岩土类材料的损伤本构模型及其在冲击动力学问题中的应用
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摘要
岩石、混凝土材料等非均匀和各向异性材料的动态本构和冲击损伤破坏规律的研究,是现阶段冲击动力学领域的重要的科学问题之一。这一科学问题的研究对材料变形损伤破坏的非线性效应、应变率效应的耦合表征提出了新的挑战。
本文首先对岩土材料本构模型的研究概况和进展进行了较为全面、系统的回顾和总结。对现有的主要的冲击载荷下的动态损伤模型进行了较系统的评述和比较,并对当前的研究热点及趋势作了讨论。在此基础上,阐述了解决本课题理论问题的思路和方法。
岩土类材料的重要特征是其静压相关塑性屈服行为,本文在静水压相关的广义热粘塑性本构的理论框架下,从修正Drucker公设和应力空间中的屈服函数出发,以材料本构关系的内变量理论为工具,推导并建立了一般形式的,特别是静水压相关的热塑性和热粘塑性增量型本构关系的普适形式,其所得到的本构关系可以包含各种内变量硬(软)化行为、应变率硬(软)化行为、损伤软化、温度软化行为以及相互间的耦合作用。所给出的本构关系是以应力屈服面为基础的,具有普适性;对任何动态程序都特别适用和方便,易于嵌入到损伤材料的冲击动力学数值计算程序,具有很强的实用性。考虑到应用的重要性,文中特别给出了若干常用的岩土本构模型的增量本构关系计算公式和流程。
在较详细地论述了分形、分形维数概念及分形测量方法的基础上,将之与岩土材料损伤破坏所具有的分形特点相联系,尝试性地将分形几何引入到岩土材料损伤定义,详细地推导了岩土材料的拉伸状态下损伤演化方程。其损伤演化方程中,分形维数及其与损伤能量耗散率的关系的引入,不仅解决了损伤的确定问题,减少了损伤模型中的所涉及的岩土特性参数,而且新构造的分形损伤模型可计及岩土的天然损伤影响和应力波传播过程中引起的裂纹扩展效应新进展。
以岩土损伤分形本构模型的研究成果为基础,由岩石损伤分形维数和能量耗散率之间的关系,建立了拉压两种不同状态下的损伤演化方程,并以等效模量理论为基础建立了岩土材料含损伤的动态本构关系;利用本文所建立的含损伤本构模型,采用有限差分方法对砂岩冲击载荷下一维应变波传播问题进行了数值模拟,得到了应力波传播过程中,应力、分形维数、裂纹密度及损伤等量得演化规律,其结果对工程应用有指导意义。
弹体对岩石、混凝土等岩土类材料侵彻问题是涉及冲击损伤破坏的另一类问题,这是防护工程的基本问题之一。本文针对弹体对岩石材料侵彻深度问题,将量纲分析方法和神经网络理论相结合,建立了弹的长径比l_p/d、弹体形状系数ψ、弹体与岩土的比σ_(yt)/σ_(yp)强度、弹体与岩土材料的密度比ρ_p/ρ_t等神经网络输入量与弹体侵彻深度h网络输出量之间的非线性映射关系。在非线性映射关系基础上,由神经网络理论建立了弹体侵彻岩土材料的神经网络模型;并分别采用改进BP及RBF网络模型,通过对岩石、混凝土类材料的文献资料试验数据的整理,得到了对网络模型进行训练的样本及检测样本;通过对网络模型的训练,获得了弹体对混凝土、花岗岩等材料侵彻深度的满意输出结果。目前将人工神经网络引入弹体侵彻岩土材料深度的这一方面的研究工作及文献资料及研究成果尚不多见。
本文的研究工作对岩土材料应力波作用下的损伤、裂纹密度及分形维数的变化发展特性,以及基于人工神经网络的弹体侵彻岩土材料深度模型研究都具有重要的理论价值和工程实际意义。
Dynamic constitutive and regularity of damage of rock and concrete,which is non-uniform and anisotropic,etc,is one of important scientific problems of impact dynamics at present. Research of the important scientific problem is real challenge to couple between nonlinear effect of deformation and damage for material and rate of straining.
In this paper,progress and general research of the constitutive model of rock and concrete,ect. are critically reviewed.Various dynamic damage models are described and compared.At same time,the trends of damage constitutive models and researches needed for further development are discussed.Based on the above discussion,the key points of difficulty that may be met in the problem are clear and some new ideas to solve it are found.
