Neural network modelling for damage behaviour of composites using full-field strain measurements

This paper presents a neural network modelling method for damage behaviour of composite materials in conjunction with full-field strain measurements. The proposed method utilises the overall structural response of a laminate composite specimen to develop the constitutive model of a single ply unidirectional laminate. Based on an energy principle, a performance function for training the neural networks is derived in terms of the applied external work and the induced strain energy. This allows the proposed method to develop the neural networks without the presence of stress information that is not necessarily obtainable in experiments with non-uniform deformation. The use of neural networks also enables the proposed method to model the damage behaviour without the constraints on the parameter space, such that a more representative model is developed for the actual material behaviour. An example of tailoring the proposed method to model the in-plane shear damage behaviour of a carbon fibre reinforced plastic (CFRP) laminate is demonstrated as well as its numerical validation. The practical application of the proposed method to multi-axial damage-related nonlinear behaviour of composite is presented using the experimental data obtained from a tensile test with an open-hole specimen.     

考虑加/卸载速率影响的Ti-Ni形状记忆合金简化本构模型

系统研究了Ti-Ni形状记忆合金丝(SMA)应力-应变曲线、特征点应力、耗能能力、等效阻尼比随材料直径、应变幅值、加载速率、加载循环次数的变化规律;针对SMA唯象Brinson本构模型无法描述SMA动态力学性能的缺点,结合前述试验结果,提出了一种可考虑加/卸载速率影响的SMA简化本构模型。应用该模型对试验用SMA丝进行模拟,所得应力-应变曲线各特征点平均误差仅为3%,结果表明:所建立的速率相关SMA简化本构模型可较为精确地描述SMA在应力诱发相变过程中的超弹性力学行为,同时可反映加/卸载速率和应变幅值等主要因素对其动力本构模型的影响;该模型结构形式简单,具有较好的工程应用前景。     

混凝土坝地震动力损伤分析

基于塑性损伤本构理论,将损伤变量作为内变量,在Drucker-Prager本构模型中引入损伤变量,考虑材料损伤引起的材料劲度的退化,基于非关联流动法则计算材料的塑性应变,根据材料的有效塑性应变计算损伤量,考虑到张开裂缝闭合时材料弹性劲度的恢复,推导了考虑塑性损伤的混凝土动态本构关系,并给出了内变量的计算步骤和动力方程的迭代格式。最后利用建立的动态本构模型对Koyna重力坝进行了非线性地震响应时程分析,并给出了关键时刻坝体最大受拉损伤分布,结果表明在坝颈和坝基处出现了较大的损伤,坝颈处的损伤最终形成由下游向上游的开裂破坏,这与该坝的实际震害较为一致。     

混凝土循环加卸载动态损伤特性研究

利用大型多功能动静力三轴仪对混凝土试件进行了5种应变速率下的动态循环加卸载压缩试验。对混凝土的物理力学参数的变化规律进行了统计分析。结果表明:峰值应力和弹性模量随加载速率的提高而增大,但峰值应变随加载速率的变化表现出较大的离散性。在此基础上,进一步研究了混凝土在不同加载速率下的刚度退化规律。最后,选用基于Weibull统计理论的分段式动态损伤本构模型对试验数据进行拟合。经验证,此模型能够较好的模拟混凝土材料的本构特性。     

三轴加载条件下混凝土的神经网络本构模型

神经网络由大量并行处理单元构成,适合于描述多影响因素的非线性复杂因果规律,为研究材料本构特性提供了一条崭新的途径。利用 BP 网络的模拟能力来代替传统的方法,建立了一个三轴加载情况下混凝土的神经网络本构模型,用于描述混凝土在侧压力恒定轴向单调加载条件下的本构关系。从模型对训练和检验样本的模拟结果可以看出,这个经过训练的含有双隐层的神经网络本构模型具有很高的学习精度和良好的泛化能力,适合在结构工程问题中应用。     

Large-Deformation Constitutive Theories for Structural Composites: Rate-Dependent Concepts and Effect of Microstructure

