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Exp-ln模型与广义黏弹性理论的橡胶本构模型及其应用研究

提出了一种描述橡胶材料不同应变率下力学响应的黏超弹本构模型。首先,利用Instron实验机和SHTB实验装置,开展橡胶材料单轴拉伸实验;其次,结合Exp-ln超弹性本构模型和广义黏弹性方法,建立了橡胶材料黏超弹本构模型;再次,推导本构模型三维增量格式,编写了用户子程序(VUMAT),验证了本构模型的一维和三维有效性;最后,建立橡胶底座冲击附加载荷计算数值模型,并将冲击附加载荷实验与数值仿真进行对比验证。结果表明:单轴拉伸实验与数值解吻合较好,冲击附加载荷实验值与仿真值误差约为7%,验证了黏超弹本构模型的正确性。     

一种改进的Yeoh超弹性材料本构模型

橡胶通常被看作一种不可压缩各向同性的超弹性材料,其本构模型通常用应变能密度方程表示。针对Yeoh模型偏软的特性,该文提出了一种改进的Yeoh超弹性材料本构模型。基于连续介质力学大变形理论,给出了改进的Yeoh模型在三种特殊变形模式下的应力-应变关系,并与原有的Yeoh模型和实验数据进行了对比。结果表明:改进的Yeoh模型在保持Yeoh模型体现反“S”形应力-应变关系的前提下,有效地克服了Yeoh模型在预测等双轴拉伸曲线时“偏软”的特性。在较大的应变范围内能够同时准确地预测单轴、平面和等双轴拉伸-压缩的应力-应变关系,具有较大的工程应用价值。     

未硫化橡胶非线性粘弹性本构模型研究

建立一种新的未硫化橡胶力学行为的描述方法。为了充分研究未硫化橡胶在不同变形模式下复杂的应力-应变行为,设计了3种不同的力学特性实验:单轴拉伸、压缩与剪切试验。发现未硫化橡胶的应力-应变关系表现出很强的非线性和率相关性。提出结合Yeoh应变能函数的广义Maxwell粘超弹性模型,拟合分析表明试验结果与模拟结果一致性较好。发现与硫化橡胶一样,必须采用多工况下的实验数据才能得到变形协调的粘弹性本构模型。实验结果和建立的本构模型有助于工程师更好的理解未硫化橡胶的力学行为,为橡胶的制造过程仿真提供理论基础。     

弹射冲击载荷作用下沥青混凝土路面面层的损伤

沥青混凝土作为一种粘弹性材料一般只研究其疲劳损伤特性,冲击损伤研究较少。针对路面在弹射载荷作用下产生中低应变率响应的特点,采用Cauchy应变表达的三维简化ZWT(朱-王-唐)非线性粘弹本构模型以及应变率相关的损伤演化模型,建立了增量形式并将Kirchhoff应力转化为Cauchy应力,编写用户材料子程序嵌入有限元软件中。推导了恒应变率条件下含损伤的简化ZWT本构表达式,使用最小二乘法拟合出本构参数。分析了沥青混凝土场坪面层的冲击损伤,阐明了损伤变化规律、分布规律,为发射场坪的选择提供了一定参考。     

弯曲型橡胶缓冲器冲击试验与数值仿真

通常进行橡胶缓冲器的冲击有限元数值分析时，由于橡胶材料的应变率效应，需要采用材料动态本构模型。但是对于受冲击载荷的弯曲型橡胶缓冲器，根据弯曲型结构力学特点，提出采用准静态超弹材料模型替代复杂的超-粘弹动态模型进行有限元数值冲击分析的思路。通过鼓型弯曲结构橡胶缓冲器水下爆炸冲击试验，对比基于通用有限元软件ABAQUS进行的弯曲型橡胶缓冲器爆炸冲击仿真（准静态材料模型），验证上述思路的合理性与有效性。研究结果表明，该思路为类似的弯曲型橡胶缓冲器的冲击有限元数值仿真提供了一种简单、合理的工程设计借鉴。     

动力荷载下聚氨酯泡沫材料本构关系研究进展

聚氨酯泡沫材料是一种应用广泛、应变率敏感、静水压力相关的多孔介质材料。文中综述了近年来国内外聚氨酯泡沫材料本构关系的研究进展。通过对几种应变率相关的本构模型,如粘弹、粘弹塑性等类型本构进展的介绍,分析了这些本构的特点和适用范围。根据已有的实验和本构关系,指出建立聚氨酯泡沫材料动态本构关系过程中需要考虑的主要问题,最后展望了聚氨酯泡沫材料的本构关系发展趋势。     

