应变局部化分析中两类不同材料模型的讨论

A DISCUSSION ON SOME RELATIONSHIPS BETWEEN TWO DIFFERENT MATERIAL MODELS RELATED WITH STRAIN LOCALIZATION ANALYSIS ~1)

特定情况下单相固体材料率相关模型与多孔介质中的渗流作用均对问题的动力应变局部化分析产生内尺度律效应,对两类问题基本解之间的关系进行讨论,给出了两类不同材料模型解之间的若干联系.

The goal of this paper is to give a detailed discussion on the relationships between the basic theories used for strain localization analysis of single and multi phase materials.Strain localization refers to the phenomenon by which deformations in materials localise into narrow bands of intense straining. For isothermal rate-independent solids, strain localization has been analysed as a material instability within a theoretical framework developed by many authors. However the analysis does not involve a length-scale parameter, and related numerical solutions show an excessive mesh dependence. Recent studies have elucidated the mathematical background of the mesh-sensitivity problem. The differential equation of motion may lose hyperbolicity as soon as softening occurs. This means that the wave speed becomes imaginary and consequently a solution without physical significance is obtained in dynamic localization problems. It is thus that in single phase materials both the effective plastic strain and the band width are strongly mesh dependent unless some regularization is introduced. Various kinds of modifications and generalisations of standard continuum plasticity have been proposed to avoid these difficulties in localization simulation. Viscoplasticity has been recognized by several authors to provide a satisfactory framework for the analysis of strain localization in solids. As indicated by many authors, rate-dependent constitutive model naturally introduces a length-scale parameter into the dynamic initial value problem. On the other hand, numerical simulations of strain localization in a multiphase media (i.e. fluid saturated geomaterials) have evidenced that the mesh dependence of the results is not so dramatic as in single phase materials. In multiphase materials, the equivalent plastic strain is only weakly mesh sensitive, and an internal length scale may exist under the dynamic case with certain conditions. However, the investigation for the relationships between the theories in these two kinds of different materials, i.e. single phase material with rate dependent model and multi-phase material with seepage action, is still needed to be performed. For this purpose, the possible presence of length scales introduced by the permeability and rate parameters in multi-phase and single phase materials are investigated in detail in this paper. Some relationships between the results of these two different problems are discussed and presented.