Elastic Instability of Pseudo-Elastic Rubber Balloons

Elastic instability for the inflation and deflation of a thin-walled spherical rubber balloon is examined within the framework of finite pseudo-elasticity. When a spherical rubber balloon is inflated, it is subject to a complex deformation after a pressure maximum has been obtained. One part of the balloon is lightly stretched while the remainder becomes highly stretched. So an aspherical deformation is observed after the initial spherical inflation. A pseudo-elastic strain energy function including a damage variable which may model the loading, unloading and reloading of rubber is used. The balloon is idealized as an elastic membrane and the inflation, deflation and re-inflation of the balloon is described in detail. Instability of solutions is discussed through energy comparison. Furthermore, the effect of temperature is discussed with a thermo-hyperelastic model and the residual strain is analyzed with a pseudo-elastic strain energy function including a residual strain variable.     

How to handle the inelastic collapse of a dissipative hard-sphere gas with the TC model

The inelastic hard sphere model of granular material is simple, easily accessible to theory and simulation, and captures much of the physics of granular media. It has three drawbacks, all related to the approximation that collisions are instantaneous: 1) The number of collisions per unit time can diverge, i.e. the “inelastic collapse” can occur. 2) All interactions are binary; multiparticle contacts cannot occur and 3) no static limit exists. We extend the inelastic hard sphere model by defining a duration of contact t _c such that dissipation is allowed only if the time between contacts is larger than t _c . We name this generalized model the TC model and discuss it using examples of dynamic and static systems. The contact duration used here does not change the instantaneous nature of the hard sphere contacts, but accounts for a reduced dissipation during “multiparticle contacts”. Kinetic and elastic energies are defined as well as forces and stresses in the system. Finally, we present event-driven numerical simulations of situations far beyond the inelastic collapse, possible only with the TC model.     

Coating of intravascular balloon with paclitaxel prevents constrictive remodeling of the dilated porcine femoral artery due to inhibition of intimal and media fibrosis

Here we investigated how a coating of intravascular balloon with paclitaxel (drug-coated balloon; DCB, Freeway?) impacted porcine peripheral artery vascular function and remodeling. Domestic swine (n = 54) underwent percutaneous overstretch balloon dilation of femoral and iliac arteries, controlled by angiography and optical coherence tomography (OCT). Paclitaxel tissue uptake was measured at 1 h and 1, 3, and 9 days post-dilation. At these time-points and at 32 ± 2 days, vascular function of the dilated arteries was assessed using the organ chamber model. Neointimal growth and remodeling indices were determined using OCT and histology at 32 ± 2 days. Intima and media fibrosis were quantified by picrosirius red staining. Post-inflation femoral artery tissue drug levels were 460 ± 214, 136 ± 123, 14 ± 6, and 0.1 ± 0.1 ng/mg at 1 h and 1, 3, and 9 days, respectively. Compared to plain balloon, Freeway? resulted in a significantly smaller neointimal area (P < 0.05), less tunica intima (8.0 ± 5.4 vs 14.2 ± 4.7 %) and media fibrosis (15.6 ± 7.7 vs 24.5 ± 5.4 %), and less femoral artery constrictive remodeling (remodeling index: 1.08 ± 0.08 vs 0.94 ± 0.08). The DCB was associated with significantly increased vasoconstrictor tone and endothelium-dependent vasodilation impairment shortly after post-overstretch injury. Overall, DCB dilation of peripheral arteries resulted in high drug uptake into arterial tissue. Compared with the plain balloon, the DCB was associated with decreased vessel wall fibrosis after balloon overstretch injury, and reduced degrees of constrictive remodeling and neointimal hyperplasia.     

