China 
Africa 
Explore chapters and articles related to this topic
Continuum theory of granular materials
Published in M. Oda, K. Iwashita, Mechanics of Granular Materials, 2020
For static conditions, the localization problem is one of the local bifurcation type instabilities. At the bifurcation point, there are two possible solutions: one is a homogeneous solution and the other has a discontinuity in the deformation gradient. Therefore, the onset condition of material instability corresponds to the loss of ellipticity of the boundary value problem. It is known that, using a conventional plasticity theory with strain softening or a non-associated flow rule, the boundary value problem may become ill-posed. Geometrical instability may occur even in the elliptic region. This type of instability corresponds to diffused type bifurcation (Hill & Hutchinson, 1975). Instability condition like a stationary wave condition is connected with other localization conditions. The inter-connections between several criteria such as uniqueness, ellipticity, etc. are summarized by Bigoni & Hueckel (1991).
The increasing of exploitation safety of potassium salt deposit based on geological-geomechanical simulation
Published in Vladimir Litvinenko, EUROCK2018: Geomechanics and Geodynamics of Rock Masses, 2018
Yu. Kashnikov, A. Ermashov, D. Shustov, D. Khvostantcev
The next step is geomechanical simulation of part of mine field that takes into account parameters of deposit exploitation and obtained physical and mechanical properties of rocks. Deformation and failure rheological model is a ground of stress state calculation of rock mass. The model considers primary, secondary and tertiary creep deformations separately. It also makes provision for weakening and failure of rocks with appearance of dilatancy (W. Wittke 1999, Doering, T. & Kiehl, J.R., 1996). Viscoplastic theory is the base of the model. Viscoplastic deformation increment corresponds to the plasticity theory: () {dεvp/dt}={εvp.}={0,F≤01ηF{∂Q/∂σ},F>0
Constitutive Models for Agricultural Soils
Published in Jie Shen, Radhey Lal Kushwaha, Soil-Machine Interactions, 2017
dεpk in equation (3.79) is determined by a work-hardening plasticity theory which involves: A yield criterion. It may be expressed by a yield function, fk(σ,εpk), for a work-hardening soil.A flow rule. It assumes that the plastic strain increments and stresses are related by the following specific form: () dεpk=βk∂gk(σ)∂σ
Ordered nitrogen complexes overcoming strength–ductility trade-off in an additively manufactured high-entropy alloy
Published in Virtual and Physical Prototyping, 2020
Dandan Zhao, Quan Yang, Dawei Wang, Ming Yan, Pei Wang, Mingguang Jiang, Changyong Liu, Dongfeng Diao, Changshi Lao, Zhangwei Chen, Zhiyuan Liu, Yuan Wu, Zhaoping Lu
On the other hand, a more heterogeneous microstructure with broader grain size distribution is obtained in the N-50. Based on the plasticity theory (Song et al. 2019; Ma and Zhu 2017), the coarse grains yield first during deformation, then the plastic deformation is constrained by the relative harder fine grains, near their grain boundaries strong plastic strain gradients are formed and result in higher strain hardening rate in the N-50 HEA with a more heterogeneous structure; a higher strain hardening rate can stabilise the plastic deformation, thus improving the ductility of the N-50. In addition, introducing nitrogen atoms into alloys with FCC structure can promote rotation of grain orientation from the 〈011〉 to 〈111〉 direction due to the lattice expansion induced by the nitrogen incorporation in octahedral interstice (Templier et al. 2010); therefore, texture is weakened in the N-50, which is also beneficial for the ductility (Lin et al. 2016; Zhang et al. 2019). Based on the above discussion, the nitrogen-doped HEA has a higher dislocation multiplication rate and more heterogeneous structure, resulting in the improvement of plastic deformation ability.
A historical review of the traditional methods and the internal state variable theory for modeling composite materials
Published in Mechanics of Advanced Materials and Structures, 2022
Ge He, Yucheng Liu, T. E. Lacy, M. F. Horstemeyer
The classical plasticity theory is a mathematical description of time-independent irreversible deformation of materials. For most composite materials, because they usually exhibit certain types of anisotropy due to the orientation of inclusions in the matrix, the yield function governing the elastic limit of these materials should have the capacity to capture the anisotropic nature as well. von Mises [73] have proposed general yield functions for some types of anisotropy but not including the transverse isotropy. This gap was later filled by Hill [19, 74, 75] who suggested using quadratic forms of the stress components to formulate the yield function for general anisotropic plastic solids. Although this theory was initially used for anisotropic metal materials, it was also promising being applied to fiber reinforced composites [76]. As an extension of Adkins and Rivlin’s elastic composites model [77], Mulhern et al. [78] formulated a general continuum model for rigid/plastic composites. This composites model is probably the simplest possible realistic model because the matrix was assumed to be incompressible without hardening and the extension of the composites along the fiber direction was constrained. These assumptions have greatly simply the model derivation but also limit its uses for different type of composite materials. For example, the fiber inextensibility assumption has limit the composites to the strong fiber reinforced ones, while for soft fibers, they will have axial non-negligible deformation during loading, and which needs to be considered by some more general composites models. As a matter of fact, in Mulhern et al.’s subsequent work [79], they allowed the fibers to be extensible and admitted an elastic strain in the fiber direction. Another important model dealing with the elastoplasticity was the self-consistent model, which experienced a history through elasticity [16], thermoelasticity [80], viscoelasticity [81] and then was employed by Dvorak and Bahei-EI-Din [82] for elastic-plastic behavior of composites. In their elastoplasticity model, the actual physical fiber was replaced by a composite cylinder consisting of a fiber surrounded by a layer of the matrix, thus the stress concentration at the fiber-matrix interface can be taken into account. In the 1990s, Spencer [83] proposed a plasticity theory which combined the yield conditions (analogous to von Mises [23, 73] and Tresca’s [84] isotropic yield conditions, respectively), associated flow rules and kinematic hardening rules for fiber reinforced metal based composites. The assumptions made in his model were mainly based on the experimental evident [85] that, for a fibrous boron-aluminium composite, the plastic yielding was independent on the tension in the fiber direction and the yield surface after plastic deformation would translate but remain the shape in stress-space.