显式方法精确模拟形状记忆聚合物热力学行为

通过构建一个热耦合的多轴可压缩应变能函数，得到应力-应变、应力-温度和应变-温度之间的函数关系，建立形状记忆聚合物的本构方程.本文引入三个基于对数应变的不变量使得模型（i）可以模拟可压缩情况；（ii）适用于单轴拉伸和等双轴拉伸至少两个基准实验；（iii）多轴有效.通过显式方法（i）给出自由能和熵的具体表达，证明模型热力学定律；（ii）给出应变-应力，温度-应力以及，温度-应变的形函数具体表达.多轴模型在特定的情况下可以自动退化到各自的单轴情况. 通过调节形函数的参数，最终得到的模型结果和实验结果能够精确匹配.新方法建立的本构模型得到的结果能更加准确地指导形状记忆聚合物的工程设计。     

类橡胶材料变形直到破坏的显式本构模型

本文通过直接、显式的方法提出一个多轴可压缩应变能弹性势来模拟类橡胶材料受载荷直到软化破坏的变形行为．首先，我们提出一个多轴可压缩应变能函数；其次，通过特定的不变量，该多轴应变能函数在单轴拉伸，平面应变和等双轴拉伸三个基准实验的情况下，可以退化为各自的单轴形函数形式；再次，我们显式给出带有软化破坏特性的形函数；最后，模型结果和试验数据可以精确匹配，同时可以预测材料临近破坏以后，接下来的变形行为．     

基于有理插值方法模拟可压缩类橡胶材料多轴变形行为

提出一个多轴应变能函数来模拟可压缩类橡胶材料在载荷作用下的大变形行为。首先,基于对数应变构造三个不变量,使得应变能函数分别具备可压缩功能、多轴有效功能以及适用于多个变形模式的功能;其次,利用有理插值方法构造单轴形函数,并结合前面引入的三个不变量,通过哈密顿插值方法构建统一的应变能函数;最后,在单轴情况下,应变能函数通过对Hencky应变求导,可以得到对应变形模式下的应力-应变关系。本文通过调节泊松比的大小来控制体积变化从而实现模型的可压缩性;此应变能函数可以模拟单轴拉伸压缩、平面应变以及等双轴拉伸等至少三个基准试验。新方法得到的伸长比-应力关系、伸长比-体积比关系与经典试验数据结果作比较,进而证明方法的准确性和有效性。     

显式模拟类橡胶材料Mullins效应滞回圈

通过显式、直接的方法提出一个多轴可压缩应变能函数,用来模拟类橡胶材料在加载-卸载作用下,由于Mullins效应而产生的应力-应变滞回圈.本文的创新点在于将表征能量耗散的变量引入到应变能函数.新的弹性势具有以下两个特点:第一,在加载情况下,新引入的变量不会对弹性势产生任何影响,因此,只要给出合适的形函数显式表达,3个基准实验,包括单轴拉伸和压缩,等双轴拉伸和压缩,以及平面应变,都可精确模拟;第二,新引入的变量在卸载情况下将被激活.在不同的卸载应力下,变量将发生改变,从而影响弹性势,使其最终产生不同的应力-应变关系卸载曲线,与对应的加载曲线共同构成应力-应变滞回圈.通过对Mullins效应实验数据进行分析和研究,得出了卸载形函数在不同卸载应力下变化的规律,并预测不同卸载应力下的应力-应变关系.最后,我们将得到精确匹配实验数据的数值模拟结果,从而证明本文方法不仅可以精确匹配至少3个基准实验,还可以模拟和预测类橡胶材料在加载-卸载作用下由于Mullins效应而产生的滞回圈.     

显式模拟类橡胶材料Mullins效应滞回圈

通过显式、直接的方法提出一个多轴可压缩应变能函数,用来模拟类橡胶材料在加载——卸载作用下,由于Mullins效应而产生的应力——应变滞回圈. 本文的创新点在于将表征能量耗散的变量引入到应变能函数.新的弹性势具有以下两个特点:第一,在加载情况下,新引入的变量不会对弹性势产生任何影响,因此,只要给出合适的形函数显式表达,3个基准实验,包括单轴拉伸和压缩,等双轴拉伸和压缩,以及平面应变,都可精确模拟;第二,新引入的变量在卸载情况下将被激活.在不同的卸载应力下,变量将发生改变,从而影响弹性势,使其最终产生不同的应力——应变关系卸载曲线,与对应的加载曲线共同构成应力——应变滞回圈.通过对Mullins效应实验数据进行分析和研究,得出了卸载形函数在不同卸载应力下变化的规律,并预测不同卸载应力下的应力——应变关系.最后,我们将得到精确匹配实验数据的数值模拟结果,从而证明本文方法不仅可以精确匹配至少3个基准实验,还可以模拟和预测类橡胶材料在加载——卸载作用下由于Mullins效应而产生的滞回圈.      