Local and overall flow in composites predicted by micromechanics

Rate-dependent inelastic flow in metal matrix composites subjected to multiaxial stress states is quantified by flow surfaces, which are geometrically analogous to yield surfaces. The definition of flow is important because the most meaningful definition from a theoretical viewpoint, dissipation, is not measurable in the laboratory. Inelastic power is measurable, but differs from the dissipation due to residual stresses and evolution of the material state. Since experiments are necessary for development and validation of models, both definitions are important and considered here. The relationship between local flow in the matrix and overall flow of the composite is explored using finite element and generalized method of cells micromechanical analyses. The loci of flow surfaces in the axial–transverse and transverse–transverse stress planes are plotted. At the threshold, the overall flow surface is the intersection of all the local flow surfaces. Beyond the threshold, the intersection of all the local flow surfaces is smaller than the overall flow surface and differences between the dissipation and inelastic power are notable. Most importantly, the directions of the overall inelastic strain rate vectors are generally not normal to the overall surface of constant dissipation after the material state has begun to evolve. Thus, an associative macroscale continuum model will be, at best, approximate. Interestingly, local flow surfaces beyond the threshold are not necessarily convex when plotted in the overall stress plane. This is due to the existence of residual stresses. In addition, the generalized method of cells was found to accurately estimate the inner and outer envelopes of the local flow surface cluster with a surprisingly small number of subcells.     

Aspects of Modeling and Computer Simulation of Soft Tissues: Applications to Arterial Walls

For treating arterial stenosis, caused by e.g. artherosclerotic plaque, the so‐called balloon‐dilation (c.f. angioplasty) is employed in most cases. Herein, high internal pressure (3‐12 bar) is applied to the infected artery. During this process damage effects are induced in the arterial wall which cause the arterial lumen to remain increased after removing the balloon. Therefore, computer simulations of arterial walls require the material modeling of these damage effects. In this paper the anisotropic damage model introduced in Balzani, Schröder and Gross [3], see also Balzani, Schröder and Gross [4], is extended in order to obtain a damage model providing a referential damage state different from the referential deformation state. This is necessary because the artery is assumed to be undamaged for deformations within the physiological range. In this we consider a numerical example wherein an artery is overstretched in order to give an indication of the performance of the model. For this purpose the proposed damage model is applied to the polyconvex stored energy introduced in Schröder and Neff [14].     

Properties of nylon 12 balloons after thermal and liquid carbon dioxide treatments

Critical design attributes of angioplasty balloons include the following: tear resistance, high burst pressures, controlled compliance, and high fatigue. Balloons must have tear resistance and high burst pressures because a calcified stenosis can be hard and nominal pressures of up to 16 atm can be used to expand the balloon. The inflated balloon diameter must be a function of the inflation pressure, thus compliance is predictable and controlled. Reliable compliance is necessary to prevent damage to vessel walls, which may be caused by over-inflation. Balloons are often inflated multiple times in a clinical setting and they must be highly resistant to fatigue. These design attributes are dependent on the mechanical properties and polymer morphology of the balloon. The effects of residual stresses on shrinkage, crystallite orientation, balloon compliance, and mechanical properties were studied for angioplasty nylon 12 balloons. Residual stresses of these balloons were relieved by oven heat treatment and liquid CO₂ exposure. Residual stresses were measured by quantifying shrinkage at 80 °C of excised balloon samples using a dynamic mechanical analyzer. Shrinkage was lower after oven heat treatment and liquid CO₂ exposure compared to the as-received balloons, in the axial and radial directions. As-received, oven heat treated, and liquid CO₂-exposed balloon samples exhibited similar thermal properties (T_g, T_m, X_t). Crystallite orientation was not observed in the balloon cylindrical body using X-ray scattering and polarized light microscopy, which may be due to balloon fabrication conditions. Significant differences were not observed between the stress–strain curves, balloon compliance, and average burst pressures of the as-received, oven heat treated, and liquid CO₂-exposed balloons.     

Dialysis access venous stenosis: Treatment with balloon angioplasty 30‐second vs. 1‐minute inflation times