基于不可逆热力学的Ni-Ti合金动态本构模型及其有限元实现

为了准确描述Ni-Ti形状记忆合金在高应变率下的动态压缩力学行为,基于不可逆热力学理论框架假定了两个内变量表征Ni-Ti合金应力诱发马氏体相变与塑性屈服的不可逆变形过程,分别推导了马氏体相变与塑性屈服演化规律的主控方程,构建了Ni-Ti合金的三维动态本构模型。根据材料单轴动态压缩实验的应力-应变曲线并采用最小二乘法对本构参数进行了优化识别,然后采用应力补偿更新算法,通过隐式用户子程序接口UMAT将动态本构模型嵌入ABAQUS有限元软件,实现了Ni-Ti合金在高应变率下动态压缩力学行为的数值模拟。通过比对发现,模拟结果与实验数据吻合良好,验证了动态本构模型与UMAT子程序的准确性。本工作为Ni-Ti合金在高速冲击、切削等极端条件下的工程应用奠定了基础。     

丁羟包覆层的黏超弹本构模型

为了准确地描述丁羟（HTPB）包覆层在有限变形下的拉伸力学特性,研究了HTPB包覆层的黏超弹本构模型。分别构建了含率相关函数的本构模型和并联式本构模型,前者由超弹模型与率相关项相乘得到,后者由超弹模型与含损伤因子的黏弹模型并联而成。进行了HTPB包覆层的单步松弛、多步松弛和不同速率的单轴拉伸试验,并将试验数据用于拟合模型参数。结果表明,HTPB包覆层对应变率极其敏感,且具有很大的延伸率,表现出明显的黏超弹特性;两种模型均能很好地预测HTPB包覆层较大形变范围内的拉伸力学性能,其中含率相关函数的模型的描述更加准确,其研究具有重要的军事意义。     

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.     

Thermomechanical analysis,modelling and simulation of the forming of pre-impregnated thermoplastics composites

In this paper, the viscoelastic behaviours of pre-impregnated (prepreg) thermoplastic composites are analysed using the bias-extension test. A new constitutive model is proposed in order to simulate the forming of thermoplastic composite prepregs at the macroscopic scale. The model is based on a continuous approach. Hyperelastic behaviours are associated with dry reinforcements. Four principal deformation modes, all considered independent, define the hyperelastic potential: the elongation in warp direction, the elongation in weft direction, the in-plane shear strain and the bending contribution. Experience shows that viscoelastic behaviour is mainly associated with the in-plane shear deformation. A non-linear visco-hyperelastic model based on the generalisation of Maxwell rheological model is considered for this type of deformation mode. The finite element simulation of a stamping case using this model is introduced. The influence of temperature on the forming stage and the performance of the model are evaluated.     

Visco-hyperelastic constitutive law for modeling of foam’s behavior

This paper proposes a new visco-hyperelastic constitutive law for modeling the finite-deformation strain rate-dependent behavior of foams as compressible elastomers. The proposed model is based on a phenomenological Zener model, which consists of a hyperelastic equilibrium spring and a Maxwell element parallel to it. The hyperelastic equilibrium spring describes the steady state response. The Maxwell element, which captures the rate-dependency behavior, consists of a nonlinear viscous damper connected in series to a hyperelastic intermediate spring. The nonlinear damper controls the rate-dependency of the Maxwell element. Some strain energy potential functions are proposed for the two hyperelastic springs. compressibility effect in strain energy is described by entering the third invariant of deformation gradient tensor into strain energy functions. A history integral method has been used to develop a constitutive equation for modeling the behavior of the foams. The applied history integral method is based on the Kaye–BKZ theory. The material constant parameters, appeared in the formulation, have been determined with the aid of available uniaxial tensile experimental tests for a specific material.     

橡胶减振元件中高频机械阻抗的数值模拟

由于驻波效应,橡胶减振元件受宽频带激励会产生中高频段共振,导致减振效果下降,舰船水下中高频段声辐射量增大,因此掌握橡胶减振元件中高频振动隔离性能非常重要.基于有限元高频适用范围的关系理论结合大型通用有限元软件ABAQUS,采用结构阻尼法分析减振元件的高频振动特性（点阻抗、传递阻抗和隔振传递率）,获得了与试验数据结果相一致分析结果,表明采用结构阻尼数值方法分析橡胶减振元件的动态性能是一种可行的中高频振动隔离性能评估手段.     

