Computation of Residual Stress Distributions and Opening Angles of 3D Patient-Specific Arterial Walls

A method to incorporate residual stresses in arteries, based on the assumption of smooth transmural stress measure distributions with slight slopes, is discussed. The artery is first loaded with the internal blood pressure without considering any residual stresses. With help of suitable stress invariants and volume averaged mean values on specific sectors domains, the stress gradient is iteratively decreased in radial direction. In order to assess the accuracy of the method, a three-dimensional patient-specific arterial geometry, suffering from atherosclerosis, is considered. These was reconstructed from ultrasound based medical imaging, see [2]. Moreover, the radially sliced arteries can be loaded exclusively with the calculated residual stresses in order to predict the opening angle. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of Anisotropic Damage in Arterial Walls

In a certain range of overexpansion arterial walls are characterized by an orthotropic elastic material behavior. Due to different stabilities of the helically arranged fibers, i.e. breakage of collagen crosslinks between the fibers, damage effects are observed in experiments. Because of the fibrous composition it is assumed that damage mainly occurs in the fiber direction. The proposed damage model is extended to arterial wall applications by introducing a referential damage state. The damage approach is applied to a polyconvex model for the hyperelastic behavior of arteries in order to obtain a materially stable model, which guarantees the existence of solutions of the underlying boundary value problem. The performance of the proposed model is presented in a numerical example, where the overexpansion of an atherosclerotic artery is simulated. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermal Residual Stresses and Triaxiality Measures

High performance ceramics have found their way into many highly challenging engineering tasks. For example silicon nitride is one of the best choices, if a material for demanding applications like metal forming and cutting is required. Due to the brittle nature of these hard and strong materials it is useful to know about thermal residual stresses, which can arise during the sintering process. In order to gain insight into the material behaviour, a single grain inclusion is exposed to thermal loads. Due to thermal mismatch, it undergoes a residual stress and strain field. The geometry of the model and the material data are motivated by the properties of silicon nitride. The stress fields are analyzed by three different measures for stress triaxiality. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical Calculation of Fiber Orientation in Three-Dimensional Arterial Walls

In this contribution an approach for the fiber reorientation in three-dimensional arterial walls is presented. In detail the load-bearing capacity of the tissue is increased by re orienting the fibers with respect to the principal stresses, cf. [1]. The improved fiber reorientation algorithm is combined with the polyconvex nonlinear anisotropic material model presented in [3]. The results of a three-dimensional finite element simulation, where the reorientation approach is applied to a short segment of a patient-specific arterial geometry, are presented. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical Simulations of Arterial Walls Based on IVUS-Data

Atherosclerosis has become one of the most frequent causes of death in the last decades. So the analysis and improvement of corresponding medical treatments, e.g., balloon-angioplasty or stenting, are significant tasks in the fields of biomechanics and biomedical engineering. One important component of the simulation of arterial walls, especially of atherosclerotically degenerated ones, is the knowledge of their anatomical and physiological composition. The intravascular ultrasound and the interpretation by the Virtual Histology provide cross-sectional images of the diseased arterial walls where the different components are characterized by color-coding. The topic of this contribution is the 3D reconstruction and discretization of the artery using these color-coded images and the biplane angiography. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

玻壳成型过程诱导残余应力的数值预测

建立了玻壳压制成型固化过程中残余应力预测的数值模拟模型,采用平行平板间玻璃熔体的固化问题来描述成型过程中残余应力形成的机理,并假定材料为热流变简单粘弹性材料．基于板壳理论,将产品视为平板单元的组合,并采用有限元法来求解,这种方法可以象全三维计算一样一层层地计算残余应力,非常适合复杂形状的薄压制成型产品．最后通过实验比较验证了所提出的模型和方法．     

Adjustment of Residual Stresses in Unsymmetric Fiber-Reinforced Composites Using Genetic Algorithms

During the manufacturing process of multilayered fiber-reinforced composites with variable fiber orientations, residual stresses build up in these composites due to the directional expansion of single unidirectionally reinforced layers. Depending on the laminate lay-up, the inhomogeneous residual stresses, which are caused by thermal effects, moisture absorption, and chemical shrinkage, can lead to large multistable out-of-plane deformations. Instead of avoiding these curvatures, they can be advantageously used for technical applications following the near-net-shape technology. In order to adjust the deformations to the technical requirements, genetic algorithms in combination with a nonlinear calculation method have been developed, which can purposefully adapt the laminate lay-up depending on the loading and process parameters.     

