Mechanical property characterization of mouse zona pellucida

Previous intracytoplasmic sperm injection (ICSI) studies have indicated significant variation in ICSI success rates among different species. In mouse ICSI, the zona pellucida (ZP) undergoes a "hardening" process at fertilization in order to prevent subsequent sperm from penetrating. There have been few studies investigating changes in the mechanical properties of mouse ZP post fertilization. To characterize mouse ZP mechanical properties and quantitate the mechanical property differences of the ZP before and after fertilization, a microelectromechanical systems-based multiaxis cellular force sensor has been developed. A microrobotic cell manipulation system employing the multiaxis cellular force sensor is used to conduct mouse ZP force sensing, establishing a quantitative relationship between applied forces and biomembrane structural deformations on both mouse oocytes and embryos. An analytical biomembrane elastic model is constructed to describe biomembrane mechanical properties. The characterized elastic modulus of embryos is 2.3 times that of oocytes, and the measured forces for puncturing embryo ZP are 1.7 times those for oocyte ZP. The technique and model presented in this paper can be applied to investigations into the mechanical properties of other biomembranes, such as the plasma membrane of oocytes or other cell types.     

Estimating Young's modulus of zona pellucida by micropipette aspiration in combination with theoretical models of ovum

The zona pellucida (ZP) is the spherical layer that surrounds the mammalian oocyte. The physical hardness of this layer plays a crucial role in fertilization and is largely unknown because of the lack of appropriate measuring and modelling methods. The aim of this study is to measure the biomechanical properties of the ZP of human/mouse ovum and to test the hypothesis that Young''s modulus of the ZP varies with fertilization. Young''s moduli of ZP are determined before and after fertilization by using the micropipette aspiration technique, coupled with theoretical models of the oocyte as an elastic incompressible half-space (half-space model), an elastic compressible bilayer (layered model) or an elastic compressible shell (shell model). Comparison of the models shows that incorporation of the layered geometry of the ovum and the compressibility of the ZP in the layered and shell models may provide a means of more accurately characterizing ZP elasticity. Evaluation of results shows that although the results of the models are different, all confirm that the hardening of ZP will increase following fertilization. As can be seen, different choices of models and experimental parameters can affect the interpretation of experimental data and lead to differing mechanical properties.     

A multiplicative finite strain finite element framework for the modelling of semicrystalline polymers and polycarbonates

This paper presents a phenomenological model for the simulation and analysis of stress‐induced orientational hardening in semicrystalline polymers and polycarbonates at finite strains. The notion of intermediate (local) stress‐free configuration is used to develop a set of constitutive equations, and its relation to the multiple natural (stress‐free) configurations in the class of materials being considered here is discussed. A hyperelastic stored energy function, written with respect to the intermediate stress‐free configuration is presented to model the finite elastic response. It is then combined with the J₂‐flow theory to model the finite inelastic response. The isochoric constraint during inelastic deformation is treated via an exact multiplicative decomposition of the deformation gradient into volume‐preserving and spherical parts. The numerical solution algorithm is based on the use of operator splitting technique that results in a product formula algorithm with elastic‐predictor/inelastic‐corrector components. Numerical results are presented to show the behaviour of the model. Copyright © 2000 John Wiley & Sons, Ltd.     

Interactions between cross-links and dislocations in polyethylene crystals: a model of irradiation hardening

The irradiation hardening of polyethylene (PE) crystals is explained in terms of the intersection and interaction between cross-links and dislocations. The elastic energies and forces of interaction between cross-links and the dislocations responsible for the various plastic deformation modes are calculated using a force dipole model of a cross-link and the strain field of the dislocation. The elastic energies of interaction are in all cases less than 0.7 eV (1.12×10^–19 J) and they are greater for edge than for screw dislocations. The hardening which arises from the direct intersections is calculated using a Morse potential model for the cross-link strength, and it is found that these interactions involve energies of the order of 3.6 eV (5.76×10^–19 J). From these results it is concluded that at 0 K both types of interaction produce similar hardening. However, since the elastic interaction energies are small, the hardness of cross-linked PE crystals at moderate temperatures is due solely to direct intersections of cross-links and dislocations. The strongest interactions take place between cross-links and those dislocations which produce chain-axis slip and this explains why this mode of deformation is readily suppressed by irradiation. The forces of interaction between cross-links and twin dislocations are not negligible, but since their interaction energies are of the order of 0.1 eV (0.16×10^–19 J), twinning deformation, at moderate temperatures, should not be affected by irradiation. By combining all the possible deformation modes, the relationship _c=4^1/2, is derived for the increase in yield stress, _c (GPa), in terms of the atomic concentration of cross-links,, provided that these are uniformly distributed in the crystal.     

