酚醛层压材料的本构模型研究

文中讨论了雷管生产线中使用的酚醛层压材料的本构模型,使用分离式Hopkinson压杆(SHPB)研究了材料在高应变率下的力学行为.通过对实验结果的分析,材料的动态应力—应变曲线符合ZWT(朱王唐)非线性热弹粘性本构模型.利用最小二乘法拟合了方程参数,同时对拟合的理论结果与实验结果进行比较,发现在低应变区,拟合并不很好,试件内存在应力应变分布不均的影响因素;在高应变区,拟合与实验结果比较吻合.     

三维正交机织玻璃纤维/环氧树脂复合材料动态力学性能的实验和理论研究

通过实验系统研究了三维正交机织玻璃纤维/环氧树脂复合材料厚度方向和面内方向的动、 静态压缩力学性能。结果表明, 动、 静态压缩载荷作用下该材料响应表现出明显的各向异性、 非线性和应变率敏感性。针对三维正交机织玻璃纤维/环氧树脂复合材料高速变形过程中不同形式的内部缺陷和微损伤的演化, 提出了一个依赖应变、 应变率的宏观损伤量, 建立了一种含损伤的非线性黏弹性本构模型。采用数据处理方法拟合了其本构方程材料参数, 在加载过程中, 模型计算值与实验结果吻合较好。     

高聚物材料动态本构关系对PP/PA共混物的应用研究

用霍布金森实验技术(SHPB)研究了两种PP/PA共混高聚物材料在高应变率(102～103s-1)下的粘弹性力学行为.实验表明,PP/PA共混高聚物材料的动态应力-应变曲线能用一个简单实用的非线性粘弹性本构方程(ZWT方程)较好地表达;通过最小二乘法拟合了材料参数;在加载过程中,理论计算值与实验结果较吻合.     

隔振橡胶本构建模研究

提出适合描述隔振橡胶在宽频振动时力学行为的本构模型。本构模型包含超弹性和粘弹性两个部分，超弹性部分表征橡胶材料的静态特性；非线性粘弹性部分描述橡胶材料在振动、冲击载荷下的动态响应。基于该本构模型，对橡胶材料在宽应变率范围内进行试验，九个材料参数通过高、低应变率下的试验数据拟合确定。模型预测结果与试验结果是相当吻合的。     

纤维应变率相关的统计本构模型的理论与实验研究

本文根据经典的纤维强度统计理论,并在某些假设的基础土,建立了纤维的应变率相关的统计本构模型及其对应的本构方程.由该模型得到了利用纤维束冲击拉伸试验确定单丝应变率相关的统计本构方程中力学参量的原理和方法.在应变率为10-4～103 l/S范围内,用玻璃纤维束的拉仲试验检验该模型和确定本构方程参量的方法.试验结果和分析表明,该模型的假设和有关理论是正确的,方法是可行的.该模型能较好地解释玻纤在应变率为10-4～1.1×102 l/S范围内的力学性能.     

一种描述温度与应变率效应的大应变非线性热粘超弹本构模型

通过橡胶材料在不同温度及应变率下的霍普金森杆冲击试验(SHPB),结合粘弹、超弹理论,建立了一种能反映橡胶材料温度、应变率效应的大应变非线性热粘超弹性本构模型,并开发了相应模型的ABAQUS(VUMAT)软件材料用户子程序。数值模拟很好地再现了橡胶片的SHPB试验,验证了本构模型及材料用户子程序的有效性。     

基于应变空间的碾压混凝土各向异性损伤本构模型

根据碾压混凝土材料的力学特性和损伤拉压显著不同的特点,分别在拉应变和压应变空间建立了碾压混凝土的本构关系和损伤演化方程.在拉应变空间,碾压混凝土的变形特性表现为脆弹性,考虑弹性与损伤耦合,应用正交各向异性损伤理论描述碾压混凝土的刚度退化和应变软化;在压应变空间,考虑弹塑性与损伤耦合,应用内时理论来描述碾压混凝土的弹塑性特性,正交各向异性损伤理论来描述微裂缝扩展引起的刚度退化和应变软化,内时理论没有屈服面,使模型的参数和方程大大减少,从而简化了非线性计算过程.计算结果表明,该模型能够较好地描述碾压混凝土在单轴和多轴加载下的性质.     

大块非晶合金复杂应力状态塑性本构方程

为得到复杂应力状态下大块非晶合金的塑性本构方程,对Zr41.2Ti13.8Ni10Cu12.5Be22.5大块非晶合金进行简单拉伸、压缩和扭转实验,得到相应的一维本构关系,并应用弹塑性力学的相关理论,将一维本构方程延拓到多维应力空间.研究结果表明:该材料符合Mises屈服条件并具有强化特性;利用简单压缩和扭转实验结果可推导出材料在复杂应力状态下的塑性本构方程,且这两个塑性本构方程是一致的.     