A selective smoothed finite element method with visco-hyperelastic constitutive model for analysis of biomechanical responses of brain tissues

Brain tissues are known for exhibiting complex nonlinear and time-dependent properties, which require visco-hyperelastic constitutive models for proper simulation. In this paper, a Total Lagrangian Explicit Selective Smoothed Finite Element Method (Selective S-FEM) is formulated to analyze the dynamic behavior of incompressible brain tissues undergoing extremely large deformation. The proposed Selective S-FEM deals with three-dimensional problems using four-node tetrahedron elements that can be automatically generated for geometrically complex soft tissues. It consists of the three key ingredients. (i) A visco-hyperelastic constitutive model is developed within the framework of S-FEM in the first time, allowing adequate modeling of the dynamic brain tissue behavior. (ii) Selective S-FEM strategy is used for overcome the mesh distortion and the volumetric locking that often occurs in soft tissues. (iii) Total Lagrangian formulation is used in an explicit algorithm allowing rigorous simulation of extreme large deformation. (iv) A combined implementation of Selective S-FEM with the visco-hyperelastic constitutive model for dynamic simulations. The shear deformation is calculated by Face/Edge-based S-FEM, and the volume deformation is calculated by NS-FEM. Numerical experiments show that Selective S-FEM is a robust solver with good accuracy, and excellent ability to reduce element distortion effects in simulate time-dependence behavior of bio-tissues.     

Uni-axial strain loading of a rubber rod by planar shock waves

Summary The uni-axial strain loading of a rubber rod struk head-on by a planar shock wave is studied experimentally and numerically. A physical model capable of describing the rubber response to its collision with the incident shock wave is proposed. This model takes into account the rubber compressibility and the friction forces developed in the contact surface between the rubber and its surrounding rigid walls. The good agreement that exists between experiments and their numerical simulations verifies the validity of the proposed physical model and the accuracy of the numerical scheme used for the numerical simulations. It is found that for the considered loading mode, i.e., uni-axial strain loading, no shock waves exists in the rubber rod. The stresses measured/calculated in the rod result from compression wave motion (with constant velocity) in it. It is also found that the friction developed between the rubber rod and its bordering rigid walls plays an important role in damping the intensity of the wave propagating in the rubber due to its collision with the incident shock wave. The larger is the friction, the larger is the stress damping rate in the rubber.     

Baseline rolling resistance for tires’ on-road fuel efficiency using finite element modeling

Calculation of truck tires rolling resistance, using the finite element method and considering variables such as incompressible visco-hyperelastic rubber materials, accurate tire geometry and steady temperature distribution, is presented. The model was validated using experimentally measured contact area and contact stresses. Rolling resistance was calculated for three values of axle load, tire inflation pressure, temperature and speed. In addition, regression analysis was used to propose a mathematical expression for predicting rolling resistance as a function of the considered variables. Finally, the contribution of tire’s rubber components to the internal energy was quantified, and it was found that sidewall and subtread were the most relevant. The results of this study will help differentiate the contribution of pavement parameters, such as mean profile depth and international roughness index, to fuel efficiency.     

A visco-hyperelastic constitutive description of elastomeric foam

This study focuses on the constitutive modelling of finite deformation in elastomeric polyurethane foams—in particular, PORON-4701-59-25045-1648 (0.4 g/cm³ density) and PORON-4701-59-20093-1648 (0.32 g/cm³ density). Their mechanical properties under compression, for engineering strains up to about 80%, are characterized over a range of strain rates between 10⁻² and 10³/s. Dynamic compression is applied using a split Hopkinson pressure bar device. Experimental results show that the behaviour of elastomeric foam is sensitive to strain rate and can be described by a visco-hyperelastic material model. In this model, the quasi-static response is defined by compressible hyperelasticity, whereby the strain energy potential is assumed to be representable by a newly proposed polynomial series with three independent parameters. Strain rate sensitivity is characterized by incorporating a nonlinear Maxwell relaxation model with four parameters. The (seven) material parameters in the constitutive model are determined from high-speed mechanical testing methods tailored for high-compliance materials. A comparison of predictions based on the proposed frame-independent constitutive equation with experiments shows that the model is able to describe the rate dependent behaviour of the elastomeric foams examined.     

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。