有机相对骨组织力学性能影响的有限元分析

骨组织主要由有机相和矿物质相间排列而成,其显微组织结构与纤维增强材料相似。基于矿化程度构建三种胶原微纤维模型,以原胶原分子和有机交联键为出发点,综合探索有机相对微纤维力学性能的作用机制,再与文献数据进行对照验证。数值结果表明：随着矿化程度的加深,微纤维模型的刚度值和塑性趋势均显著上升。原胶原分子的收缩会导致其弹性模量上升,韧性明显下降。交联键数量增多会提高骨组织的力学性能,也增大骨组织的脆性。研究结果有助于揭示骨组织活性成分和微观结构对其力学性能的影响,为骨组织修复材料的开发提供理论依据。     

An elastic-viscoplastic model exhibiting continuity of solid and fluid states

In this paper specific unified constitutive equations for an elastic-viscoplastic material are developed which in the limit of infinite resistance to plastic flow become those of a general hyperelastic isotropic material; and in the limit of zero resistance to plastic flow become those of a general Reiner-Rivlin fluid. The constitutive equations satisfy the restrictions imposed by continuum thermodynamics and are hyperelastic in the sense that the symmetric Piola-Kirchhoff stress is related to a derivative of the Helmholtz free energy. In this formulation the Helmholtz free energy depends on five scalar invariants: two new scalars which are pure measures of “elastic” distortional deformation, a measure of total dilatation, a measure of plastic dilatation, and temperature. Specifically, the stress is not characterized by a hypoelastic equation so no special rates of stress need be considered. Both isotropic hardening and a measure of directional hardening which models the Bauschinger effect are included. Finally, examples of simple shear are considered to examine the solid-like and fluid-like response to large deformations including cycles of loading, unloading and reloading.     

Two‐point constitutive equations and integration algorithms for isotropic‐hardening rate‐independent elastoplastic materials in large deformation

This paper presents alternative forms of hyperelastic–plastic constitutive equations and their integration algorithms for isotropic‐hardening materials at large strain, which are established in two‐point tensor field, namely between the first Piola–Kirchhoff stress tensor and deformation gradient. The eigenvalue problems for symmetric and non‐symmetric tensors are applied to kinematics of multiplicative plasticity, which imply the transformation relationships of eigenvectors in current, intermediate and initial configurations. Based on the principle of plastic maximum dissipation, the two‐point hyperelastic stress–strain relationships and the evolution equations are achieved, in which it is considered that the plastic spin vanishes for isotropic plasticity. On the computational side, the exponential algorithm is used to integrate the plastic evolution equation. The return‐mapping procedure in principal axes, with respect to logarithmic elastic strain, possesses the same structure as infinitesimal deformation theory. Then, the theory of derivatives of non‐symmetric tensor functions is applied to derive the two‐point closed‐form consistent tangent modulus, which is useful for Newton's iterative solution of boundary value problem. Finally, the numerical simulation illustrates the application of the proposed formulations. Copyright © 2008 John Wiley & Sons, Ltd.     

On visco-elastic modelling of polyethylene terephthalate behaviour during multiaxial elongations slightly over the glass transition temperature

The mechanical response of Polyethylene Terephthalate (PET) in elongation is strongly dependent on temperature, strain and strain rate. Near the glass transition temperature T_g, the stress–strain curve presents a strain softening effect vs strain rate but a strain hardening effect vs strain under conditions of large deformations. The goal of this work is to propose a visco hyperelastic model to predict the PET behaviour when subjected to large deformations and to manage the identification of the material properties from the experimental data by an original method. To represent the non-linear effects, an elastic part depending on the elastic equivalent strain and a non-Newtonian viscous part depending on both viscous equivalent strain rate and cumulated viscous strain are tested. The model parameters can then be accurately obtained through a comparison with the experimental uniaxial and biaxial tests. The influence of the temperature on the viscous part is also modelled and an evaluation of the adiabatic self heating of the specimen is compared to experimental results.     

