超弹性材料的不稳定性问题

超弹性材料是一类性能独特、不可替代且有广泛工程应用的高分子材料,对其独特的材料不稳定性问题的研究极大地推动了连续介质力学有限变形理论和超弹性理论的发展.综述了超弹性材料中的材料不稳定性问题的研究成果和最新进展,包括Rivlin立方块问题、薄壁球壳和薄壁圆筒的内压膨胀问题、圆柱的扭转问题、块体的表面不稳定性问题、空穴的生成、增长和闭合问题等.阐述了这类材料中各类非线性不稳定性问题的特点、问题的求解、主要结果及今后进一步的研究方向等.      

Mechanical performance and negative pressure instability for venous walls

Mechanical properties, such as the deformation and stress distributions for venous walls under the combined load of transmural pressure and axial stretch, are examined within the framework of nonlinear elasticity with one kind of hyper-elastic strain energy functions. The negative pressure instability problem of the venous wall is explained through energy comparison. First, the deformation equation of the venous wall under the combined loads is obtained with a thin-walled circular cylindrical tube. The deformation curves and the stress distributions for the venous wall are given under the normal transmural pressure, and the regulations are discussed. Then, the deformation curves of the venous wall under the negative transmural pressure or the internal pressure less than the external pressure are given. Finally, the negative pressure instability problem is discussed through energy comparison.     

Modeling on monitoring the growth and rupture assessment of saccular aneurysms

The unpredictable rupture of saccular aneurysms especially of the intracerebral aneurysm is a knotty problem that always results in high mortality.Traditional diagnosis of medical images,which gives the aneurysm size and compares with a speculated critical size from clinical statistics,was demonstrated inadequate to forecasting rupture.Here,we propose a new detecting strategy that uses a dielectric elastomer(DE)capacitance sensor to monitor the growth of saccular aneurysms and deliver both the wall stress and geometric parameters.Based on the elastic growth theory together with the finite deformation analyses,the correlation between the real-time output capacitance of the DE sensor and the wall stress and/or geometry of an aneurysm is derived.Compared to clinic statistics and biomechanics simulations,the wall stress and geometric size may be used as combined indicators to assess the rupture risk of a saccular aneurysm.Numerical results show that an output relative capacitance of 30 indicates a high risk of rupture.Finally,the sensitivity and resolution of the DE sensor are proved adequately high for monitoring the growth state and evaluating the rupture risk of a saccular aneurysm.     

A robust hyper-elastic beam model under bi-axial normal-shear loadings

In this paper, a simple and robust constitutive model is proposed to simulate mechanical behaviors of hyper-elastic materials under bi-axial normal-shear loadings in the finite strain regime. The Mooney–Rivlin strain energy function is adopted to develop a two-dimensional (2D) normal-shear constitutive model within the framework of continuum mechanics. A motion field is first proposed for combined normal and shear deformations. The deformation gradient of the proposed field is calculated and then substituted into right Cauchy–Green deformation tensor. Constitutive equations are then derived for normal and shear deformations. They are two explicit coupled equations with high-level polynomial non-linearity. In order to examine capabilities of the developed hyper-elastic model, uniaxial tensile responses and non-linear stability behaviors of moderately thick straight and curved beams undergoing normal axial and transverse shear deformations are simulated and compared with experiments. Fused deposition modeling technique as a 3D printing technology is implemented to fabricate hyper-elastic beam structures from soft poly-lactic acid filaments. The printed specimens are tested under tensile/compressive in-plane and compressive out-of-plane forces. A finite element formulation along with the Newton–Raphson and Riks techniques is also developed to trace non-linear equilibrium path of beam structures in large defamation regimes. It is shown that the model is capable of predicting non-linear equilibrium characteristics of hyper-elastic straight and curved beams. It is found that the modeling of shear deformation and finite strain is essential toward an accurate prediction of the non-linear equilibrium responses of moderately thick hyper-elastic beams. Due to simplicity and accuracy, the model can serve in the future studies dealing with the analysis of hyper-elastic structures in which two normal and shear stress components are dominant.     