Under theory of generalized them-visco-plastic constitutive related with hydrostatic pressure, the universal form of the thermoplastic and thermo-visco-plastic incrernental constitutive relations related with hydrostatic pressure and the computational routine are established from the modified Drucker's postulate and theory of internal variables in the constitutive relations and yield function in stress space.This constitutive relation can cover various kinds of plastic hardening(softening) behaviors,thermo-softening behaviors,damage-softening behaviors and their coupling effects between each other.This constitutive is based on stress yield surface in stress space and has universality.At same time,it can be used in program or commercial software of dynamics and can be easily inserted in program of numerical calculation of impact dynamics.The practicability is obvious.
Base on describing of fractal,fractal dimension and measuring of fractal in detail,relationship or comparison of fractal characteristics in damage of rock and concrete,ect is established by analysis.At same time,evidences for fractal distribution of micro-crack are given by documentation.Then variable of damage of material is defined related with fractal.Through describing damage of materials by fractal dimension,evolutionary equations of damage of rock and concrete,ect.under state of tension is are deduced in detail.Through introducing relationship between fractal dimension and dissipation of energy of damage in evolutionary equation,problem of excessive variables of damage model of rock or concrete,etc.is solved.The new model of fractal damage have advantages in influence of self-damage and in law of development of cracks in rock or concrete,ect.under stress waves.Fractal damage dynamic constitutive model is based on theory of model of equivalent modulus.Numerical simulations are carried out by existing program code of impact damage model.
Numerical simulations is based on fractal damage constitutive of rock or concrete,ect.And evolutionary damage equations are established by relationship between fractal dimension and dissipation of energy of damage.Numerical simulations on impulse loads are carried out by implementing the constitutive model of fractal damage sandrock in one dimcnsional strain stress by finite difference code.The variables such as waveforms of stress,mean density of crack,fractal dimension,and damage ect.are obtained.The numerical results such as variation of fractal,mean density of crack,and damage,ect.with propagation of stress are show good agreement with documents.
Penetration depth of projectiles into geo-medium,such as:rock and concrete etc.,is one of important problems of protective projects.In this article,nonlinear mapping relation between input of variables of l_p/d andσ_(yt)/σ_(yp) etc and output of penetration depth h is established by dimensional analysis and theory of artificial neural networks for problem of penetration depth of projectiles into geo-medium.Neural model of penetration depth of projectiles into geo-medium is got by nonlinear mapping relation.At same time,samples of neural network model is got from document data,which is treated according to need of modeling.Moreover,a satisfied output about penetration dcpth from modified BP neural networks and RBF neural network are gotten by a group of input sets and corresponding output sets,which comes from experimental data of document about concrete and granite.
本文首先对岩土材料本构模型的研究概况和进展进行了较为全面、系统的回顾和总结。对现有的主要的冲击载荷下的动态损伤模型进行了较系统的评述和比较,并对当前的研究热点及趋势作了讨论。在此基础上,阐述了解决本课题理论问题的思路和方法。
岩土类材料的重要特征是其静压相关塑性屈服行为,本文在静水压相关的广义热粘塑性本构的理论框架下,从修正Drucker公设和应力空间中的屈服函数出发,以材料本构关系的内变量理论为工具,推导并建立了一般形式的,特别是静水压相关的热塑性和热粘塑性增量型本构关系的普适形式,其所得到的本构关系可以包含各种内变量硬(软)化行为、应变率硬(软)化行为、损伤软化、温度软化行为以及相互间的耦合作用。所给出的本构关系是以应力屈服面为基础的,具有普适性;对任何动态程序都特别适用和方便,易于嵌入到损伤材料的冲击动力学数值计算程序,具有很强的实用性。考虑到应用的重要性,文中特别给出了若干常用的岩土本构模型的增量本构关系计算公式和流程。
在较详细地论述了分形、分形维数概念及分形测量方法的基础上,将之与岩土材料损伤破坏所具有的分形特点相联系,尝试性地将分形几何引入到岩土材料损伤定义,详细地推导了岩土材料的拉伸状态下损伤演化方程。其损伤演化方程中,分形维数及其与损伤能量耗散率的关系的引入,不仅解决了损伤的确定问题,减少了损伤模型中的所涉及的岩土特性参数,而且新构造的分形损伤模型可计及岩土的天然损伤影响和应力波传播过程中引起的裂纹扩展效应新进展。
以岩土损伤分形本构模型的研究成果为基础,由岩石损伤分形维数和能量耗散率之间的关系,建立了拉压两种不同状态下的损伤演化方程,并以等效模量理论为基础建立了岩土材料含损伤的动态本构关系;利用本文所建立的含损伤本构模型,采用有限差分方法对砂岩冲击载荷下一维应变波传播问题进行了数值模拟,得到了应力波传播过程中,应力、分形维数、裂纹密度及损伤等量得演化规律,其结果对工程应用有指导意义。
弹体对岩石、混凝土等岩土类材料侵彻问题是涉及冲击损伤破坏的另一类问题,这是防护工程的基本问题之一。本文针对弹体对岩石材料侵彻深度问题,将量纲分析方法和神经网络理论相结合,建立了弹的长径比l_p/d、弹体形状系数ψ、弹体与岩土的比σ_(yt)/σ_(yp)强度、弹体与岩土材料的密度比ρ_p/ρ_t等神经网络输入量与弹体侵彻深度h网络输出量之间的非线性映射关系。在非线性映射关系基础上,由神经网络理论建立了弹体侵彻岩土材料的神经网络模型;并分别采用改进BP及RBF网络模型,通过对岩石、混凝土类材料的文献资料试验数据的整理,得到了对网络模型进行训练的样本及检测样本;通过对网络模型的训练,获得了弹体对混凝土、花岗岩等材料侵彻深度的满意输出结果。目前将人工神经网络引入弹体侵彻岩土材料深度的这一方面的研究工作及文献资料及研究成果尚不多见。