Computational method of inverse elastostatics for anisotropic hyperelastic solids

The paper presents a computational method for predicting the initial geometry of a finitely deforming anisotropic elastic body from a given deformed state. The method is imperative for a class of problem in stress analysis, particularly in biomechanical applications. While the basic idea has been established elsewhere Comput. Methods Appl. Mech. Eng. 1996; 136 :47–57; Int. J. Numer. Meth. Engng 1998; 43 : 821–838), the implementation in general anisotropic solids is not a trivial exercise, but comes after a systematic development of Eulerian representations of constitutive equations. In this paper, we discuss the general representation in the context of fibrous hyperelastic solids, and provide explicit stress functions for some commonly used soft tissue models including the Fung model and the Holzapfel model. A three‐field mixed formulation is introduced to enforce quasi‐incompressibility constraints. The practical utility of this method is demonstrated using an example of aneurysm stress analysis. Copyright © 2006 John Wiley & Sons, Ltd.     

材料参数对高强不锈钢管数控绕弯成形失稳起皱的影响

目的研究材料参数波动对管材数控绕弯成形失稳起皱的影响规律。方法基于ABAQUS有限元平台,建立了21-6-9高强不锈钢管数控绕弯成形过程三维弹塑性有限元模型,并验证了模型的可靠性;采用该模型模拟分析了材料参数波动对其数控绕弯成形过程失稳起皱的影响规律。结果随着厚向异性指数、屈服强度的增大或弹性模量、硬化指数的减小,弯管的起皱趋势增大,泊松比和强度系数对弯管起皱趋势的影响较小。结论材料参数对弯管起皱趋势影响的大小依次为:屈服强度、弹性模量、厚向异性指数、硬化指数、强度系数和泊松比。     

Coupling of finite element and boundary integral methods for a capsule in a Stokes flow

We introduce a new numerical method to model the fluid–structure interaction between a microcapsule and an external flow. An explicit finite element method is used to model the large deformation of the capsule wall, which is treated as a bidimensional hyperelastic membrane. It is coupled with a boundary integral method to solve for the internal and external Stokes flows. Our results are compared with previous studies in two classical test cases: a capsule in a simple shear flow and in a planar hyperbolic flow. The method is found to be numerically stable, even when the membrane undergoes in‐plane compression, which had been shown to be a destabilizing factor for other methods. The results are in very good agreement with the literature. When the viscous forces are increased with respect to the membrane elastic forces, three regimes are found for both flow cases. Our method allows a precise characterization of the critical parameters governing the transitions. Copyright © 2010 John Wiley & Sons, Ltd.     

Micropolar hyper‐elastoplasticity: constitutive model,consistent linearization,and simulation of 3D scale effects

A computational model for micropolar hyperelastic‐based finite elastoplasticity that incorporates isotropic hardening is developed. The basic concepts of the non‐linear micropolar kinematic framework are reviewed, and a thermodynamically consistent constitutive model that features Neo‐Hooke‐type elasticity and generalized von Mises plasticity is described. The integration of the constitutive initial value problem is carried out by means of an elastic‐predictor/plastic‐corrector algorithm, which retains plastic incompressibility. The solution procedure is developed carefully and described in detail. The consistent material tangent is derived. The micropolar constitutive model is implemented in an implicit finite element framework. The numerical example of a notched cylindrical bar subjected to large axial displacements and large twist angles is presented. The results of the finite element simulations demonstrate (i) that the methodology is capable of capturing the size effect in three‐dimensional elastoplastic solids in the finite strain regime, (ii) that the formulation possesses a regularizing effect in the presence of strain localization, and (iii) that asymptotically quadratic convergence rates of the Newton–Raphson procedure are achieved. Throughout this paper, effort is made to present the developments as a direct extension of standard finite deformation computational plasticity. Copyright © 2012 John Wiley & Sons, Ltd.     

A Cauchy‐stress based solution for a necking elastic constitutive model under large deformation

A finite element based method for solution of large‐deformation hyperelastic constitutive models is developed, which solves the Cauchy‐stress balance equation using a single rotation of stress from principal directions to a fixed co‐ordinate system. Features of the method include stress computation by central differencing of the hyperelastic energy function, mixed integration‐order incompressibility enforcement, and an iterative solution method that employs notional ‘small strain’ stiffness. The method is applied to an interesting and difficult elastic model that replicates polymer ‘necking’; the method is shown to give good agreement with published results from a well‐established finite element package, and with published experimental results. It is shown that details of the manner in which incompressibility is enforced affects whether key experimental phenomena are clearly resolved. Copyright © 2005 John Wiley & Sons, Ltd.     