Percutaneous balloon angioplasty is the standard of care in the endovascular treatment of dialysis access venous stenosis. The significance of balloon inflation times in the treatment of these stenoses is not well defined. Our objective was to examine the outcomes of 30‐second vs. 1‐minute balloon inflation times on primary‐assisted patency of arteriovenous fistulae and grafts. Using a prospectively collected vascular access database, we identified a total of 75 patients referred for access dysfunction during a 5‐year period. These patients received 223 interventions (178 with 30‐second inflations and 45 with 1‐minute inflations). We compared primary‐assisted patency during the subsequent 9 months across groups defined by inflation times. Demographics and baseline characteristics were similar across groups. Immediate technical success and patency in the first 3 months were similar across groups (hazard ratio [HR] = 0.86; 95% confidence interval [CI]: 0.34–2.20). After 3 months, however, a 1‐minute inflation time was associated with greater incidence of access failure (adjusted HR [aHR] = 1.74; 95% CI: 1.09–2.79). Other predictors of access failure included age over 60 (aHR = 1.02; 95% CI: 1.01–1.04), central location of the lesion (aHR = 2.49; CI: 1.27–4.89), and three or more prior procedures (aHR 2.48; CI: 1.19–5.16). Our data suggest that shorter balloon inflation times may be associated with improved longer term access patency, although the benefit was not observed until after 3 months. Given the increasing demands of maintaining access patency in the era of the National Kidney Foundation Kidney Disease Outcomes Quality Initiative and Fistula First, the role of angioplasty times requires further study.     

A damage-plasticity interface approach to the meso-scale modelling of concrete subjected to cyclic compressive loading

Concrete is characterised by stiff inclusions in a soft matrix separated by weak interfacial transition zones (ITZs). Subjected to cyclic loading, this material exhibits a strongly nonlinear response, which is characterised by the occurrence of hysteresis loops. Furthermore, for cyclic loading, failure may occur before the equivalent strength for monotonic loading is reached. The present work investigates, whether the occurrence of permanent displacements in different phases of the meso-structure of quasi-brittle heterogeneous materials, such as concrete, leads to damage evolution during repeated loading.A new three-dimensional interface model based on a combination of damage mechanics and the theory of plasticity is proposed, which allows one to control the ratio of permanent and total inelastic displacements. The model is based on only a few material parameters, which can be directly determined by experiments.The interface model is applied to the plane-stress analysis of an idealised heterogeneous material with cylindrical inclusions and ITZs subjected to cyclic compressive stresses.     

球囊扩张式血管支架介入对弯曲血管的生物力学损伤研究

构建了球囊扩张式血管支架介入系统的非线性有限元模型,考虑了血管斑块类型对其本构模型的影响,分析了A型与B型血管支架在血管狭窄率-24%、40%、50%,曲率半径-6 mm、10 mm、20 mm,狭窄血管的壁面应力分布规律,研究了血管支架构型、狭窄血管几何参数和血管生物力学损伤的关系。数值分析结果表明,血管壁面应力随着狭窄率的增加而显著升高,随着血管曲率半径的增加而下降相对平缓;但是,扩张加载阶段的血管壁面应力显著高于卸载阶段,易于引起血管斑块的脆性断裂引起血管生物力学损伤。由于A型血管支架相对于B型血管支架具有纵向柔顺性更优的联接筋构型,导致A型血管支架引起的血管壁面应力低于B型支架,因而降低了A型血管支架对于血管的生物力学损伤。     

Evaluation of Stresses in Reinforced-Concrete Beam Elements,Their Strength,and Crack Resistance

We develop a procedure for the evaluation of strength and crack resistance of reinforced-concrete beam elements based on the approaches of fracture mechanics. A model for the numerical analysis of stresses is proposed and the formulas for finding normal stresses in the reinforcement and compressed concrete fibers are deduced by taking into account the inelastic zones in the vicinity of the crack tip. The established relations are checked experimentally and compared with the formulas proposed by SNiP 2.03.01-84.     

Fatigue and inelasticity of metals under nonuniform stressed state

Based on the review of the available publications and the findings of the original studies, the author demonstrates that with cyclic stresses in the maximum-stressed surface layer being equal the inelastic strains in the presence of stress gradients are smaller than those in the material under uniform stressed state. As a result, there is a difference in the cyclic stress–strain diagrams between these cases. An equation for the cyclic stress–strain diagram is put forward, which allows for the stress gradient effect. A model is substantiated, which provides an explanation for the difference between fatigue strength characteristics under uniform and nonuniform stressed states.     