单向玻璃纤维增强环氧树脂在冲击拉伸时的一维本构方程

本文在自行研制的冲击拉伸装置上首次实现了单向玻璃纤维增强环氧树脂的冲击拉伸加卸载试验,结合试件在冲击拉伸过程中的瞬态温升和能量分析的结果,提出了完整的复合丝束模型,推出了冲击拉伸时的一维本构方程;并对该材料在300～2000s-1的应变范围内进行了全面的冲击拉伸试验,通过对试验结果的数值统计分析和应变率相关性分析拟合出具体的本构方程,结果表明这个方程是有效的,有明显的物理意义.     

朱-王-唐非线性粘弹性本构模型在有限元分析中的实现及其应用

LS-DYNA可以满足用户对某些材料本构关系子程序开发的要求.本文首先编制了各向同性线弹性材料本构模型子程序,计算单轴拉伸作用,得到材料子程序开发的可行性;另外主要编制了飞机风挡材料采用的具有应变率效应的非线性粘弹性朱-王-唐本构模型,结果能很好地对朱-王-唐模型进行描述,特别是应变率对该模型的影响.并用于真实风挡的计算,得到的数值结果与试验值比较吻合.     

各向同性弹性介质非线性本构方程

从张量函数出发,围绕共轭应力、应变变量,研究了各向同性非线性弹性介质各种形式的本构方程以及各种形式方程之间的关系。推导出用张量不变量,标量不变量表示的两种形式非线性Green弹性介质本构方程。证明了方程是完备的,不可约的。作为应用举例,研究了橡胶材料的工程应用问题。     

Constitutive equation for a class of non-simple elastic materials

Summary Initial yield is the upper limit of the purely elastic deformation behaviour of an elasticplastic solid. Thus the choice of the constitutive equation describing the purely elastic deformation behaviour determines the initial yield function. The constitutive equation of a simple elastic material is only compatible with von Mises yield criterion, a conclusion which applies also to the classical infinitesimal theory. A more general form of constitutive equation for an elastic material is formulated by way of the concept of a stress loading function, the proposed constitutive equation being quadratic in the stress. The two loading coefficients associated with the stress loading function are assumed to be deriveable from a generalised isotropic yield criterion which is now assumed to hold over the entire range of deformation, and in this context is referred to as the stress intensity function. The proposed constitutive equation has the same representation in terms of the left Cauchy-Green deformation tensor as that for a simple elastic material. Using the Cayley-Hamilton theorem, this representation is rearranged and expressed in terms of a measure of finite strain which is defined to be one quarter of the difference between the left Cauchy-Green deformation tensor and its inverse. In this way the strain properties of the proposed constitutive equation are formulated by way of the concept of a strain response function. The three response coefficients associated with the strain response function are assumed to be deriveable from a generalised, isotropic, strain intensity function. The predictions of the proposed constitutive equation are considered in the context of the combined stressing of a thin sheet of incompressible material. In this way, it is shown that the proposed constitutive equation is not limited in the same way as the constitutive equation of a simple elastic material.     

复合材料蠕变本构关系及实验测定Ⅰ.本构关系

蠕变是复合材料最重要的力学性能之一,实验表明:复合材料在蠕变条件下的变形可以分为弹性变形、粘弹性变形和粘塑性变形.应用不可逆过程的热力学和广义变量的概念可以分析材料的蠕变变形.本文首先回顾了热力学的基本方程;基于Schapery本构关系的假设和思路推导了蠕变本构关系的一般形式,其中包括弹性变形、粘弹性变形和粘塑性变形;考虑到广义力选取的不唯一性,本文提出了广义力选取的原则以使得到的本构关系尽可能地简单;由此本文给出了复合材料的一维蠕变,各向同性复合材料的二维蠕变和纤维增强复合材料平面内的蠕变的本构关系.     

On the nonlinear viscoelastic behaviour of nylon fiber

Nonlinear time-dependent stress relaxation was determined experimentally in nylon fiber in the small strain domain. This process is accounted for on the basis of a quasi-linear viscoelastic theory. A nonlinear modified constitutive equation for the viscoelastic medium is deduced. In processing the experimental data it turned out to be necessary to keep the nonlinear terms up to cubic in the constitutive equation for nylon fiber. The elastic and rheological constants in the constitutive equation for nylon fiber are evaluated.     