Abstract:  Polymer-based composite materials are widely used in applications subjected to a variety of loading types, including shock and impact loading in the range of hundreds of strain per second. The behaviour of composite laminates loaded at those rates is typically nonlinear and may involve rather large strains to failure. In the present study, the large-deformation characteristics and constitutive representations of structural composites were investigated as functions of strain rate and temperature. A plain-weave vinyl ester composite material was selected for the study. Tensile tests of off-axis coupon specimens were conducted over several orders of strain rates and limited change of temperatures. A three-parameter constitutive model was proposed to model the large-deformation stress–strain relationship. The constitutive model was then used to predict the material response at different strain rates. The model predictions were verified by a different set of tests. The basic concepts and methodologies involved in reducing such data to constitutive equations that can be used in commercial computational codes to enable structural analysis in the presence of large-strain progressive damage under dynamic loading is discussed.     

A phenomenological constitutive modelling of polyethylene foam under multiple impact conditions

This paper extends the knowledge into the mechanical behaviour characterizations and constitutive modelling of polyethylene (PE) foam under multiple loading and unloading. The mechanical properties of PE foam subjected to single loading cases can be obtained by uniaxial compressive tests at quasi‐static and dynamic states. And the multiple loading and unloading behaviours of the foam can be revealed by consecutive drop tests. The major objective of this research is to propose a phenomenological model consists of shape function and modulus function, which can be predicted compressive response of PE foam for single loading cases. The constitutive models of foamed PE under multiple loading and unloading conditions are established by both using hyperbolic function, where the relations between coefficients and residual strain are introduced. And then, experiments are conducted to validate the proposed model by comparing the constitutive models proposed in this paper and those predicting by finite element software ABAQUS with those by experiments, showing that the proposed models are more accurate for predicting acceleration‐times curves of multiple drop scenarios.     

Modeling constitutive relationship of Ti40 alloy using artificial neural network

Constitutive relationship equation reflects the highly non-linear relationship of flow stress as function of strain, strain rate and temperature. It is a necessary mathematical model that describes basic information of materials deformation and finite element simulation. In this paper, based on the experimental data obtained from Gleeble-1500 Thermal Simulator, the constitutive relationship model for Ti40 alloy has been developed using back propagation (BP) neural network. The predicted flow stress values were compared with the experimental values. It was found that the absolute relative error between predicted and experimental data is less than 8.0%, which shows that predicted flow stress by artificial neural network (ANN) model is in good agreement with experimental results. Moreover, the ANN model could describe the whole deforming process better, indicating that the present model can provide a convenient and effective way to establish the constitutive relationship for Ti40 alloy.     

损伤材料的动力响应特性

研究了工程材料在动力载荷下损伤演化的计算模型。提出了一般材料在各向异性损伤状态下的两种动力损伤模型。第一种以有效应力的等效值的幂函数为基础 ,第二种以损伤应变能释放率为基础。通过数值分析研究了损伤结构元件的动力响应及损伤材料的动力特性。说明了结构元件中损伤发展的分析方法和它们的有限元程序的执行过程。该研究表明 :损伤结构的频谱下移 ,损伤材料的阻尼比变高 ,响应的振幅明显增加 ,损伤结构可能发生由于损伤发展引起的共振。     

Phenomenological formulation of viscoplastic constitutive equation for polyethylene by taking into account strain recovery during unloading

A viscoplastic constitutive equation for polyethylene that properly describes significant strain recovery during unloading was proposed. The constitutive equation was formulated by combining the kinematic hardening creep theory of Malinin and Khadjinsky with the nonlinear kinematic hardening rule of Armstrong and Frederick. In order to describe the strain recovery, the nonlinear kinematic hardening rule was modified. First, a loading surface was defined in a viscoplastic strain space. A loading–unloading criterion was then introduced using the loading surface. Moreover, a new parameter was defined by the relationship between the loading surface and the current state of the viscoplastic strain, and the evolution equation of back stress was modified using this parameter, which has some value only during unloading. Experimental results for polyethylene were simulated by using the modified constitutive equations, and cyclic inelastic deformation in both uniaxial and biaxial states of stress was predicted. Finally, the validity of the above-described modification was verified, and the features of the constitutive equation and the deformation were discussed.