An integral equation analysis of inelastic shells

This paper presents an integral equation approach for the analysis of deformation and stresses in inelastic shells of arbitrary shape subjected to arbitrary loading. The proposed mathematical model is completely consistent and is derived by transforming the three-dimensional equations from the Cartesian to the appropriate curvilinear coordinates of the shell. Appropriate kinematic assumptions for the dependence of the displacements on the thickness coordinate of the shell and assumptions regarding the loads at the ends are introduced consistently in the model to take advantage of the thinness of the shell. Numerical implementation and numerical results are presented for elastic and inelastic deformation of axisymmetric shells subjected to axisymmetric loading. These results are compared against exact elasticity, Love-Kirchoff model analysis of inelastic cylindrical shells and finite element solutions.     

冠脉血管支架介入耦合系统力学行为数值模拟研究

针对冠脉支架植入术后引起的血管内再狭窄问题,开展了冠脉支架介入耦合系统力学行为的数值模拟研究。基于Ogden非线性弹性理论,构建了冠脉血管和动脉粥样硬化斑块的超弹性本构模型。通过非线性有限元法,建立了冠脉支架与狭窄血管的耦合作用模型,研究了冠脉支架在经历压握收缩、压握卸载、球囊扩张与球囊收缩等介入过程后的体内扩张性能,分析了冠脉支架的介入对狭窄血管损伤及再狭窄的力学影响因素。对比分析了S型支架和N型支架介入后狭窄冠脉血管的生物力学响应,数值计算结果表明：狭窄冠脉血管在支架支撑体波峰处存在较高的应力梯度,而且由于2种支架联接筋结构的类似性,血管内膜与斑块的应力分布规律一致。但是,N型支架的径向回弹率与轴向短缩率均小于S型支架,导致了更高的狭窄血管壁面峰值应力和应力梯度,更易于引起冠脉血管损伤造成血管内再狭窄。综上,该文提出的冠脉支架介入耦合系统力学模型,对于优化支架结构、抑制冠脉血管再狭窄问题,提供了重要的理论依据和临床参考。     

Multi-axial thermo-mechanical analysis of power plant components from 9–12% Cr steels at high temperature

The aim of this paper is to analyze local changes of stress and strain states in a power plant component under a transient thermal environment. A robust constitutive model is developed to describe inelastic behavior of advanced 9–12% Cr heat-resistant steels at high temperature and in a multi-axial stress state. The model includes the constitutive equation for the inelastic strain rate tensor, the evolution equation for a tensor-valued state variable to reflect hardening/recovery processes and two evolution equations for two scalar-valued variables that characterize softening and damage states. The model is calibrated against experimental creep curves and verified for inelastic responses under different isothermal and non-isothermal loading paths. Steam temperature and loading profiles that correspond to an idealized start-up, holding and shut-down sequence of a power plant component are assumed. To estimate the thermal fields, transient heat transfer analysis is performed. The results are applied in the subsequent structural analysis using the developed inelastic constitutive model. The outcome is a multi-axial thermo-mechanical fatigue loop which can be used for damage assessment.     

Influence of autofrettage on metal matrix composite reinforced gun barrels

Advanced materials are considered as candidates for the replacement of traditional gun barrel steel with the hope that weapons as durable as steel but at a fraction of the weight will be developed. Through an analytical model that simulates the effects of autofrettage on a cylindrical gun barrel, the resultant compressive residual stresses are quantified, and different materials examined as to their possible resistance to fracture under repeated internal pressure loads. This study investigates a traditional low-alloy gun steel, a high temperature SiC/titanium-alloy metal matrix composite, as well as various hybrid combinations of these materials, for their ability to develop the necessary residual stress and inelastic strain states necessary for durability. It is discovered that a hybrid composite comprised of low-alloy gun steel on the inner region of the gun barrel and circumferentially wound SiC/Ti–24Al–11Nb on the outer region can still exhibit the same compressive residual stress (and corresponding inelastic strains) seen in homogeneous steel barrels, but with a weight savings of up to 37%, while maintaining the original barrel dimensions.     