Application of kinetic theory to the analysis of high-temperature creep rupture of metals under complex stress (review)

This paper gives an analytical review of the results obtained using the kinetic theory of creep and creep rupture to analyze the creep rupture of metals under complex stress. Special note is made of the outstanding contribution of Soviet scientists L. M. Kachanov and Yu. N. Rabotnov, who introduced the concept of material damage and developed the fundamentals of the kinetic theory. Different versions of this theory are used in studies of Russian and foreign scientists. The possibility of applying the kinetic theory to model the deformation and fracture of metals under creep conditions using scalar, vector, and tensor damage parameters and their combinations is considered.     

Blood flow dynamics and fluid–structure interaction in patient‐specific bifurcating cerebral aneurysms

Hemodynamics plays an important role in the progression and rupture of cerebral aneurysms. The current work describes the blood flow dynamics and fluid–structure interaction in seven patient‐specific models of bifurcating cerebral aneurysms located in the anterior and posterior circulation regions of the circle of Willis. The models were obtained from 3D rotational angiography image data, and blood flow dynamics and fluid–structure interaction were studied under physiologically representative waveform of inflow. The arterial wall was assumed to be elastic, isotropic and homogeneous. The flow was assumed to be laminar, non‐Newtonian and incompressible. In one case, the effects of different model suppositions and boundary conditions were reported in detail. The fully coupled fluid and structure models were solved with the finite elements package ADINA. The vortex structure, pressure, wall shear stress (WSS), effective stress and displacement of the aneurysm wall showed large variations, depending on the morphology of the artery, aneurysm size and position. The time‐averaged WSS, effective stress and displacement at the aneurysm fundus vary between 0.17 and 4.86 Pa, 4.35 and 170.2 kPa and 0.16 and 0.74 mm, respectively, for the seven patient‐specific models of bifurcating cerebral aneurysms. Copyright © 2008 John Wiley & Sons, Ltd.     

Non‐Newtonian blood flow dynamics in a right internal carotid artery with a saccular aneurysm

Flow dynamics plays an important role in the pathogenesis and treatment of cerebral aneurysms. The temporal and spatial variations of wall shear stress in the aneurysm are hypothesized to be correlated with its growth and rupture. In addition, the assessment of the velocity field in the aneurysm dome and neck is important for the correct placement of endovascular coils. This work describes the flow dynamics in a patient‐specific model of carotid artery with a saccular aneurysm under Newtonian and non‐Newtonian fluid assumptions. The model was obtained from three‐dimensional rotational angiography image data and blood flow dynamics was studied under physiologically representative waveform of inflow. The three‐dimensional continuity and momentum equations for incompressible and unsteady laminar flow were solved with a commercial software using non‐structured fine grid with 283 115 tetrahedral elements. The intra‐aneurysmal flow shows complex vortex structure that change during one pulsatile cycle. The effect of the non‐Newtonian properties of blood on the wall shear stress was important only in the arterial regions with high velocity gradients, on the aneurysmal wall the predictions with the Newtonian and non‐Newtonian blood models were similar. Copyright © 2005 John Wiley & Sons, Ltd.     

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讨论由一类超弹性材料—Blatz-Ko材料所组成的薄壁圆管在内压力作用下平面有限变形问题,得到了管径变化与内压力之间的解析关系．     

Intra-aneurysmal blood flow based on patient-specific CT angiogram

To discuss the validity of the hemodynamic hypothesis of aneurysm rupture, we used a patient-specific, realistic aneurysm model to reveal the flow structure and wall shear stress distribution in two cases: one with an unruptured aneurysm and the other with a ruptured aneurysm. We used particle imaging velocimetry and laser Doppler velocimetry to measure velocity profiles of intra-aneurysmal flow. Both cases had a circulating flow along the aneurysm wall, although the second case had a recirculating zone only in the minimum phase. Differences in the wall shear stress profile may identify aneurysm rupture.     

