岩土介质应变局部化问题的广义塑性梯度理论研究
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摘要
进一步探索岩土介质的强度与变形机理,就必然要深入分析其细观变形和破坏性态。大量实验表明,由于试样的微细观层面上的不均匀性的影响,试样在破坏时常常出现狭窄带状高应变梯度区的应变局部化现象。研究应变局部化问题实质上是研究岩土工程的基本科学问题——岩土介质的一种真实破坏过程。基于传统连续介质力学的应变梯度理论难以反映岩土介质最基本的力学性质,如果能将广义塑性力学同应变梯度理论结合起来,应该能够得到一些新的启迪。
本文通过对宏观实验结果和CT实验结果的分析,提出一种可包含局部化变形的“相当小而非无穷小”的研究基元——“塑性梯度体元”,基于塑性梯度体元分析了应变局部化启动机制:建立起塑性应变的微分表达式后,随着硬(软)化模量从正值变为负值,变形模式将由均匀变形模式变为局部化变形模式。
进而,基于广义塑性力学的双屈服面模型和对本文的塑性梯度体元的分析,构造了由梯度依赖的双屈服面得到的塑性剪切应变和塑性体积应变的微分方程表达式,从而建立了广义塑性梯度模型的理论框架,使其在反映岩土介质的基本力学性质的同时,也能反映介质的应变局部化特征。给出了一种可能的梯度依赖的双屈服面的形式。阐述了广义塑性梯度模型模拟局部化变形模式的机理。提出了模型各个参数,尤其是其中“局部化”参数的物理意义和通过宏观可测量的物理量结合数值分析反推材料局部化参数的途径。
然后,在将位移进行离散的同时,也通过构造的C 1连续性的插值函数将塑性乘子在空间离散,得到一组以节点位移向量和节点塑性乘子向量为基本未知量的非线性方程组,从而建立了广义塑性梯度模型的数值模型,给出了相应的边界条件处理方法和数值算法。
最后,编制了2维FORTRAN90数值分析程序和VB后处理程序;给出了数值算例。算例显示了塑性应变局限于局部处发生和急剧发展的过程;塑性剪切应变和塑性体积应变进入局部化变形模式后都主要集中在局部化带内,反映出岩土在一定条件下的剪胀机理;避免了病态的网格敏感性;局部化带宽度受局部化参数影响。
In order to explore the strength and deformation mechanism of the geo-materials, some researches on the deformation and failure process in meso-scope must be performed. Many experiments have shown that the strain localization is caused by asymmetrical of the sample in micro-scope occurred during failure. In fact, the purpose to investigate the strain localization is to describe the actual failure process of geo-materials. It is expected that some new revelations will be obtained if the Generalized Plastic Mechanics is combined with strain-gradient theory to establish the Gradient-dependent Generalized Plasticity Mechanics by which the strain localization characteristics and the basic mechanics characteristics of geo-materials can be described at the same time.
The progress in this paper can be summarized as:
1、Based on the results of macro-experiment and some CT-experiment for geo-materials, A new plasticity gradient volume unit is proposed, which can describle the local deformation. The startup mechanism of strain localization is analysised: when the hardening Modulus (or sofftting Modulus) change from positive to negative, the deformation pattern will change from uniformity pattern to localization pattern.
2、Based on the theoretical frame of the Generalized Plastic Mechanics and the plastic strain gradient-dependent in the double yield functions, the differential expressions of plastical strains are constructed, then the frame of the Generalized Gradient-dependent Plastic Mechanics is established sequentially to describe the strain localization characteristics andthe basic mechanics characteristics of geo-materials. The model parameters, especially the parameters reflecting localization are also discussed and determined.
3、Both the displacement and the plastic factor are discretized by interpolation function with C 1 continuity in space. A set of non-linear equations taking the displacements and the plastic factors of nodes as the unknown variables are obtained to solve the new proposed mechanic model, the border condition and the increment algorithm are also gived in this paper.
