Professor T. C. Papanastasiou's contributions to rheology and computational fluid mechanics

Professor T. C. Papanastasiou's contributions to rheology and computational fluid mechanics are numerous and have a lasting effect. In the short span of a professional career of about 10 years, and in such diverse places as the University of Minnesota, the University of Michigan, and the Aristotle University of Thessaloniki, he developed and implemented new ideas in the fields of rheology and computational fluid mechanics. He dealt with such important topics as: i) modelling of viscoelasticity and viscoplasticity through appropriate constitutive equations; ii) numerical techniques based on the finite element method, streamline integration, inverse of the unknown, and Newton iteration for integral-differential equations; iii) numerical simulation of important polymer processes, such as fiber spinning, film blowing, film casting, extrusion and coextrusion of polymeric liquids; iv) stability analysis of multiple flows; v) three-dimensional computational techniques for generalized Newtonian flows; vi) numerical analysis of viscoplastic flows; vii) solidification problems; viii) outflow boundary conditions, etc.His many contributions include authoring two books in the area of fluid mechanics, one for undergraduate and the other for graduate use. He was a mentor and an advisor to a dozen people, his former students, who have, in their own right, successful careers, some as professors, others as research engineers in major industries. The ideas and foundations of his work are currently pursued and studied by many researchers world-wide, and in this manner it is the most appropriate tribute to him and a guarantee that his name will be remembered for years to come.Dedicated to the memory of Professor Tasos C. Papanastasiou     

Adiabatic shear band localization of inelastic single crystals in symmetric double-slip process

Summary The main objective of the present paper is the development of a viscoplastic regularization procedure valid for an adiabatic dynamic process for multi-slips of single crystals. The next objective is to focus attention on the investigation of instability criteria, and particularly on shear band localization conditions.To achieve this aim, an analysis of acceleration waves is given, and advantage is taken of the notion of the instantaneous adiabatic acoustic tensor. If zero is an eigenvalue of the acoustic tensor, then the associated discontinuity does not propagate, and one speaks of a stationary discontinuity. This situation is referred to as the strain localization condition, and corresponds to a loss of hyperbolicity of the dynamical equations. It has been proved that for an, adiabatic process of rate-dependent (elastic-viscoplastic) crystal, the wave speed of discontinuity surface always remains real and different from zero. It means that for this case the initial-value problem is well-posed. However, for an adiabatic process of rate-independent(elastic-plastic) crystal, the wave speed of discontinuity surface can be equal zero. Then the necessary condition for a localized plastic deformation along the shear band to be formed is as follows: the determinant of the instantaneous adiabatic acoustic tensor is equal to zero. This condition for localization is equivalent to that obtained by using the standard bifurcation method. Based on this idea, the conditions for adiabatic shear band localization of plastic deformation have been investigated for single crystals. Particular attention has been focused on the discussion of the influence of thermal expansion, thermal plastic, softening and spatial covariance effects on shear band localization criteria for a planar model of an f.c.c. crystal undergoing symmetric primary-conjugate double slip. The results obtained have been compared with available experimental observations.Finally, it is noteworthy that the viscoplasticity regularization procedure can be used in the developing of an unconditionally stable numerical integration algorithm for simulation of adiabatic inelastic flow processes in ductile single crystals, cf. [21].The paper has been prepared within research programme sponsored by the Committee of Scientific Research under Grant 3 P404 031 07.     

多晶金属弹粘塑性的取向元模型

基于“三维组集式本构模型”［１～３］，运用功共轭原理和场平均方法，发展了一种“取向元”概念——多晶聚集体内具有相同取向的滑移系集的一个体积平均意义上的代表性元素；由一维的率（粘性）敏感“取向元”，通过在取向空间里的积分，获得了三维的弹粘塑性本构方程式，并模拟了蠕变和松弛现象．与以往的粘塑性模型相比，本文模型不仅能同时考虑多晶金属材料的率相关性和路径相关性，而且由于引入了物理机制，因而具有较强的预测能力．数值算例也展示了该模型的合理性     

一维非线性黏弹体和黏塑性体中的最优应变路径

得出了一维非线性黏弹体和黏塑性体中最优应变路径方程，并揭示了它们的某些特性，如：（１）当非线性黏弹本构方程中的黏性部分与应变的关系具有上凸形式时，相应的最优应变路径具有下凸性质；（２）对于过应力和Ｂｏｄｎｅｒ－Ｐａｒｔｏｎ黏塑性体，它们的最优应变路径是塑性应变为线性形式，即塑性应变率为常数，而弹－黏塑性体的最优应变路径则不同。     

