Ⅰ阶梯度损伤理论

从热力学基本定律出发,将应变张量、标量损伤变量、损伤梯度作为Helmholtz自由能函数的状态变量,利用本构泛函展开法在自然状态附近作自由能函数的Taylor展开,未引入附加假设,推导出Ⅰ阶梯度损伤本构方程的一般形式．该形式在损伤为0时可退化为线弹性应力-应变本构方程,在损伤梯度为0时可退化为基于应变等效假设给出的线弹性局部损伤本构方程．一维解析解表明,随着应力增大,损伤场逐步由空间非周期解变为关于空间的类周期解,类周期解的峰值区域形成局部化带．局部化带内的损伤变量将不同于局部化带外的损伤变量,由此可以反映出介质的局部化特征．损伤局部化并不是与损伤同时发生,而是在损伤发生后逐渐显现出来,模型的局部化机制开始启动;损伤局部化的宽度同内部特征长度成正比．     

From Damage to Delamination

Delamination models are derived as the limits of models for partial isotropic volume damage via dimension reduction. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Damage Localization of Carbon-Fibre-Reinforced Plastic Plates

Due to increasing application of light weight structures such as carbon-fibre-reinforced plastics well-known procedures for the examination of components are not always applicable because of inadequate efforts or costs. Therefore, the development of a complementary system is suggested which allows for detecting damages of the structure. A new wave migration model enables to determine the damage location for non-isotropic plates. The method is based on the propagation of waves reflected at the damage. Piezo-electric sensors capture the strain caused by the propagating wave. The evaluation and processing of the signals of at least four sensors allow for the calculation of the damage location from the runtime of the signals. In the case of non-isotropic material the shape of the wave front has to be known for the structure under investigation. These shapes can be obtained for example experimentally due to measurement and monitoring of the wave propagation by a laservibrometer or analytically by calculating this shapes using classical laminate and plate theory. Experiments show that the model indicates the damage location reliably. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Damage processes coupled with phase separation in elastically stressed alloys

In micro-electronic materials such as solder alloys, phase-separation and coarsening as well as damage phenomena occur at the same time and influences each other. In this note, a unifying model which couples multi-component Cahn-Hilliard systems with elasticity and uni-directional damage processes is presented. We outline the equations and their initial-boundary conditions in a classical setting and cite some existence results for weak solutions recently proved in [8, 9]. The damage is assumed to be incomplete, i.e. the maximal damaged material parts still feature elastic properties. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Damage models for multi-component systems

A series system of n components is subject to a damage process. The damage to each component is cumulative and when it exceeds a certain threshold the component, and hence the device, fails. For various optimality criteria related to system lifetime and system reliability, we find the optimal allocation of resources among the components where the total resources are limited and the allocation of the resources determines the threshold level of each component. Various inventory-type applications are noted.     

考虑损伤的修正梯度弹性理论

梯度弹性理论在描述材料微结构起主导作用的力学行为时具有显著优势,将其与损伤理论相结合,可在材料破坏研究中考虑微结构的影响.基于修正梯度弹性理论,将应变张量、应变梯度张量和损伤变量作为Helmholtz自由能函数的状态变量,并在自然状态附近对自由能函数作Taylor展开,进而由热力学基本定律,推导出修正梯度弹性损伤理论本构方程的一般形式.编制有限元程序,模拟土样损伤局部化带的发展演化过程.结果表明,修正梯度弹性损伤理论消除了网格依赖性;损伤局部化带不是与损伤同时发生,而是在损伤发展到一定程度后再逐渐显现出来.     

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)     

Damage and fracture behavior in dynamic tension tests: Modelling and numerical simulations

The continuum damage model is based on a general thermodynamic framework for the modeling of rate and temperature dependent behavior of anisotropically damaged elastic-plastic materials subjected to fast deformation. The introduction of damaged and fictitious undamaged configurations allows the definition of damage tensors and the corresponding free energy functions lead to material laws affected by damage and temperature. The damage condition and the corresponding damage rule strongly depend on stress triaxiality. Furthermore, the rate and temperature dependence is reflected in a multiplicative decomposition of the plastic hardening and damage softening functions. The macro crack behavior is characterized by a triaxiality dependent fracture criterion. The continuum damage model is implemented into LS-DYNA as user defined material model. Corresponding numerical simulations of unnotched and notched tension tests with high strain rates demonstrate the plastic and damage processes during the deformation leading to final fracture numerically predicted by an element erosion technique. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

具损伤压电智能层合板的非线性主动控制和损伤监测

基于Hamilton原理、高阶剪切变形板理论、von Krmn型几何非线性应变-位移关系以及应变能等效原理,考虑压电层的质量和刚度及复合材料层内的损伤效应,建立了具损伤压电智能层合板的非线性运动方程．采用耦合正、逆压电效应的负速度反馈控制原理,形成闭环控制回路,实现了对压电智能层合板的主动控制和损伤监测．数值计算中,以四边简支面内不可动的层合矩形板为例,讨论了压电层位置对振动控制的影响,以及损伤程度和损伤位置对传感层输出电压的影响,提出一种损伤监测的方法．     