本文的研究工作对岩土材料应力波作用下的损伤、裂纹密度及分形维数的变化发展特性,以及基于人工神经网络的弹体侵彻岩土材料深度模型研究都具有重要的理论价值和工程实际意义。
Dynamic constitutive and regularity of damage of rock and concrete,which is non-uniform and anisotropic,etc,is one of important scientific problems of impact dynamics at present. Research of the important scientific problem is real challenge to couple between nonlinear effect of deformation and damage for material and rate of straining.
In this paper,progress and general research of the constitutive model of rock and concrete,ect. are critically reviewed.Various dynamic damage models are described and compared.At same time,the trends of damage constitutive models and researches needed for further development are discussed.Based on the above discussion,the key points of difficulty that may be met in the problem are clear and some new ideas to solve it are found.
Under theory of generalized them-visco-plastic constitutive related with hydrostatic pressure, the universal form of the thermoplastic and thermo-visco-plastic incrernental constitutive relations related with hydrostatic pressure and the computational routine are established from the modified Drucker's postulate and theory of internal variables in the constitutive relations and yield function in stress space.This constitutive relation can cover various kinds of plastic hardening(softening) behaviors,thermo-softening behaviors,damage-softening behaviors and their coupling effects between each other.This constitutive is based on stress yield surface in stress space and has universality.At same time,it can be used in program or commercial software of dynamics and can be easily inserted in program of numerical calculation of impact dynamics.The practicability is obvious.
Base on describing of fractal,fractal dimension and measuring of fractal in detail,relationship or comparison of fractal characteristics in damage of rock and concrete,ect is established by analysis.At same time,evidences for fractal distribution of micro-crack are given by documentation.Then variable of damage of material is defined related with fractal.Through describing damage of materials by fractal dimension,evolutionary equations of damage of rock and concrete,ect.under state of tension is are deduced in detail.Through introducing relationship between fractal dimension and dissipation of energy of damage in evolutionary equation,problem of excessive variables of damage model of rock or concrete,etc.is solved.The new model of fractal damage have advantages in influence of self-damage and in law of development of cracks in rock or concrete,ect.under stress waves.Fractal damage dynamic constitutive model is based on theory of model of equivalent modulus.Numerical simulations are carried out by existing program code of impact damage model.
Numerical simulations is based on fractal damage constitutive of rock or concrete,ect.And evolutionary damage equations are established by relationship between fractal dimension and dissipation of energy of damage.Numerical simulations on impulse loads are carried out by implementing the constitutive model of fractal damage sandrock in one dimcnsional strain stress by finite difference code.The variables such as waveforms of stress,mean density of crack,fractal dimension,and damage ect.are obtained.The numerical results such as variation of fractal,mean density of crack,and damage,ect.with propagation of stress are show good agreement with documents.
Penetration depth of projectiles into geo-medium,such as:rock and concrete etc.,is one of important problems of protective projects.In this article,nonlinear mapping relation between input of variables of l_p/d andσ_(yt)/σ_(yp) etc and output of penetration depth h is established by dimensional analysis and theory of artificial neural networks for problem of penetration depth of projectiles into geo-medium.Neural model of penetration depth of projectiles into geo-medium is got by nonlinear mapping relation.At same time,samples of neural network model is got from document data,which is treated according to need of modeling.Moreover,a satisfied output about penetration dcpth from modified BP neural networks and RBF neural network are gotten by a group of input sets and corresponding output sets,which comes from experimental data of document about concrete and granite.
引文
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