Thermo-mechanical constitutive modeling of shape memory polyurethanes using a phenomenological approach

This study examined the constitutive modeling of shape memory polyurethanes (SMPUs). SMPUs exhibit a thermo-responsive shape memory behavior, i.e., a thermally fixed temporary shape at a low temperature that returns to its original (permanent) shape when heated. This unique property arises from the molecular configuration of their hard and soft segments; the latter can form a variable state ranging from a rubbery (active) to rigid (frozen) phase according to temperature, while the former undergoes little deformation and acts as a fixed net between the soft segments. In this study, a three-phase phenomenological model (one hard segment phase and two (active and frozen) soft segment phases) was developed to describe the deformation behavior of SMPUs according to their microstructure. The stress and strain relationships of each phase are described mathematically using one three-element viscoelastic and two Mooney–Rivlin hyperelastic equations, respectively. The total stress was calculated by combining those equations via some internal variables that can track the volume fractions of the active and frozen phases and a non-mechanical frozen strain. For validation, the cyclic thermo-mechanical behavior of a SMPU was predicted. These predictions were compared with the experimental results with reasonable agreement between them.     

有限变形下单晶变温本构模型

论文构造了单晶热弹粘塑性的本构模型,模拟材料在不同温度下的力学行为.该模型以晶体热运动学作为分析变形的基础,即考虑温度变化情况下总体变形梯度的乘式分解,建立温度影响下的以弹性变形梯度为基本变量的控制方程来描述单晶材料的变形,算法采用隐式积分方法来求解控制方程以保证计算的稳定性.模型能反映单晶材料变形过程中温度对应力-应变响应的影响.     

DH36钢拉伸塑性流动特性及本构关系

对DH36钢在温度从293~800 K、应变率为0.001和0.1 s-1的拉伸塑性流动特性进行实验研究,通过端口形貌图对变形前后的试样进行了微观分析,结果表明：(1)在实验温度范围内,0.001和0.1 s-1的应变率下,第三型应变时效现象出现,随应变率的增加,时效发生的温度区域移向更高温度;(2)第三型应变时效的发生与合金原子在晶界和晶粒中大量的第二相析出强化有关联;(3)建立包含第三型应变时效现象的统一本构模型,通过比较该模型能够较好的预测DH36的塑性拉伸流动应力。     

DH-36钢的塑性流动统一本构关系研究

通过对DH-36钢动态应变时效的规律和试验数据进行系统分析, 发展和建立了描写第3种动态应变时效的本构模型. 然后基于热激活物理概念本构模型和塑性流动应力组合原理, 加入对第3种动态应变时效的描述, 获得了统一本构模型. 该模型不仅可以描写第3种动态应变时效, 还可以预测DH-36钢在温度77K~1000K, 应变率0.001s^{-1}~3000s^{-1}范围内的塑性流动应力,通过比较发现统一本构模型预测结果与试验结果吻合很好.      

钛合金TC-4在高应变率下的动态本构关系

利用分离式Hopkinson扭杆对钛合金TC-4进行了高应变率下动态剪切本构关系的实验研究。结果表明TC-4对应变率高度敏感,对应变率的敏感性随应变率的提高而增加。其动态应力应变关系呈线性强化形式。但动态强化模量随应变率的提高而略有减少。采用Malvern给出的过应力模式_p={exp[(1/)(-f())]-1}/b可以较好地描述TC-4的动态剪切本构关系。     

弹塑性本构积分算法

本文运用模态应力,模态应变等概念,发展了一种本构积分中点算法。在简正坐标系下得到简单的算法公式。并对算法的精度和稳定性进行了计算验证和理论分析。本文算法的精度和稳定性比通用的屈服面校正方法——切线刚度—径向拉回方法要好。该法对复杂载荷情况下的弹塑性分析有一定的价值。     

