) simulations shows very good agreement. We highlight some distinct advantages of the new model, like the avoidance of re-triangulations and the stable inclusion of surface tension. Further, we demonstrate how simple it is to include contact dynamics into the model, by simulating a ball bouncing off a wall. We extend this scenario to include adhesion of the ball, which to our knowledge, cannot be simulated with any other FSI model. While we have restricted simulations to fluid–structure interaction, the model is capable to simulate any combination of viscous fluids, visco-elastic fluids and elastic solids.

A comparative study of two constitutive models within an inverse approach to determine the spatial stiffness distribution in soft materials

A comparative study is presented to solve the inverse problem in elasticity for the shear modulus (stiffness) distribution utilizing two constitutive equations: (1) linear elasticity assuming small strain theory, and (2) finite elasticity with a hyperelastic neo-Hookean material model. Assuming that a material undergoes large deformations and material nonlinearity is assumed negligible, the inverse solution using (2) is anticipated to yield better results than (1). Given the fact that solving a linear elastic model is significantly faster than a nonlinear model and more robust numerically, we posed the following question: How accurately could we map the shear modulus distribution with a linear elastic model using small strain theory for a specimen undergoing large deformations? To this end, experimental displacement data of a silicone composite sample containing two stiff inclusions of different sizes under uniaxial displacement controlled extension were acquired using a digital image correlation system. The silicone based composite was modeled both as a linear elastic solid under infinitesimal strains and as a neo-Hookean hyperelastic solid that takes into account geometrically nonlinear finite deformations. We observed that the mapped shear modulus contrast, determined by solving an inverse problem, between inclusion and background was higher for the linear elastic model as compared to that of the hyperelastic one. A similar trend was observed for simulated experiments, where synthetically computed displacement data were produced and the inverse problem solved using both, the linear elastic model and the neo-Hookean material model. In addition, it was observed that the inverse problem solution was inclusion size-sensitive. Consequently, an 1-D model was introduced to broaden our understanding of this issue. This 1-D analysis revealed that by using a linear elastic approach, the overestimation of the shear modulus contrast between inclusion and background increases with the increase of external loads and target shear modulus contrast. Finally, this investigation provides valuable information on the validity of the assumption for utilizing linear elasticity in solving inverse problems for the spatial distribution of shear modulus associated with soft solids undergoing large deformations. Thus, this work could be of importance to characterize mechanical property variations of polymer based materials such as rubbers or in elasticity imaging of tissues for pathology.

The influence of large deformations on mechanical properties of sinusoidal ligament structures

Studies of mechanical properties of materials, both theoretical and experimental, usually deal with linear characteristics assuming a small range of deformations. In particular, not much research has been published devoted to large deformations of auxetic structures – i.e. structures exhibiting negative Poisson’s ratio. This paper is focused on mechanical properties of selected structures that are subject to large deformations. Four examples of structure built of sinusoidal ligaments are studied and for each geometry the impact of deformation size and geometrical parameters on the effective mechanical properties of these structures are investigated. It is shown that some of them are auxetic when compressed and non-auxetic when stretched. Geometrical parameters describing sinusoidal shape of ligaments strongly affect effective mechanical properties of the structure. In some cases of deformation, the increase of the value of amplitude of the sinusoidal shape decreases the effective Poisson’s ratio by 0.7. Therefore the influence of geometry, as well as the arrangement of ligaments allows for smart control of mechanical properties of the sinusoidal ligament structure being considered. Given the large deformation of the structure, both a linear elastic material model, and a hyperelastic Neo-Hookean material model are used.

Micromechanics methods for evaluating the effective moduli of soft neo-Hookean composites

Most biological soft tissues are multiphase composite materials, and the determination of their effective constitutive relations is a major concern in medical engineering. In this paper, we consider a class of soft two-phase composites, in which both phases are isotropic and hyperelastic neo-Hookean materials. For such an isotropic composite consisting of inclusions uniformly distributed but randomly oriented in a matrix, two constitutive parameters are required to characterize its hyperelastic constitutive relation. Micromechanics methods, including dilute concentration method, Mori–Tanaka method, self-consistent method, and differential method are extended to predict the effective properties of this kind of composites. Analytical solutions are given for the hyperelastic neo-Hookean composites reinforced by spherical particles, long fibers, and penny-shaped platelets, respectively. Finite element simulations are performed to evaluate the accuracy of these theoretical methods.

The anti-plane shear elastostatic fields near the wedge vertex of an incompressible hyperelastic bimaterial

The anti-plane shear transformation corresponding to a bimaterial wedge problem is studied within the framework of finite elasticity. Two wedges of arbitrary angles are assumed to be incompressible hyperelastic Neo–Hookean materials, and have a common perfect interface and a traction free surface. The resolution of the boundary value problem near the vertex of a bimaterial wedge by means of asymptotic procedure leads to an eigenequation connecting wedges angles and materials properties. Results proved that, contrary to linear elasticity predictions, it is needed to extend development to higher orders because of their contribution in stress singularity.

Sensitivity analysis based crack propagation criterion for compressible and (near) incompressible hyperelastic materials

Sensitivity analysis of an XFEM crack propagation model is developed for shape and material parameters, where the direct differentiation method is applied to large strain problems with hyperelastic neo-Hookean materials. The presence of level set functions to describe the crack position requires the development of a proper differentiation technique which is also addressed. In order to compute the analytical derivatives of such a complex numerical model the capabilities of the symbolic system AceGen are employed.A crack propagation criterion based on the sensitivity formulation is developed, allowing the direct calculation of the crack growth length and direction without post-processing. Special attention is paid to the ability of satisfying incompressibility and near-incompressibility conditions.The performance of the XFEM sensitivity analysis is assessed by the Cook's Membrane and Pre-crack Plate benchmark tests where sensitivities of displacements and crack propagation criteria based on potential energy have been analysed with respect to crack length and crack growth parameters. The techniques presented in this paper can be extended to anisotropic materials and non-linear materials exhibiting plasticity and viscoplasticity. Additionally, this formulation constitutes a base for further analysis of crack branching and crack joining problems.

A study of breast motion using non-linear dynamic FE analysis

This paper presents a new method to simulate non-linear breast motion by using a three-dimensional (3D) dynamic finite element model (FEM). The model consists of a thorax with two breasts and three skin layers with specific mechanical properties. Using free breast vibration, the viscous damping ratios were ascertained to be 0.215 for an 80B size breast. The shear modulus for the breast was derived as the value that gave the minimum difference between the FEM-predicted results and the experimental data. A hyper-elastic neo-Hookean material model simulated the large deformation of breast tissue. The mode shapes of breast motions at different natural frequencies were established. The highest breast displacement amplitude ratio relative to the thorax was at 4 Hz. The study showed that FEM can predict breast displacement with sufficient accuracy and thereby provide the basis by which bras may be engineered more ergonomically in the future. Practitioner Summary: To facilitate a theoretical analysis of breast motion to enable the design of more supportive bras, a dynamic FEM based on reliable non-linear properties of breast tissues has been developed. The methods and findings have potential widespread benefit for developing new products to promote women's health and comfort.