生长对超弹性球壳变形和稳定性的影响

应用连续介质力学有限变形理论建立受内压作用不可压超弹性球壳大变形问题的力学模型, 且运用基于变形梯度张量极分解的弹性体积生长理论分析生长对不可压超弹性球壳变形和稳定性的影响. 通过对球壳变形与内压关系式的数值计算得到不同生长条件下球壳的变形曲线和应力分布曲线及由生长引起的残余变形和残余应力分布. 计算结果表明生长对球壳变形特性有明显的影响, 生长影响球壳可产生不稳定变形的临界壁厚和临界内压, 且在某些情况下可改变球壳的稳定性. 生长在球壳中可产生一定的残余变形和残余应力, 对球壳中的应力分布有一定的影响. 另外当生长的程度足够大时, 即便没有外力作用,球壳仅在生长引起的残余应力作用下也可产生不稳定变形.      

Creep rupture of specimens with random material properties

Possible sources of the observed scatter in creep deformation and rupture time are discussed. The scatter due to random material properties in creep is considered.A constitutive equation describing these random material properties is formulated. The rupture time of a specimen under constant load is calculated using Hoff s theory of ductile rupture. Rupture is shown to occur at finite elongation, in contrast to Hoff's original analysis.The probability distribution of the rupture time is determined with extremum value analysis and compared with experimentally observed ones.     

Acoustomechanical constitutive theory for soft materials

Acoustic wave propagation from surrounding medium into a soft material can generate acoustic radiation stress due to acoustic momentum transfer inside the medium and material, as well as at the interface between the two. To analyze acoustic-induced deformation of soft materials, we establish an acoustomechanical constitutive theory by com-bining the acoustic radiation stress theory and the nonlinear elasticity theory for soft materials. The acoustic radiation stress tensor is formulated by time averaging the momen-tum equation of particle motion, which is then introduced into the nonlinear elasticity constitutive relation to construct the acoustomechanical constitutive theory for soft materials. Considering a specified case of soft material sheet subjected to two counter-propagating acoustic waves, we demonstrate the nonlinear large deformation of the soft material and ana-lyze the interaction between acoustic waves and material deformation under the conditions of total reflection, acoustic transparency, and acoustic mismatch.     

一般大气环境下锈蚀钢筋混凝土梁的时变可靠度分析

根据一般大气环境下锈蚀钢筋混凝土梁中的钢筋截面损失时变模型和抗剪、抗弯承载力退化模型,建立了考虑其随机性的极限状态方程。基于概率守恒原理分析得到满足该极限状态方程的概率密度演化方程,并引入吸收边界条件,提出了梁时变可靠度的计算方法。以受对称集中荷载的锈蚀钢筋混凝土简支梁为例,展示了目标函数的概率密度演化过程,并讨论了配置不同直径箍筋和不同厚度保护层时的时变可靠度。结果表明,在保证梁具有足够初始抗剪强度和抗弯强度的前提下,适当增大保护层厚度和箍筋直径(具有相同配箍率)能延缓混凝土构件力学性能的退化。通过和100万次蒙特卡洛模拟结果的对比可知,选用本文方法能在以付出较小计算代价的前提下,获得计算精度良好的分析结果。     

Constitutive relation of viscoelastic dielectric elastomer

In this paper, we present a modified model describing the constitutive relation of viscoelastic dielectric elastomer (DE). The uniform uniaxial tension-recovery experiment was carried out at different stretching rates. Based on Yeoh hyper-elastic model, model-fitting approach is put forward to obtain the relationship between parameters of Yeoh model and stretching rate, thus the modified model was obtained. From the approximate relationship between harmonic motion and uniform reciprocating motion, the stress–strain curve in the recovery process was also identified through the hysteresis between stress and strain. The modified model, with concise form and evident physical concept, can describe the strong nonlinear behavior between deformation and mechanical stress of the material in a common stretching rate range (from 0.01s^?1 to 0.8s^?1 at least). The accuracy and reliability of the modified model was examined.     