Nonlinear Mechanical Response of Polymer Matrix Composites: A Review

Abstract

The present article provides a review on the nonlinear mechanical behavior of polymer matrix composites (PMCs). Initially, essential mechanisms driving the nonlinear response of PMCs under different loading conditions are discussed. Rate-dependence, tension-compression asymmetry, viscous behavior, unloading characteristics, interaction between stress components and effects of environmental factors on mechanical properties are briefly reviewed. This is followed by a review of major approaches and constitutive models for predicting stress–strain behavior of PMCs. Following an increasing degree of complexity, models are categorized into four major classes: nonlinear elasticity models, elastic-plastic models, elastic-plastic-viscous models and Damage-Plasticity models. The vast number of existing models is mainly due to the anisotropy and inhomogeneity of PMCs. In brief, this review focuses on informing the reader of major frameworks, rather than addressing all the models in detail.     

A model of traps for yield in amorphous glassy polymers

Summary  Constitutive equations are derived for the viscoelastic and viscoplastic behavior of amorphous glassy polymers at isothermal loading with small strains. The model is based on the trapping concept: a disordered medium is treated as an ensemble of plastic flow units (with the characteristic size of micrometers), which, in turn, consist of a number of cooperative rearranging regions (with the characteristic length of nanometers). The viscoelastic response is described by rearrangement of relaxing regions, whereas the viscoplastic behavior is modeled as irreversible deformation of plastic units. Adjustable parameters are found by fitting observations for aromatic polyesters, nylon-66, polycarbonate block copolymers and an epoxy glass. Fair agreement is demonstrated between experimental data and results of numerical simulation. Received 17 November 1999; accepted for publication 23 March 2000     

Sn60Pb40钎料合金的具有蠕变和塑性边界的粘塑性本构方程

采用具有蠕变和塑性边界的粘塑性本构方程对Sn-Pb共晶合金的基本力学行为进行了模拟和预测。结果表明：在较宽的外部变量范围（应变率为10^-5-10^-2S^-1,温度为－55－125℃）内,模拟结果与实验结果吻合良好。证明了该方程用于描述Sn-Pb共晶合金的力学行为具有良好的预测能力。     

Cyclic multiaxial and shear finite deformation responses of OFHC Cu. Part II: An extension to the KHL model and simulations

In this part, the Khan–Huang–Liang (KHL) constitutive model was extended to account for kinematic hardening characteristic behavior of materials. The extended model is then generalized and used to simulate experimental response of oxygen free high conductivity (OFHC) copper under cyclic shear straining and biaxial tension–torsion (multiaxial ratchetting) experiments presented in Part I (Khan et al., 2007). In addition, a new modification for the non-linear kinematic hardening rule of Karim–Ohno (Abdel-Karim and Ohno, 2000) is proposed to simulate multiaxial ratchetting behaviors. Although, the kinematic hardening contributes the most to the response, it is shown that, the loading rate effect, and a coupled isotropic and kinematic hardening effect should also be considered while simulating the multiaxial ratchetting behavior of OFHC copper. Furthermore, the newly modified kinematic hardening rules is able to fairly well simulate the multiaxial ratchetting experiments under different loading conditions, irrespective of the value of applied axial tensile stress, shear strain amplitude, pre-cyclic hardening and/or loading sequence.     

纤维加强金属基复合材料热机械疲劳模型的研究进展

纤维增强金属基复合材料的热机械疲劳(thermomechanical fatigue 简称TMF)特性的研究在近年受到高度重视.本文根据国内外近期进行的理论研究以及获得的主要成果作一概要介绍.对于热机械循环特性,主要介绍基于细观力学方法的轴向性质模型,以及基于断裂与损伤理论的横向性质模型.对于热机械疲劳性能研究,结合横向性质导出两种热机械疲劳模型,然后分析基体的细观结构对疲劳寿命的影响.      

Coupled viscoplasticity damage constitutive model for concrete materials

A coupled viscoplasticity damage constitutive model for concrete materials is developed within the framework of irreversible thermodynamics.Simultaneously the Helmholtz free energy function and a non-associated flow potential function are given, which include the internal variables of kinematic hardening,isotropic hardening and dam- age.Results from the numerical simulation show that the model presented can describe the deformation properties of the concrete without the formal hypotheses of yield criterion and failure criteria,such as the volume dilatancy under the compression,strain-rate sen- sitivity,stiffness degradation and stress-softening behavior beyond the peak stress which are brought by damages and fractures.Moreover,we could benefit from the application of the finite element method based on this model under complex loading because of not having to choose different constitutive models based on the deformation level.