A SimpleModel for Anisotropic Damage with Applications to Soft Tissues

Arteries are reinforced by helically arranged collagen fibers and posses orthotropic elastic properties. In this paper a polyconvex anisotropic energy is used in order to guarantee the existence of minimizers for the purely elastic boundary value problem. Anisotropic discontinuous damage effects, which are induced by decreasing stiffness of particular fibers, are observed in a certain range of overexpansion. A simple thermodynamical consistent anisotropic damage model is constructed, basing on the assumption that damage mainly takes place in the fiber directions as a result of breakage of collagen cross‐links.Finally a cycled overexpansion of a test material from an artery is analyzed in order to show the main characteristics of the proposed model. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

混凝土材料的粘塑性损伤本构模型

基于不可逆热力学,引入运动硬化、等向硬化和损伤内变量,构造了相应的自由能函数和流动势函数,推导出了混凝土材料的粘塑性损伤本构模型．数值模拟的结果表明,该模型能够避开屈服面和破坏准则的基本假设来描述混凝土材料的以下特性:压缩载荷作用下的体积膨胀现象;应变率敏感性;峰值后由损伤和破坏引起的应力软化和刚度退化现象A·D2由于此模型避开了根据各种变形阶段选择与其相应的本构模型的繁琐计算,因此更便于纳入复杂工况下应力分析有限元程序中．     

Relaxed Incremental Variational Formulation for Damage in Fiber-Reinforced Materials

An incremental variational formulation for damage at finite strains is proposed based on the classical continuum damage mechanics. Since loss of convexity is obtained at some critical deformations a relaxed incremental stress potential is constructed which convexifies the original non-convex problem. The resulting model can be interpreted as the homogenization of a micro-heterogeneous material bifurcated into a strongly and weakly damaged phase at the microscale. A one-dimensional relaxed formulation is derived and based thereon, a model for fiber-reinforced materials is given. Finally, some numerical examples illustrate the performance of the model. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of Damage Hysteresis in Soft Biological Tissues

Arterial lumen reductions result in hypertension and possibly rupture of plaque deposits as a consequence of atherosclerotic degeneration which can finally cause a heart attack or a stroke. Hence, therapeutical treatments such as balloon angioplasty and stenting are required. The aim of this work is to propose a new model for the softening hysteresis observed in overstretched arterial tissues and related computer simulations. The physiological loading domain is described by a purely elastic polyconvex anisotropic strain-energy function, which is decoupled into an isotropic part related to the non-collagenous matrix material, and into a transversely isotropic part related to the embedded (collagen) fibers. A scalar-valued damage variable is taken into account for the fibers to cover a saturation function converging to a maximal damage value at a fixed maximum load level. In addition, the model captures remnant strains in the fiber direction after unloading. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

岩土材料弹塑性正交异性损伤耦合本构理论

在不可逆热力学框架内建立了岩土材料的正交异性损伤塑性耦合宏观唯象本构理论。主要结果有：1）给出了耦合的塑性和损伤的演化律;2）从对含裂纹单元的细观分析入手,通过均匀化（Homogenization）处理,将损伤引入到Mohr-Coulomb条件下,模型同时考虑了损伤对剪切强度及摩擦角的影响,扩容现象则通过损伤应变来计算。     

环境激励下基于柔度矩阵分解的损伤诊断

为了解决环境激励作用下结构自由度不完备对损伤诊断的影响,提出了一种基于自由度缩聚的比例柔度矩阵分解损伤诊断法.利用附加质量法求解出环境激励作用下振型关于质量归一化因子.进而根据质量归一化因子和比例柔度矩阵系数之间的关系,构建出其比例柔度矩阵,再通过使用QR矩阵分解法对构建出的比例柔度矩阵进行分解.以分解后得到的三角矩阵...     

聚合物材料损伤理论

本文研究了外界环境如载荷、温度、湿度、辐射、腐蚀介质、非相容介质等对聚合物材料变形的影响,给出了微分型和积分型损伤演化方程;讨论了非线性弹性体和非线性粘弹性损伤变形以及腐蚀损伤.给出了粘弹性损伤变分原理.     

采用组合参数的神经网络结构损伤检测分析研究

提出由结构前几阶固有频率变化率、频率变化比值和动柔度置信因子构成的组合参数作为神经网络的输入向量的方法进行结构损伤检测,全面分析了不同参数作为神经网络输入向量的损伤效果,利用数值模拟对悬臂梁、桁架结构进行分析,采用不同的输入参数进行比较·　分析结果表明,采用组合参数训练的神经网络,对结构损伤位置和程度识别较采用单一参数具有更好的识别效果·     

Damage and delamination processes in thermo-viscoelastic materials

This contribution addresses several models for rate-independent damage and delamination processes in thermo-viscoelastic materials. In the spirit of continuum damage mechanics, both degradation phenomena are modeled by means of internal variables, governed by a rate-independent flow rule. The latter is coupled in a highly nonlinear way with the heat equation and the momentum balance for the displacements. We present a suitable weak formulation for this class of models, and discuss existence and approximation results in the framework of variational convergence. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Availability and Hazard of a System Under a Cumulative Damage Process With Replacements

Zacks (Failure distribution associated with general renewal damage processes. In: Nikulin M, Commenges D, Haber C (eds) Probability statistics and modelling in public health. Springer, Berlin, pp 465–475, 2006) studied the reliability function, the hazard function and the distribution of the failure time when a system is subject to a cumulative, compound renewal damage process. The failure occurs when the damage process crosses a threshold β. In the present paper these results are generalized to the model where the system is replaced after failures. Two cases are considered: instant replacement and random positive replacement time. The distribution of the age of the current renewal cycle, as well as its excess life, and the availability function are studied. We derive also the distribution of total time in (0, t) at which the system has been operational.