基于单轴数据决定橡胶类材料多轴刚性化有界超弹性势

指出表征橡胶类材料应变刚化效应的现有超弹性模型涉及应变能无穷发散困难,提出新方法解决该困难。基于对数应变不变量的多轴扩张和多轴匹配步骤,建议直接构造橡胶类材料大变形弹性势的显式直接方法。该方法从单轴应力-应变关系直接得到多轴弹性势,所得结果避免了现有各方法决定待定参数组的复杂数值计算,能够准确描述应变刚性化效应,且给出有界弹性应变能,从而避免了前述发散困难。数值结果表明,从单轴数据所得到的弹性势可同时很好的拟合平面应变拉伸(剪切)数据以及等双轴拉伸数据。     

混凝土单轴受拉的非局部本构模型

混凝土受拉本构行为存在很强的局部软化现象,使得单轴受拉试验无法给出应力-应变关系,而只能给出应力-位移关系。本文根据内变量理论和等效应变假设建立了基于真实应变的混凝土单轴受力本构方程,并根据Weibull分布可以描述混凝土等脆性材料断裂过程的试验现象,建立了关于弹性应变的损伤演化规律。然后,通过假设平均应变与真实弹性应变的函数关系,在应力-平均应变的本构关系中采用平均弹性应变以描述其非局部行为,而在材料的损伤演化规律中采用真实弹性应变以描述其局部行为,由此建立了单轴受拉荷载条件下的非局部本构模型。最后,对一个单调受拉试验和一个反复受拉试验的仿真结果表明所提出的非局部本构模型可以准确地模拟试验结果。     

半结晶聚合物损伤演化的实验表征与数值模拟

损伤本构模型对研究材料的断裂失效行为有重要意义, 但聚合物材料损伤演化的定量表征实验研究相对匮乏. 通过4种高密度聚乙烯(high density polythylene, HDPE)缺口圆棒试样的单轴拉伸实验获得了各类试样的载荷-位移曲线和真应力-应变曲线, 采用实验和有限元模拟相结合的方法确定了HDPE材料不同应力状态下的本构关系, 并建立了缺口半径与应力三轴度之间的关系;采用两阶段实验法定量描述了4种HDPE试样单轴拉伸过程中的弹性模量变化, 并建立了基于弹性模量衰减的损伤演化方程, 结合中断实验和扫描电子显微镜分析了应力状态对HDPE材料微观结构演化的影响. 结果表明缺口半径越小, 应力三轴度越大, 损伤起始越早、演化越快; 微观表现为: 高应力三轴度促进孔洞的萌生和发展, 但抑制纤维状结构的产生;基于实验和有限元模拟获得的断裂应变、应力三轴度、损伤演化方程等信息提出了一种适用于聚合物的损伤模型参数确定方法, 最后将本文获得的本构关系和损伤模型用于HDPE平板的冲压成形模拟, 模拟结果与实验结果吻合良好.      

人工冻结深部软岩单轴力学性能试验及蠕变模型1）

为了了解深部软岩在冻结条件下的单轴力学性能,以东北地区的原状泥砂岩为试验对象,利用自行研制的WDT-100型人工冻土试验仪器,对其进行不同温度下的人工冻土单轴抗压强度试验和单轴蠕变试验,得到泥砂岩单轴压缩应力-应变关系曲线,各温度下试样的单轴抗压强度以及蠕变曲线.单轴压缩试验结果表明：试样在给定温度和加载速率条件下,单轴压缩应力-应变关系曲线都有较为明显的屈服点,并且都在屈服点后,强度有所提高,出现硬化现象.单轴蠕变试验结果表明：单轴压缩蠕变曲线有非线性特征,单轴压缩蠕变的等时应力-应变曲线向应变轴靠拢;单轴压缩时蠕变模量随时间的增长而降低.最后采用遗传算法优化模型参数,得出泥砂岩蠕变经验方程.与试验结果对比,发现拟合情况较好.     

人工冻结深部软岩单轴力学性能试验及蠕变模型

为了了解深部软岩在冻结条件下的单轴力学性能,以东北地区的原状泥砂岩为试验对象,利用自行研制的WDT-100型人工冻土试验仪器,对其进行不同温度下的人工冻土单轴抗压强度试验和单轴蠕变试验,得到泥砂岩单轴压缩应力-应变关系曲线,各温度下试样的单轴抗压强度以及蠕变曲线.单轴压缩试验结果表明:试样在给定温度和加载速率条件下,单轴压缩应力-应变关系曲线都有较为明显的屈服点,并且都在屈服点后,强度有所提高,出现硬化现象.单轴蠕变试验结果表明:单轴压缩蠕变曲线有非线性特征,单轴压缩蠕变的等时应力-应变曲线向应变轴靠拢;单轴压缩时蠕变模量随时间的增长而降低.最后采用遗传算法优化模型参数,得出泥砂岩蠕变经验方程.与试验结果对比,发现拟合情况较好.     

