The plastic strain of the material is irreversible and nonlinear. The material produces new plastic strain when loading. The total plastic strain is the result superimposed by plastic strain increments and depends on the loading history of the material. It is difficult to directly establish the relationship between total plastic strain and stress state. Therefore, the stress-strain relationship in the plastic deformation stage is generally expressed in the form of increment. In the geotechnical plasticity theory, there are two limitations for current modeling methods in determining the plastic strain increment. One is that the environmental factors affecting the mechanical properties of materials are not considered constitutive variables. The second is that an additional plastic potential function is required to determine the direction of plastic strain increment. The two limitations restrict the development of the plasticity model for geomaterials in unsteady environments. In this chapter, the authors propose a non-orthogonal plasticity modeling method to establish the incremental stress-strain-environment relationship in unsteady environments. When determining the magnitude of plastic strain increment, the environmental factors are used as the constitutive variables to describe the plastic strain behavior in unsteady environments. When determining the direction of plastic strain increment, a non-orthogonal flow rule without plastic potential function is proposed to obtain the non-orthogonal gradient of yield function. In addition, based on the geometric relationship between yield surface and generalized load increment, which is composed of mechanical load increment and environmental load increment, a loading/unloading criterion in unsteady environments is established in the strain-environment space, and it is applicable to both hardening and softening stages. It is worth noting that environmental factors not only affect the plastic deformation properties of materials but also their elastic deformation properties. In this book, our research interest mainly focuses on the former.

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Multi-physical and Non-orthogonal Geotechnical Plasticity Theory

  • Dechun Lu,
  • Xin Zhou,
  • Jingyu Liang,
  • Xiuli Du

摘要

The plastic strain of the material is irreversible and nonlinear. The material produces new plastic strain when loading. The total plastic strain is the result superimposed by plastic strain increments and depends on the loading history of the material. It is difficult to directly establish the relationship between total plastic strain and stress state. Therefore, the stress-strain relationship in the plastic deformation stage is generally expressed in the form of increment. In the geotechnical plasticity theory, there are two limitations for current modeling methods in determining the plastic strain increment. One is that the environmental factors affecting the mechanical properties of materials are not considered constitutive variables. The second is that an additional plastic potential function is required to determine the direction of plastic strain increment. The two limitations restrict the development of the plasticity model for geomaterials in unsteady environments. In this chapter, the authors propose a non-orthogonal plasticity modeling method to establish the incremental stress-strain-environment relationship in unsteady environments. When determining the magnitude of plastic strain increment, the environmental factors are used as the constitutive variables to describe the plastic strain behavior in unsteady environments. When determining the direction of plastic strain increment, a non-orthogonal flow rule without plastic potential function is proposed to obtain the non-orthogonal gradient of yield function. In addition, based on the geometric relationship between yield surface and generalized load increment, which is composed of mechanical load increment and environmental load increment, a loading/unloading criterion in unsteady environments is established in the strain-environment space, and it is applicable to both hardening and softening stages. It is worth noting that environmental factors not only affect the plastic deformation properties of materials but also their elastic deformation properties. In this book, our research interest mainly focuses on the former.