The Sensitivity of Residual Stresses of Cross-Ply Laminates to Manufacturing and Material Parameters

By using a finite-element model elaborated, the sensitivity of residual stresses of polyester/glass cross-ply laminates to manufacturing and material parameters is investigated. The development of residual stresses in the laminates and the significance of the parameters for the problem are discussed. It is found that the main attention in calculating residual stresses should be focused on the properties of resin, which must be measured with care. The most important parameters related to the resin are, of course, its stiffness, thermal expansion, and chemical shrinkage, while the properties of fibers can be obtained from material handbooks with a sufficient accuracy. In curing a thin laminate in an autoclave, the simulation of chemical reactions and the parameters needed in thermal analysis are quite insignificant, because, in practice, the autoclave temperature and the properties of the mold determine the laminate temperature history.     

关于某些多边形积的剩余有限性

讨论嵌入子群是循环群的有限p-群的多边形积,得到了多边形积为剩余有限的一个充分条件.     

关于某些多边形积的剩余有限性

讨论嵌入子群是循环群的有限p-群的多边形积,得到了多边形积为剩余有限的一个充分条件.     

On the Regularity of Stresses in the Closed Domain for the Linear Theory of Elasticity

The article deals with the estimates of the first derivatives of the solutions of the system L(u) u + ( + )(u) = –f(x). The solutions are fixed at the boundary u| = 0. The estimates are obtained in the whole closed domain in terms of the right-hand term f in a certain strong norm. If the norm of f in l ₂ is sufficiently small as compared to its strong norm, one can obtain estimates in an explicit form.     

On the Sensitivity of Transient Elastic Stresses in a Solid to the Form of Surface Loading

This work is an extension of studies made by Blowers (1969)of transient stresses induced in turbine blades by high speedimpact of water-drops. A uniform surface pressure was assumedover the impact area, but this seems very dubious in real situations.In this paper two extreme forms of surface loading are considered.Blowers' results for a uniform pressure loading are comparedand contracted with results for a delta function ring pressureloading, It is seen that all singularities for the delta functioncase are an order of magnitude sharper than the Blowers singularities.Since most of the elastic distortion energy is concentratedin these regions, this leads to significant differences in thesurface damage in the two cases. Since any form of loading will affect the concentration of elasticdistortion energy, the results indicate that the nature of theloading should be considered in all studies of erosion.     

一类多重循环群的剩余有限性质

设A是秩为n(n≥2)的自由Abel群,A的自同构群Aut(A)= GL(n,Z).对整数m,取 α =(0 1 0…0 0 0(………)(…………)0 0 0…0 1 1 0…0 m)∈ Aut(A).记Γm(n)=A(×)〈α〉,则它是一个2元生成的多重循环群.本文给出了 Γm(n)的准确的剩余有限性质.     

On Residual Nilpotence of Projective Crossed Modules

Abstract

Let F be a free group, (M,?, F) a non-aspherical projective F-crossed module. We prove that the action of Coker (?) on Ker (?) is faithful. Also we show that if (M,?, F) is a residually nilpotent crossed module, then Coker (?) is a residually nilpotent group. As a corollary, we get an alternative proof of Conduche's translation of Whitehead's asphericity conjecture in terms of residual nilpotence of certain crossed modules.     

On the Residual Finiteness of Outer Automorphisms of Hyperbolic Groups

We show that every virtually torsion-free subgroup of the outer automorphism group of a conjugacy separable hyperbolic group is residually finite. As a result, we are able to prove that the group of outer automorphisms of every finitely generated Fuchsian group and of every free-by-finite group is residually finite.     

On the Visualization of Patient Specific Arterial Geometries Using the Virtual Histology

The simulation of a balloon–angioplasty (clinical treatment of atherosclerotically degenerated arteries) requires information of the anatomical and physiological composition of the arterial wall. The intravascular ultrasound and the interpretation by a virtual histology provide cross–sectional images of the diseased arterial walls where the different components are characterized by color–coding. Using these information and the reconstruction of the vessel path from biplane angiography the patient specific data are visualized and discretized. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

有限域上幂剩余正规元的存在性

GF(q)是q个元的有限域,q是素数的方幂,n是正整数,GF(q~n)为GF(q)的n次扩张.用指数和估计的方法给出了3种情形下幂剩余正规元存在的充分条件,即(1)GF(q~n)中存在元ξ为GF(q)上的幂剩余正规元;(2)GF(q~n)中存在元ξ与ξ~(-1)同时为GF(q)上幂剩余正规元;(3)对GF(q~n)~*中任意给定的非零元a和b,GF(q~n)中存在元ξ与ξ~(-1)同时为GF(q)上d次幂剩余正规元,且满足Tr(ξ)=a,Tr(ξ~(-1))=b.