Micromechanical approach to damage mechanics of composite materials with fabric tensors

The purpose of this study is to apply continuum damage mechanics – introduced through the concept of fabric tensors – to composite materials within the framework of the theory of elasticity. A directional data model of damage mechanics for composite materials will be developed using fabric tensors. The introduction of fabric tensors into the analysis of damage of composite materials will allow for an enhanced and better understood physical meaning of damage. The micromechanical approach will be used here to relate the damage effect through fabric tensors to the behavior of composite materials. In this approach, damage mechanics is introduced separately to the constituents of the composite material through different constituents’ damage effect tensors. The damaged properties of the composite system as a whole can then be obtained by proper homogenization of the damaged properties of the constituents.

The derivation of a generalized formulation of damage evolution will be shown here in a mathematically consistent manner that is based on sound thermodynamic principles. Numerical examples will be presented to show applicability. In addition, damage evolution for the one-dimensional tension case is also illustrated.     

Averaging method and long-wave asymptotics in vibrational convection in layers with an interface

A scheme for applying an averaging method to the problem of convection in a two-layer system with an interface under the influence of high-frequency vibration is proposed. The derivation of the averaging equations is given, and the stability of the equilibrium of the averaged problem is considered. Long-wavelength asymptotics of steady and oscillatory instability are constructed. The results of numerical calculations for acetonitrile?Cn-hexane and silicone oil?Cfluorinert systems are given. The directions in which the investigation of thermovibrational convection in problems with free surfaces and interfaces can be continued, are indicated.     

Effects of size distribution on the combustion efficiency of a liquid propellant rocket motor

Abstract

A new algorithm is presented to generate the parameters of the Schwarz canonical form. This new algorithm is simpler than the Routh algorithm in evaluating the Schwarz canonical form. The similarity transformation from a state‐space model in the phase‐variable form to that in the Schwarz canonical form is naturally established.     

混凝土坝地震动力损伤分析

基于塑性损伤本构理论,将损伤变量作为内变量,在Drucker-Prager本构模型中引入损伤变量,考虑材料损伤引起的材料劲度的退化,基于非关联流动法则计算材料的塑性应变,根据材料的有效塑性应变计算损伤量,考虑到张开裂缝闭合时材料弹性劲度的恢复,推导了考虑塑性损伤的混凝土动态本构关系,并给出了内变量的计算步骤和动力方程的迭代格式。最后利用建立的动态本构模型对Koyna重力坝进行了非线性地震响应时程分析,并给出了关键时刻坝体最大受拉损伤分布,结果表明在坝颈和坝基处出现了较大的损伤,坝颈处的损伤最终形成由下游向上游的开裂破坏,这与该坝的实际震害较为一致。     

A stabilized volume‐averaging finite element method for flow in porous media and binary alloy solidification processes

A stabilized equal‐order velocity–pressure finite element algorithm is presented for the analysis of flow in porous media and in the solidification of binary alloys. The adopted governing macroscopic conservation equations of momentum, energy and species transport are derived from their microscopic counterparts using the volume‐averaging method. The analysis is performed in a single domain with a fixed numerical grid. The fluid flow scheme developed includes SUPG (streamline‐upwind/Petrov–Galerkin), PSPG (pressure stabilizing/Petrov–Galerkin) and DSPG (Darcy stabilizing/Petrov–Galerkin) stabilization terms in a variable porosity medium. For the energy and species equations a classical SUPG‐based finite element method is employed. The developed algorithms were tested extensively with bilinear elements and were shown to perform stably and with nearly quadratic convergence in high Rayleigh number flows in varying porosity media. Examples are shown in natural and double diffusive convection in porous media and in the directional solidification of a binary‐alloy. Copyright © 2004 John Wiley & Sons, Ltd.     

A transformation of Cauer's third form realized by integrators

Abstract

A new formulation is presented for the Cauer's third form of continued fraction expansion realized by integrators. A transformation of the state‐space model of this new form and the state‐space model of the phase‐variable canonical form is given.     