Towards causally cohesive genotype–phenotype modelling for characterization of the soft-tissue mechanics of the heart in normal and pathological geometries

A scientific understanding of individual variation is key to personalized medicine, integrating genotypic and phenotypic information via computational physiology. Genetic effects are often context-dependent, differing between genetic backgrounds or physiological states such as disease. Here, we analyse in silico genotype–phenotype maps (GP map) for a soft-tissue mechanics model of the passive inflation phase of the heartbeat, contrasting the effects of microstructural and other low-level parameters assumed to be genetically influenced, under normal, concentrically hypertrophic and eccentrically hypertrophic geometries. For a large number of parameter scenarios, representing mock genetic variation in low-level parameters, we computed phenotypes describing the deformation of the heart during inflation. The GP map was characterized by variance decompositions for each phenotype with respect to each parameter. As hypothesized, the concentric geometry allowed more low-level parameters to contribute to variation in shape phenotypes. In addition, the relative importance of overall stiffness and fibre stiffness differed between geometries. Otherwise, the GP map was largely similar for the different heart geometries, with little genetic interaction between the parameters included in this study. We argue that personalized medicine can benefit from a combination of causally cohesive genotype–phenotype modelling, and strategic phenotyping that captures effect modifiers not explicitly included in the mechanistic model.     

Some theoretical results about second-order work,uniqueness, existence and controllability independent of the constitutive equation

When they are studied as continuum media, granular materials and other soils and rocks exhibit a complex behavior. Contrary to metals, their isotropic and deviatoric behavior are coupled. This implies some mathematical difficulties concerning boundary-value problems solved with constitutive equations modelling the salient features of such geomaterials. One of the well-known consequences is that the so-called second-order work can be negative long before theoretical failure occurs. Keeping this in mind, the starting point of this work is the pioneering and illuminating work of Nova (1994), who proved that using an isotropic hardening elasto-plastic model not obeying the normality rule, it is possible to exhibit either loss of uniqueness or loss of existence of the solution of a boundary-value problem as soon as the second-order work is negative. Because the geomaterial behavior is quite difficult to model, in practice many different constitutive equations are used. It is then important to study the point raised by Nova for other constitutive equations. In this paper, his result is generalized for any inelastic rate-independent constitutive equation. Similarly the link between localization and controllability proved by Nova (1989) is extended to some extent to a general inelastic model.     

Some theoretical results about second-order work, uniqueness, existence and controllability independent of the constitutive equation

When they are studied as continuum media, granular materials and other soils and rocks exhibit a complex behavior. Contrary to metals, their isotropic and deviatoric behavior are coupled. This implies some mathematical difficulties concerning boundary-value problems solved with constitutive equations modelling the salient features of such geomaterials. One of the well-known consequences is that the so-called second-order work can be negative long before theoretical failure occurs. Keeping this in mind, the starting point of this work is the pioneering and illuminating work of Nova (1994), who proved that using an isotropic hardening elasto-plastic model not obeying the normality rule, it is possible to exhibit either loss of uniqueness or loss of existence of the solution of a boundary-value problem as soon as the second-order work is negative. Because the geomaterial behavior is quite difficult to model, in practice many different constitutive equations are used. It is then important to study the point raised by Nova for other constitutive equations. In this paper, his result is generalized for any inelastic rate-independent constitutive equation. Similarly the link between localization and controllability proved by Nova (1989) is extended to some extent to a general inelastic model.     

3D Residual Stress Field in Arteries: Novel Inverse Method Based on Optical Full‐field Measurements

Abstract: Arterial tissue consists of multiple structurally important constituents that have individual material properties and associated stress‐free configurations that evolve over time. This gives rise to residual stresses contributing to the homoeostatic state of stress in vivo as well as adaptations to perturbed loads, disease or injury. The existence of residual stresses in an intact but load‐free excised arterial segment suggests compressive and tensile stresses, respectively, in the inner and outer walls. Accordingly, an artery ring springs open into a sector after a radial cut. The measurement of the opening angle is commonly used to deduce the residual stresses, which are the stresses required to close back the ring. The opening angle method provides an average estimate of circumferential residual stresses but it gives no information on local distributions through the thickness and along the axial direction. To address this lack, a new method is proposed in this article to derive maps of residual stresses using an approach based on the contour method. A piece of freshly excised tissue is carefully cut into the specimen, and the local distribution of residual strains and stresses is determined from whole‐body digital image correlation measurements using an inverse approach based on a finite element model.