A constitutive model for finite deformation response of layered polyurethane-montmorillonite nanocomposites

A constitutive model is developed to predict the finite deformation response of multilayered polyurethane (PU)-montmorillonite (MTM) nanocomposites. In PU-MTM nanocomposites, the PU matrix in the vicinity of the MTM nanoparticles is modified leading to an interphase region, and its effect on the finite deformation response of these nanocomposites is largely neglected in many existing models. In this work, the entire spatial volume is considered to be occupied by multi-layers of bulk PU and effective particles which consist of MTM nanoparticles and the modified PU interphase region. A Langevin chain based eight chain model is used to capture the large stretch hyperelastic behavior of bulk PU. The effective particle component of the model consists of a linear elastic spring to capture the initial elastic response, a non-linear viscoplastic dash-pot for the strain-rate dependent yield strength of nanocomposites, and a non-linear spring element in parallel to the dash-pot for the strain-hardening response. The model adopts the concept of amplified strain of the confined PU chains to accommodate the applied strain owing to the limited strain in the MTM nanoparticles. The constitutive model predicts all the major features of the stress-strain constitutive response of a family of PU-MTM nanocomposites including the initial linear elastic response, yield strength and post yield strain hardening for all volume fractions of MTM nanoparticles, thus confirming the efficacy of the proposed constitutive model.     

A fully non-linear axisymmetrical quasi-kirchhoff-type shell element for rubber-like materials

An axisymmetrical shell element for large deformations is developed by using Ogden's non-linear elastic material law. This constitutive equation, however, demands the neglect of transverse shear deformations in order to yield a consistent theory. Therefore, the theory can be applied to thin shells only. Eventually a ‘quasi-Kirchhoff-type theory’ emerges. Within this approach the computation of the deformed director vector d is a main assumption which is essential to describe the fully non-linear bending behaviour. Furthermore, special attention is paid to the linearization procedure in order to obtain quadratic convergence behaviour within Newton's method. Finally, the finite element formulation for a conical two-node element is given. Several examples show the applicability and performance of the proposed formulation.     

Elastic deformation of a tapered vascular prosthesis

An approximate analysis of the elastic properties of tapered microfibrous polyurethane arterial prostheses is presented by considering a tapered conduit to consist of a series of short cylindrical segments. Using this approach, the relatively simple, non-linear finite deformation models developed for cylindrical arterial specimens may be applied to each segment. A constitutive equation based on a polynomial form of strain energy density function is used in this study. The constitutive constants are determined using experimental data obtained from uniform cylindrical grafts and are used to predict the mechanical response of tapered grafts. The variation in local compliance for linear, tapered grafts of uniform and variable wall thickness is determined. Similarly, the variation in longitudinal strain for tapered grafts subjected to various longitudinal tensions is calculated. The primary purpose of this analysis is to provide data for the design of tapered, compliant vascular grafts. It may also be used to characterize the elastic properties of other non-uniform axi-symmetric elastomeric conduits.     

传递函数法在非局部弹性梁动力学分析中的应用

采用传递函数方法进行了非局部弹性梁的动力学分析。非局部弹性梁内一点的应力与梁某一区域内任意一点的应变均有关系。本文基于Eringen的非局部弹性积分型本构关系,采用幂指数型核函数,利用Laplace变换导出梁的四阶偏微分形式振动方程,通过定义状态向量,将控制方程化为一阶微分方程组,并采用传递函数方法进行了求解,针对两种边界条件给出了非局部弹性梁的固有频率和固有振型。结果表明,同阶频率下,非局部弹性梁的频率比局部梁的频率低,振型基本一致。     

Non-linear constitutive model for plain-weave composites

A non-linear constitutive model for plain-weave composites is developed which is based on the micromechanical behavior of a representative unit cell. The global constitutive relationships are consistently derived from the total strain energy of the system. Compatibility of the constituent's geometric non-linearities is fully taken into account where the matrix plays the role of an elastic foundation and is thus modeled as a continuum.     

考虑应变梯度及刚度劣化的剪切带局部变形分析

基于梯度塑性理论,研究了应变软化阶段的刚度劣化对剪切带内部的局部应变及相对剪切位移的影响。剪切带被看作一维剪切问题,本构关系为线弹性及线性应变软化。考虑刚度劣化后,剪切带的弹性应变由弹性剪切模量、损伤变量及残余剪切模量确定。剪切带的非局部总应变由双线性的本构关系确定。将非局部总应变减去弹性应变,可得剪切带的非局部塑性应变。剪切带非局部塑性应变与流动应力及损伤变量等参数有关,此关系即为在经典弹塑性理论框架之内的考虑刚度劣化的屈服函数。将二阶应变梯度项引入该函数,可得剪切带内部的局部塑性剪切应变及局部总剪切应变的分布规律。对局部塑性剪切应变积分,得到了局部塑性剪切位移。结果表明:考虑了刚度劣化后,剪切带内部的弹性剪切应变及位移增加,而局部塑性剪切应变及位移降低。若不考虑刚度劣化,理论结果可蜕化为以前的结果。理论结果与岩石局部变形的观测结果在定性是一致的。