New finite strain elastoplastic equations for accurately and explicitly simulating pseudoelastic-to-plastic transition effects of shape memory alloys

A new finite strain elatoplastic J₂-flow model with coupling effects of both isotropic and anisotropic hardening is proposed with the co-rotational logarithmic rate. In terms of certain single-variable shape functions representing uniaxial loading and unloading curves, explicit multi-axial expressions for the three hardening quantities incorporated in the new model proposed are derived in unified forms for the purpose of automatically and accurately simulating complex pseudoelastic-to-plastic transition effects of shape memory alloys (SMAs) under multiple loading-unloading cycles. Numerical examples show that with only a single parameter of direct physical meaning for each cycle, accurate and explicit simulations may be achieved for extensive data from multiple cycle tests.     

The multi-axial deformation behavior of bulk metallic glasses at high homologous temperatures

In this work, we study the behavior of a recently-developed Lanthanum-based bulk metallic glass under uniaxial and multi-axial stress-states using the constitutive model developed by Thamburaja and Ekambaram (2007). The material parameters in the constitutive model are fitted to match the stress–strain responses obtained from a set of simple compression experiments conducted at temperatures within the supercooled liquid region under a variety of strain rates spanning approximately three decades. With the material parameters calibrated, we show that the aforementioned constitutive model is able to accurately predict the force vs. displacement responses of representative experiments conducted under multi-axial stress-states at temperatures within the supercooled liquid region, namely three-point bending and the superplastic forming of a miniature gear component. In particular, the evolution of the specimen geometry during the deformation under multi-axial loading conditions are also well-predicted by the constitutive model.     

A constitutive theory for shape memory polymers. Part II: A linearized model for small deformations

A constitutive theory is developed for shape memory polymers. It is to describe the thermomechanical properties of such materials under large deformations. The theory is based on the idea, which is developed in the work of Liu et al. [2006. Thermomechanics of shape memory polymers: uniaxial experiments and constitutive modelling. Int. J. Plasticity 22, 279-313], that the coexisting active and frozen phases of the polymer and the transitions between them provide the underlying mechanisms for strain storage and recovery during a shape memory cycle. General constitutive functions for nonlinear thermoelastic materials are used for the active and frozen phases. Also used is an internal state variable which describes the volume fraction of the frozen phase. The material behavior of history dependence in the frozen phase is captured by using the concept of frozen reference configuration. The relation between the overall deformation and the stress is derived by integration of the constitutive equations of the coexisting phases. As a special case of the nonlinear constitutive model, a neo-Hookean type constitutive function for each phase is considered. The material behaviors in a shape memory cycle under uniaxial loading are examined. A linear constitutive model is derived from the nonlinear theory by considering small deformations. The predictions of this model are compared with experimental measurements.     

A constitutive theory for shape memory polymers. Part I: Large deformations

A constitutive theory is developed for shape memory polymers. It is to describe the thermomechanical properties of such materials under large deformations. The theory is based on the idea, which is developed in the work of Liu et al. [2006. Thermomechanics of shape memory polymers: uniaxial experiments and constitutive modeling. Int. J. Plasticity 22, 279-313], that the coexisting active and frozen phases of the polymer and the transitions between them provide the underlying mechanisms for strain storage and recovery during a shape memory cycle. General constitutive functions for nonlinear thermoelastic materials are used for the active and frozen phases. Also used is an internal state variable which describes the volume fraction of the frozen phase. The material behavior of history dependence in the frozen phase is captured by using the concept of frozen reference configuration. The relation between the overall deformation and the stress is derived by integration of the constitutive equations of the coexisting phases. As a special case of the nonlinear constitutive model, a neo-Hookean type constitutive function for each phase is considered. The material behaviors in a shape memory cycle under uniaxial loading are examined. A linear constitutive model is derived from the nonlinear theory by considering small deformations. The predictions of this model are compared with experimental measurements.     

Deformation of plastically compressible hardening-softening-hardening solids

Motivated by a model of the response of vertically aligned carbon nanotube (VACNT) pillars in uniaxial compression, we consider the deformation of a class of compressible elastic-viscoplastic solids with a hardening-softening-hardening variation of flow strength with plastic strain. In previous work (Hutchens et al. 2011) a constitutive relation was presented and used to model the response of VACNT pillars in axisymmetric compression. Subsequently, it was found that due to a programming error the constitutive relation presented in the paper (Hutchens et al. 2011) was not the one actually implemented. In particular, the plastic flow rule actually used did not satisfy plastic normality. Here, we present the constitutive formulation actually implemented in the previous work (Hutchens et al. 2011). Dynamic, finite deformation, finite element calculations are carried out for uniaxial compression, uniaxial tension and for indentation of a "half-space" by a conical indenter tip. A sequential buckling-like deformation mode is found in com- pression when there is plastic non-normality and hardening-softening-hardening. The same material characterization gives rise to a Lüders band-like deformation mode in ten- sion. When there is a deformation mode with a sharp front along mesh boundaries, the overall stress-strain response contains high frequency oscillations that are a mesh artifact. The responses of non-softening solids are also analyzed and their overall stress-strain behavior and deformationmodes are compared with those of hardening-softening- hardening solids. We find that indentation with a sharp in- denter tip gives a qualitatively equivalent response for hardening and hardening-softening-hardening solids.