考虑尺度效应的微梁静态弯曲数值分析

基于修正偶应力理论及表面弹性理论,本文提出了一种新的双曲线剪切变形梁模型,用于均匀微尺度梁的静态弯曲分析。该理论可以直接利用本构关系获得横向剪切应力,满足梁顶部和底部的无应力边界条件,避免了引入剪切修正因子。根据广义Young-Laplace方程建立了梁的内部与表面层的应力连续性条件,单一的变量场可以描述梁的位移模式。通过在位移场中考虑表面层厚度以及表面层的应力连续条件,可以使新模型能够更准确地预测微尺寸和表面能相关的尺度效应。通过Hamilton原理推导出了梁的控制方程和边界条件。应变能除了考虑经典弹性理论,还要考虑微结构效应和表面能。Navier-type的解析解适用于简支边界条件,而基于拉格朗日插值的微分求积法(DQEM)可以研究在不同边界条件下的力学响应。把该数值解与Navier方法得出的解析解作了对比,得出:微尺度梁在考虑表面能或微尺寸效应、不同载荷和梁高变化下的响应一致;当不考虑微结构相关性和表面能效应时,该模型退化为经典的欧拉梁模型。     

多孔Mooney-Rivlin材料矩形板的单向拉伸

本文利用不同可压超弹性材料大变形的Mooney-Rivlin应变能函数研究了含有多个微孔的矩形板在单向拉伸作用下的有限变形和受力分析。首先利用不可压条件得到了文中所给的含有某种对称性分布的多个微孔的矩形板的变形模式函数，其中所含的一个参数可由远离微孔的无穷远处的变形状态确定，另一个参可用最小势能原理导出变分近似解。文中详细分析了板中微孔（一个，三个和五个）随载荷作用的增长情况和微孔边缘应力的分布情况，并进行了比较。讨论了微孔的个数和排列方式，微孔的孔间距离等因素对微孔增长和应力分布的影响。     

动脉瘤内流场以及瘤体尺寸的影响的数值研究

采用计算流体动力学(CFD)数值模拟的方法,在周期性脉动速度入流条件下,建立刚性动脉瘤模型并研究了动脉瘤模型中流场的特征(速度、压力、壁面剪切应力)。得到了脉动入流一个周期内流场特征的变化规律,发现动脉瘤的后端有相当高的压力和壁面剪切应力,而且高压力和壁面剪切应力分布的位置几乎是固定的。探讨了不同动脉瘤尺寸对内部流场的影响,动脉瘤的直径与瘤体长度之比越大,瘤壁承受的剪切应力就越大,动脉瘤破裂的危险性就越高。     

Comparison between computational fluid dynamics,fluid–structure interaction and computational structural dynamics predictions of flow-induced wall mechanics in an anatomically realistic cerebral aneurysm model

Haemodynamically induced stress plays an important role in the progression and rupture of cerebral aneurysms. The current work describes computational fluid dynamics (CFD), fluid–structure interaction (FSI) and computational structural dynamics (CSD) simulations in an anatomically realistic model of a carotid artery with two saccular cerebral aneurysms in the ophthalmic region. The model was obtained from three-dimensional (3D) rotational angiographic imaging data. CFD and FSI were studied under a physiologically representative waveform of inflow. The arterial wall was assumed elastic or hyperelastic, as a 3D solid or as a shell depending on the type of modelling used. The flow was assumed to be laminar, non-Newtonian and incompressible. The CFD, FSI and CSD models were solved with the finite elements package ADINA. Predictions of velocity field and wall shear stress (WSS) on the aneurysms made using CFD and FSI were compared. The CSD model of the aneurysms using complete geometry was compared with isolated aneurysm models. Additionally, the effects of hypertensive pressure on CSD aneurysm models are also reported. The vortex structure, WSS, effective stress, strain and displacement of the aneurysm walls showed differences, depending on the type of modelling used.