基于随机平均的非线性随机最优控制

首先建立非线性随机系统的最优控制问题,并介绍通过随机平均法导出平均系统、再由随机动态规划原理确定控制律的平均系统的非线性随机最优控制方法。然后,对于非线性随机系统的动态规划方程,提出应用随机平均法简化该方程、从而得到最优平均控制律的方法,并证明该最优平均控制律等价于平均系统的最优控制律。最后用一个例子说明方法及等价性,并指出在一定条件下,最优平均控制律将是动态规划方程的精确解。     

多自由度非线性振动分析的平均法

将单自由度非线性振动分析的平均法推广到多自由度，基于平均化方程可以导出系统的幅频响应特性。结合具体算例，将数值方法求解微分方程而得到幅频特性与本文平均法的结果进行了比较。     

General theory of three-dimensional radiance measurements with optical microprobes

Measurements of the radiance distribution and fluence rate within turbid samples with fiber-optic radiance microprobes contain a large variable instrumental error caused by the nonuniform directional sensitivity of the microprobes. A general theory of three-dimensional radiance measurements is presented that provides correction for this error by using the independently obtained function of the angular sensitivity of the microprobes.     

A damage-mechanics-based approach for modelling decohesion in adhesively bonded assemblies

A cohesive interface model formulated within the framework of damage mechanics is presented for the simulation of decohesion in adhesively bonded assemblies. Characteristic features of the model are: the introduction of a single energy-based damage variable for describing the damage state of the interface; use of a decohesion propagation condition relying upon the linear elastic fracture mechanics (LEFM) energy balance; a treatment for the mixed-mode situation based on the definition of an equivalent energy release rate whose expression is consistently derived from the formulation. The comparisons between numerical and experimental responses obtained for typical test problems illustrate the capabilities of the proposed approach.     

An integrated continuous-discontinuous approach towards damage engineering in sheet metal forming processes

This paper addresses the simulation of ductile damage and fracture in metal forming processes. A combined continuous-discontinuous approach has been used, which accounts for the interaction between macroscopic cracks and the surrounding softening material. Softening originates from the degradation processes taking place at a microscopic level, and is modelled using continuum damage mechanics concepts. To avoid pathological localisation and mesh dependence and to incorporate length scale effects due to microstructure evolution, the damage growth is driven by a non-local variable via a second order partial differential equation. The two governing equations, i.e. equilibrium and non-local averaging, are solved in an operator-split manner. This allows one to use a commercial finite element software to solve the equilibrium problem, including contact between the tools and work piece. The non-local averaging equation is solved on a fixed configuration, through a special purpose code which interacts with the commercial code. A remeshing strategy has been devised that allows: (i) to capture the localisation zone, (ii) prevent large element distortions and (iii) accommodate the crack propagation. To illustrate the capabilities of the modelling tool obtained by combining these continuum mechanics concepts and computational techniques, process simulations of blanking, fine-blanking and score forming are presented.     

Shape sensitivity analysis of magnetic forces

This paper presents a shape sensitivity analysis of magnetic forces evaluated using the Maxwell stress tensor and the finite element method. The formulation is based upon a discrete approach which takes the analytical derivatives of the finite element equations with respect to the shape variables and also on the adjoint variable method in order to carry out the derivation procedure. Sensitivity analysis is developed in the context of the axisymmetrical nonlinear magnetostatic field problem with a modified magnetic vector potential as state variable. Numerical results are presented to validate this methodology. Shape sensitivity analysis is then applied to the optimization of the force-displacement characteristic of a linear actuator. A sequential quadratic programming method is used in the optimization process     

Smoothing artificial stress concentrations in voxel-based models of textile composites

Voxel meshing is an effective method to discretise the internal architectures of multi-phase materials. Spurious stresses are however introduced in the vicinity of a multi-material interface due to the stepped, block-like representation of smooth boundaries. A stress averaging technique is presented to eliminate artificial mesh-imposed stress concentrations. The effect of the local averaging domain size, averaging weight function, and mesh dependence is explored. The voxel finite element method with stress averaging is then further developed to study progressive damage propagation and failure analysis of composites. An additional control, based on the failure plane angle of each element, is included to ensure propagation of damage in the direction dictated by the physics of the process rather than mesh artefacts. It is found that the stress averaging technique is an effective way to alleviate local stress concentrations and can ensure correct damage and failure mode prediction when compared to a conformal mesh.     