含孔洞粘塑性材料剪切带的正交性条件

本文通过对粘塑性材料剪切带中含孔洞的代表体元的细观力学分析，得到了剪切带的宏观本构热和本构关系。采用上限方法，给出了多孔粘塑性材料正交流动法则存在的条件。     

The “decaying springs” model for irreversibility in polymer melts

In this work, entanglements in a polymer melt are modeled as a system of parallel springs which form and decay spontaneously. The springs are assumed to be nonlinear, and a certain fraction of them is torn apart by a certain strain.Based on these assumptions, a model of behavior in simple shear is developed. This model is shown to predict a behavior comprising that of a Wagner fluid, and is generalized to a tensorial model of single integral type. The integrand depends on a product of a material function, modeling reversible behavior, and a material functional which takes irreversible processes into account.Irreversibility of network disentanglement, which may occur when deformation changes or reverses direction, can be modeled in this way. It is shown that the two well-known Wagner constitutive equations with and without irreversibility assumptions are special cases of the model developed. In case of a deformation which does not change directions, the new material function and the material functional are multiplied to yield Wagner's damping function.When the rate of spring formation is a function of temperature, the developed model is shown to predict thermorheologically simple behavior. A constitutive equation for non-isothermal flow of polymers is developed with this assumption.     

CONSTITUTIVE MODELS AND HYPERGRAVITY PHYSICAL SIMULATION OF SOILS$^{\bf 1)}$

数值模拟和物理模拟是分析土体沉降和稳定性的主要手段. 本构模型作为描述土体应力应变关系的数学表达式, 是数值模拟的基础. 土体具有碎散性, 这一基本物理特性导致了其具有压硬性、摩擦性和剪胀性, 这是土的力学特性区别于金属的主要特征, 在土体的本构模型中必须反映这3个基本特性. 传统土力学将土体的变形和强度分离考虑, 分别采用弹性理论和基于刚塑性模型的极限平衡理论分析, 虽然应用广泛, 但由于不能全面地反映土的基本力学特性, 计算结果的精度常常难以满足定量分析的需要. 剑桥模型作为第一个全面反映压硬性、摩擦性和剪胀性的弹塑性本构模型, 实现了变形和强度的统一, 能较好地描述饱和正常固结黏土的应力应变关系, 被视为是现代土力学的开端; 统一硬化模型通过引入一个独特的硬化参数进一步发展了剑桥模型, 将适用范围扩大到超固结黏土. 作者认为, 未来岩土体本构模型研究的挑战是: 如何考虑岩土体在受力过程中土骨架相变与多场耦合, 以解决目前本构模型尚无法定量分析的能源、交通、环境和水利相关的重大岩土工程问题. 超重力物理模拟具有缩尺效应和缩时效应, 克服了常重力物理模拟中模型的应力水平低于原型的缺点, 特别适用于大尺度、长历时问题的模拟. 相较数值模拟, 超重力物理模拟的优势在于能够检验本构模型的合理性, 揭示本构模型无法描述的未知特性. 最后, 介绍了采用数值模拟和物理模拟联合分析大直径钢管桩水平受荷特性的工程案例.     

ANISOTROPIC STRENGTH CRITERION BASED ON T CRITERION AND THE TRANSFORMATION STRESS METHOD 1)

岩土材料通常呈现出成层水平分布特点, 即可将其视为横观各向同性材料, 横观各向同性对于岩土材料的变形以及强度值都会产生显著的影响. 基于已提出的t强度准则, t强度准则是基于各向同性单元体中存在有效滑移面来构建的, 并根据该空间有效滑移面上主剪应力与主法向应力的比值达到一定阈值为破坏条件. 在空间中存在有效滑移面与物理沉积面, 基于上述两个面在空间的位置关系, 用两面夹角作为表征横观各向同性对剪切强度影响程度的参量, 并假定当该夹角值越大, 则各向异性对强度贡献程度越大, 对应更大的应力比强度值, 反之, 则对应更小的应力比强度值. 基于上述思路并类比将其推广为正交三维各向异性准则, 基于三维各向异性材料的三维沉积面, 提出了三维特征沉积面的概念, 并基于空间滑移面与三维特征沉积面之间的夹角作为度量各向异性程度的变量, 提出了基于两面角作为参量考虑原生各向异性的应力比强度公式, 并利用该应力比强度公式来修正已提出的t强度准则, 最终建立了考虑各向异性影响的t准则公式. 在上述准则基础上, 考虑将各向异性应力空间转换为各向同性应力空间的思路, 在各向异性t准则基础上, 推导得到了基于各向异性强度t准则的变换应力公式, 利用变换应力公式可以将传统的以p, q为变量的各向同性本构模型转变为可考虑各向异性的三维本构模型. 通过对岩土材料的强度以及真三轴条件下的应力应变关系试验数据预测, 验证了所提的各向异性t准则及其变换应力公式的有效性及适用性.