Finite element analysis of partly wrinkled reinforced prestressed membranes

Wrinkling is a well known phenomenon experimented by tension membranes in Civil Engineering applications. This paper will present an efficient numerical technique for the computational simulation of such wrinkles in a prestressed membrane. In particular, the relaxed energy approach (Pipkin in IMA J Appl Math 36:85–99, 1986) is particularized for prestressed membranes (Gil in Textile composites and inflatable structures, CIMNE, 2003) undergoing moderate strains. Wrinkling conditions in terms of the Euler-Lagrange finite deformation tensor along principal directions will be obtained. This will provide a framework to describe properly the initial instant when wrinkles start to be encountered in a prestressed Saint Venant–Kirchhoff hyperelastic membrane. Subsequently, a modified Helmholtz’s free energy functional will be introduced with the purpose of describing the modified constitutive behaviour of the continuum after the onset of wrinkling. Consistent derivations of the stress tensor as well as the constitutive tensor will de depicted. The results will be particularized for membranes and cables in a Finite Element discretization basis. Some numerical examples will prove the accuracy and robustness of the described algorithm.     

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.     

基于质点-弹簧模型的织物形象化仿真技术与展望

 针对基于质点-弹簧模型的织物变形仿真技术是当前织物仿真模拟的研究热点。本文首先简要综述了织物变形仿真技术的几种典型模型,着重阐述了由Provot提出的基于质点-弹簧模型的织物变形仿真方法。其次,着重从优化模型参数、提高模拟系统的稳定性以及减缓超弹性现象这三个方面介绍了基于质点-弹簧模型的优化手段,并分析比较各优化模型的优缺点,提出计算机视觉技术与算法应同织物的物理模型相结合的仿真思路。最后,对质点-弹簧模型的未来研究方向进行了展望,认为质点-弹簧模型应在建立仿真效果评价、提高模型整体性能与应用领域等方面有所深入,从而更加有效地帮助生产者或者设计者合理地选择和使用织物。     

Electro-thermal and -mechanical model of thermal breakdown in multilayered dielectric elastomers

Multiple breakdown phenomena may take place when operating dielectric elastomers. Thermal breakdown, which occurs due to Joule heating, becomes of special importance when using multilayered stacks of dielectric elastomers, due to the large volume-to-surface-area-ratio. In this article, a 2D axisymmetric finite-element model of a multilayered stack of dielectric elastomers is set up in COMSOL Multiphysics®. Both the electro-thermal and electro-mechanical couplings are considered, allowing for determination of the onset of thermal breakdown. Simulation results show that an entrapped particle in the dielectric elastomer drastically reduces the possible number of layers in the stack. Furthermore, the possible number of layers is greatly affected by the ambient temperature and the applied voltage. The performance of three hyperelastic material models for modeling the elastomer deformation are compared, and it is established that the Gent model yields the most restrictive prediction of breakdown point, while the Ogden model yields the least restrictive estimation.     

A Comparative Study of Several Material Models for Prediction of Hyperelastic Properties: Application to Silicone-Rubber and Soft Tissues

Abstract:  The correct modelling of constitutive laws is of critical importance for the analysis of mechanical behaviour of solids and structures. For example, the understanding of soft tissue mechanics, because of the nonlinear behaviour commonly displayed by the mechanical properties of such materials, makes common place the use of hyperelastic constitutive models. Hyperelastic models however, depend on sets of variables that must be obtained experimentally. In this study the authors use a computational/experimental scheme, for the study of the nonlinear mechanical behaviour of biological soft tissues under uniaxial tension. The material constants for seven different hyperelastic material models are obtained via inverse methods. The use of Martins's model to fit experimental data is presented in this paper for the first time. The search for an optimal value for each set of material parameters is performed by a Levenberg–Marquardt algorithm. As a control measure, the process is fully applied to silicone-rubber samples subjected to uniaxial tension tests. The fitting accuracy of the experimental stress–strain relation to the theoretical one, for both soft tissues and silicone-rubber (typically nonlinear) is evaluated. This study intents also to select which material models (or model types), the authors will employ in future works, for the analysis of human soft biological tissues.     

Energy flux associated with a plane crack along an (hyper)elastic bimaterial interface

A numerical procedure, incorporated with the finite element solutions, is developed to evaluate the energy flux vector for a crack located along the interface of 2-D hyperelastic bimaterial solids. The formulation is considered with finite strains for use with both linear and nonlinear material behavior. The formulation is verified to be path-independent in a modified sense and so the near-tip region, where singular mechanical behavior dominates, is always included. Special attention is hence addressed on appropriate modeling of the singular behavior. The numerical results show good accuracy without using any particular singular finite elements. This revised version was published online in July 2006 with corrections to the Cover Date.     

Biomechanics of oral mucosa

The prevalence of prosthodontic treatment has been well recognized, and the need is continuously increasing with the ageing population. While the oral mucosa plays a critical role in the treatment outcome, the associated biomechanics is not yet fully understood. Using the literature available, this paper provides a critical review on four aspects of mucosal biomechanics, including static, dynamic, volumetric and interactive responses, which are interpreted by its elasticity, viscosity/permeability, apparent Poisson''s ratio and friction coefficient, respectively. Both empirical studies and numerical models are analysed and compared to gain anatomical and physiological insights. Furthermore, the clinical applications of such biomechanical knowledge on the mucosa are explored to address some critical concerns, including stimuli for tissue remodelling (interstitial hydrostatic pressure), pressure–pain thresholds, tissue displaceability and residual bone resorption. Through this review, the state of the art in mucosal biomechanics and their clinical implications are discussed for future research interests, including clinical applications, computational modelling, design optimization and prosthetic fabrication.     

一种基于改进超弹性Zener模型的高阻尼橡胶隔震支座速度相关性本构模型

目前高阻尼橡胶隔震支座已在土木工程中得到广泛应用,但由于高阻尼橡胶隔震支座的材料组成成分比较复杂,特别是大量阻尼材料的采用导致支座的应力应变关系与其加载速度相关,而目前的支座本构模型很难精确地模拟这种力学特性。因此该文从高阻尼支座的橡胶材料特性出发,提出了一个基于改进超弹性Zener模型的高阻尼支座本构模型,该模型由两个超弹性弹簧和一个非线性阻尼器单元组成,能够精确表达高阻尼支座的速度相关性。在模型中,对超弹性弹簧建立新的应变能函数,并通过附加刚度系数α来模拟高阻尼橡胶材料的初始刚度。通过高阻尼橡胶材料的多步松弛试验和在不同速度下的循环剪切试验来识别模型中的参数。通过支座试验验证了提出的模型,运用基于速度控制的实时子结构试验系统分析了某隔震桥梁在地震作用下的动力反应,并基于试验结果对该文提出的本构模型在隔震结构非线性分析中的准确性进行了验证。     

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.