THE INFLUENCE OF THE HARDENING STATE ON TIME DEPENDENT DAMAGE AND ITS CONSIDERATION IN A UNIFIED DAMAGE MODEL

Abstract— A model is presented for the prediction of the lifetime of metals in the high-temperature range under arbitrary variable multiaxial load. The definition of an internal variable for damage in continuum damage mechanics is adopted, which allows indirect measurement of damage via the deformation behaviour. To acquire some knowledge of damage evolution, damage is measured in two ways during uniaxial strain controlled cyclic tests: (a) a change of the modulus of elasticity and (b) a decrease of the peak stress. Surprisingly, both methods lead to results which are in good agreement. A new damage law is then developed (with reference to known models and lifetime rules) which is a modification of the creep damage law of Rabotnov that is extended by a dependence on the inelastic strain rate instead of the dependence on internal variables to take into account the hardening state. Uniaxial as well as multiaxial formulations of the new damage model (Inelastic Strain Rate Modified (ISRM) model) are presented.
The parameters of the ISRM model are determined with a view to applying them to AISI 316 L(N) austenitic steel. Some of the parameters are derived from standard creep experiments. To determine further parameters, the ISRM model is applied to uniaxial cyclic tests. Both failure behaviour and damage evolution are well described.     

Micromechanics modeling of plastic yielding in a solid containing mode III cohesive cracks

A new micromechanics damage model is proposed by averaging distributed microcracks with cohesive zones in a two dimensional representative volume element. The cohesive microcracks are mode-III Dugdale-Bilby-Cottrell-Swinden (Dugdale-BCS) crack. The damage model may be used to construct plasticity potentials that take into account the presence of such microcracks.     

Inference of high dimensional grammars

Abstract

Inference of high‐dimensional grammars such as tree grammars and web grammars is discussed. The k‐tail inference procedure for finite‐state grammars is extended to the case of regular tree grammars. The behavior of the k‐tail procedure with variable values of k is studied. The derivation diagram of context‐free web languages is introduced. A “semantic teacher” is used for the inference of web grammars. Application examples in picture and scene analysis are presented.     

Distributions of sources and normal dipoles over a quadrilateral panel

Summary The potential due to a distribution of sources or normal dipoles on a flat quadrilateral panel is evaluated for the cases where the density of the singularities is constant, linear, bilinear, or of arbitrary polynomial form. The results in the first two cases are consistent with those derived previously, but the present derivation is considered to be simplified. In particular, the constant dipole distribution is derived from a geometric argument which avoids direct integration; this derivation applies more generally on a curvilinear panel bounded by straight edges.Also presented are multipole expansions for the same potentials, suitable for use when the distance to the field point is substantially larger than the panel dimensions. Algorithms are derived to evaluate the coefficients in these expansions to an arbitrary order.     

An EOQ Model for Items with Weibull Distribution Deterioration

An inventory model is considered for deteriorating items with a variable rate of deterioration, where deterioration means decay, damage or spoilage such that the item cannot be used for its original purpose. Specifically, the Weibull distribution is used to represent the distribution of the time to deterioration. The EOQ formula is derived under conditions of constant demand, instantaneous delivery and no shortages, and it is shown that the results can be related to previously developed simpler models. A computer program is developed to provide the numerical solution and a numerical example is used to show the solution form and verify that the solution gives minimum total cost per unit time.

An economic lot size model has been developed for situation in which the deterioration follows a Weibull distribution. The theoretical derivation was shown to reduce to the previous model found by Ghare and Schrader when the deterioration was exponential in nature and to a non deteriorating EOQ model when deterioration was made very small. A computer program was developed to provide a numerical solution and its use demonstrated on a numerical example. The computer program is available from the authors.