• Title/Summary/Keyword: Tensor Invariant

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Fracture and Hygrothermal Effects in Composite Materials (복합재의 파괴와 hygrothermal 효과에 관한 연구)

  • Kook-Chan Ahn;Nam-Kyung Kim
    • Journal of the Korean Society of Safety
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    • v.11 no.4
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    • pp.143-150
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    • 1996
  • This is an explicit-Implicit, finite element analysis for linear as well as nonlinear hygrothermal stress problems. Additional features, such as moisture diffusion equation, crack element and virtual crack extension(VCE ) method for evaluating J-integral are implemented in this program. The Linear Elastic Fracture Mechanics(LEFM) Theory is employed to estimate the crack driving force under the transient condition for and existing crack. Pores in materials are assumed to be saturated with moisture in the liquid form at the room temperature, which may vaporize as the temperature increases. The vaporization effects on the crack driving force are also studied. The Ideal gas equation is employed to estimate the thermodynamic pressure due to vaporization at each time step after solving basic nodal values. A set of field equations governing the time dependent response of porous media are derived from balance laws based on the mixture theory Darcy's law Is assumed for the fluid flow through the porous media. Perzyna's viscoplastic model incorporating the Von-Mises yield criterion are implemented. The Green-Naghdi stress rate is used for the invariant of stress tensor under superposed rigid body motion. Isotropic elements are used for the spatial discretization and an iterative scheme based on the full newton-Raphson method is used for solving the nonlinear governing equations.

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A Nonlinear Constitutive Model for Progressive Fracturing of Concrete (콘크리트의 점진적(漸進的) 파괴(破壞)에 대한 비선형(非線型) 구성(構成)모델확립연구(硏究))

  • Oh, Byung Hwan
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.4 no.2
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    • pp.55-64
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    • 1984
  • Presented is a nonlinear constitutive model for progressive tensile fracturing of concrete. The model is incremental, path-dependent, and tensorialy invariant. The total strain tensor is assumed to be a sum of a purely elastic component and an inelastic component. The material is considered to contain weak planes of all directions which characterize the planes of the microcracks. A one-to-one functional dependence is assumed between the normal stress and the normal strain across each of the weak planes. The tangential stiffness of concrete is then derived form the principle of virtual work. The present theory can be applied to loading histories which are nonproportional or during which the principal directions rotate. Good agreement with the available direct tensile test data which cover strain-softening is demonstrated.

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Heat Aging Effects on the Material Property and the Fatigue Life of Vulcanized Natural Rubber, and Fatigue Life Prediction Equations

  • Choi Jae-Hyeok;Kang Hee-Jin;Jeong Hyun-Yong;Lee Tae-Soo;Yoon Sung-Jin
    • Journal of Mechanical Science and Technology
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    • v.19 no.6
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    • pp.1229-1242
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    • 2005
  • When natural rubber is used for a long period of time, it becomes aged; it usually becomes hardened and loses its damping capability. This aging process affects not only the material property but also the (fatigue) life of natural rubber. In this paper the aging effects on the material property and the fatigue life were experimentally investigated. In addition, several fatigue life prediction equations for natural rubber were proposed. In order to investigate the aging effects on the material property, the load-stretch ratio curves were plotted from the results of the tensile test, the compression test and the simple shear test for virgin and heat-aged rubber specimens. Rubber specimens were heat-aged in an oven at a temperature ranging from $50^{\circ}C$ to $90^{\circ}C$ for a period ranging from 2 days to 16 days. In order to investigate the aging effects on the fatigue life, fatigue tests were conducted for differently heat-aged hourglass-shaped and simple shear specimens. Moreover, finite element simulations were conducted for the specimens to calculate physical quantities occurring in the specimens such as the maximum value of the effective stress, the strain energy density, the first invariant of the Cauchy-Green deformation tensor and the maximum principal nominal strain. Then, four fatigue life prediction equations based on one of the physical quantities could be obtained by fitting the equations to the test data. Finally, the fatigue life of a rubber bush used in an automobile was predicted by using the prediction equations, and it was compared with the test data of the bush to evaluate the reliability of those equations.