Thermoelastic properties of 350 grade maraging steel

The elastic moduli of 350 grade maraging steel in the annealed and hardened states have been determined in the temperature range 4.2 to 300 K. Thermal expansion of these steels and pure iron are given for the range 2 to 800 K. The elastic moduli show a normal temperature dependence, increasing with decreasing temperature, and a zero temperature derivative at 0 K. The low-temperature thermal expansion coefficient is the sum of a linear and cubic term, the former having a negative sign for the steels, which is probably due to magnetic effects. The elastic moduli increase by about 10% on hardening, and this increase is correlated with the structural changes caused by the hardening process.     

Discrete element methods for the plastic analysis of structures subjected to cyclic loading

Methods for the analysis of complex, highly redundant structures subjected to intermittent loads causing biaxial membrane stress and stress reversal into the plastic range are presented. The Bauschinger effect in multi-axial stress is taken into account by the use of Ziegler's modification of Pragers kinematic hardening theory. The implementation of this plasticity theory in the discrete element methods involves the application of the loading in small increments. A linear relationship between increments of plastic strain and of stress, arising out of the theory, is used in conjunction with a linear matrix equation that governs the elastic behaviour of the structure. In the latter equation, plastic strains are interpreted as initial strains. A solution to the linear matrix equation, expressed in terms either of stress or of total strain, may be obtained by utilizing one of two alternative procedures. The methods are capable of treating materials which exhibit elastic–plastic behaviour involving ideal plasticity, linear or non-linear strain hardening, or limited strain hardening. Application is made to several representative structures. Comparison of some of the results with existing test data for both monotonic and reversed loading shows good correlation.     

Finite element simulation for the effect of loading rate on visco‐hyperelastic characterisation of soft materials by spherical nanoindentation

Nanoindentation test performed by atomic force microscopy is highly recommended for the characterisation of soft materials at nanoscale. The assumption proposed in the characterisation is that the material is pure elastic with no viscosity. However, this assumption does not represent the real characteristics of soft materials such as bio tissue or cell. Therefore, a parametric finite element simulation of nanoindentation by spherical tip was carried out to investigate the response of cells with different constitutive laws (elastic, hyperelastic and visco‐hyperelastic). The investigation of the loading rate effect on the characterisation of cell mechanical properties was performed for different size of spherical tip. The selected dimensions of spherical tips cover commercially available products. The viscosity effects are insensitive to the varied dimensions of spherical tip in this study. A limit loading rate was found above which viscous effect has to be considered to correctly determine the mechanical properties. The method in this work can be implemented to propose a criterion for the threshold of loading rate when viscosity effect can be neglected for soft material characterisation.Inspec keywords: atomic force microscopy, viscoelasticity, finite element analysis, nanoindentation, viscosity, biomechanics, indentation, elasticityOther keywords: spherical tip, viscosity effect, viscous effect, soft material characterisation, visco‐hyperelastic characterisation, spherical nanoindentation, nanoindentation test, atomic force microscopy, bio tissue, parametric finite element simulation, loading rate effect, cell mechanical properties, constitutive laws     

Large strain constitutive modelling and computation for isotropic,creep elastoplastic damage solids

A three-dimensional fully coupled creep elastoplastic damage model at finite strain for isotropic non-linear material is developed. The model is based on the thermodynamics of an irreversible process and the internal state variable theory. A hyperelastic form of stress–strain constitutive relation in conjunction with the multiplicative decomposition of the deformation gradient into elastic and inelastic parts is employed. The pressure-dependent plasticity with strain hardening and the damage model with two damage internal variables are particularly considered. The rounding of stress–strain curves appearing in cycling loading is reproduced by introduction of the creep mechanism into the model. A numerical integration procedure for the coupled constitutive equations with three hierarchical phases is proposed. A consistent tangent matrix with consideration of the fully coupled effects at finite strain is derived. Numerical examples are tested to demonstrate the capability and performance of the present model at large strain.     

Yielding of plates with hardening and large deformations

A mixed finite element technique is used to study the influence of yielding on buckled plates. Orthogonal anisotropic hardening is determined solely by a yield condition, which is introduced into a mixed functional for the elastic plate by Lagrange Multipliers. The Euler equations of the constrained functional include Prager's normality rule. Numerical results are given for rectangular plates of different size calculated for various material properties.