4、A Fortran90 code with Post-processr in Visual Basic for the numerical modeling is given, after that, some numerical examples are implemented and the results demonstrate the development of plastic strain as well as the failure process with a localized strain in a narrow band, which reveal the failure mechanism of the samples in micro-scope.
本文通过对宏观实验结果和CT实验结果的分析,提出一种可包含局部化变形的“相当小而非无穷小”的研究基元——“塑性梯度体元”,基于塑性梯度体元分析了应变局部化启动机制:建立起塑性应变的微分表达式后,随着硬(软)化模量从正值变为负值,变形模式将由均匀变形模式变为局部化变形模式。
进而,基于广义塑性力学的双屈服面模型和对本文的塑性梯度体元的分析,构造了由梯度依赖的双屈服面得到的塑性剪切应变和塑性体积应变的微分方程表达式,从而建立了广义塑性梯度模型的理论框架,使其在反映岩土介质的基本力学性质的同时,也能反映介质的应变局部化特征。给出了一种可能的梯度依赖的双屈服面的形式。阐述了广义塑性梯度模型模拟局部化变形模式的机理。提出了模型各个参数,尤其是其中“局部化”参数的物理意义和通过宏观可测量的物理量结合数值分析反推材料局部化参数的途径。
然后,在将位移进行离散的同时,也通过构造的C 1连续性的插值函数将塑性乘子在空间离散,得到一组以节点位移向量和节点塑性乘子向量为基本未知量的非线性方程组,从而建立了广义塑性梯度模型的数值模型,给出了相应的边界条件处理方法和数值算法。
最后,编制了2维FORTRAN90数值分析程序和VB后处理程序;给出了数值算例。算例显示了塑性应变局限于局部处发生和急剧发展的过程;塑性剪切应变和塑性体积应变进入局部化变形模式后都主要集中在局部化带内,反映出岩土在一定条件下的剪胀机理;避免了病态的网格敏感性;局部化带宽度受局部化参数影响。
In order to explore the strength and deformation mechanism of the geo-materials, some researches on the deformation and failure process in meso-scope must be performed. Many experiments have shown that the strain localization is caused by asymmetrical of the sample in micro-scope occurred during failure. In fact, the purpose to investigate the strain localization is to describe the actual failure process of geo-materials. It is expected that some new revelations will be obtained if the Generalized Plastic Mechanics is combined with strain-gradient theory to establish the Gradient-dependent Generalized Plasticity Mechanics by which the strain localization characteristics and the basic mechanics characteristics of geo-materials can be described at the same time.
The progress in this paper can be summarized as:
1、Based on the results of macro-experiment and some CT-experiment for geo-materials, A new plasticity gradient volume unit is proposed, which can describle the local deformation. The startup mechanism of strain localization is analysised: when the hardening Modulus (or sofftting Modulus) change from positive to negative, the deformation pattern will change from uniformity pattern to localization pattern.
2、Based on the theoretical frame of the Generalized Plastic Mechanics and the plastic strain gradient-dependent in the double yield functions, the differential expressions of plastical strains are constructed, then the frame of the Generalized Gradient-dependent Plastic Mechanics is established sequentially to describe the strain localization characteristics andthe basic mechanics characteristics of geo-materials. The model parameters, especially the parameters reflecting localization are also discussed and determined.
3、Both the displacement and the plastic factor are discretized by interpolation function with C 1 continuity in space. A set of non-linear equations taking the displacements and the plastic factors of nodes as the unknown variables are obtained to solve the new proposed mechanic model, the border condition and the increment algorithm are also gived in this paper.
4、A Fortran90 code with Post-processr in Visual Basic for the numerical modeling is given, after that, some numerical examples are implemented and the results demonstrate the development of plastic strain as well as the failure process with a localized strain in a narrow band, which reveal the failure mechanism of the samples in micro-scope.
引文
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