• Transactions of Materials Processing
• /
• v.17 no.3
• /
• pp.161-169
• /
• 2008

In the present work, the two-back stress model is proposed and continuum damage mechanics (CDM) is incorporated into the plastic constitutive relation in order to describe the plastic deformation localization and the damage evolution in a deforming continuum body. Coupling between damage mechanics and isothermal rate independent plasticity is performed using the kinematic hardening rule, which in turn is formulated by combining the nonlinear Armstrong-Frederick rule and the Phillips rule. The numerical analyses are carried out within h deformation theory. It is noted that the damage evolution within a work piece accelerates the plastic deformation localization such that the material with lower hardening exponent results in a rapid shear band formation. Moreover, the results from the numerical analysis reflected closely with the micro-structures around the fractured regime. The effects of the various hardening parameters on deformation localization are also investigated. As the nonlinear strain rate description in the back stress evolution becomes dominant, the strain localization becomes intensified as well as the damage evolution.

• Coupled systems mechanics
• /
• v.4 no.1
• /
• pp.1-18
• /
• 2015

The state-based peridynamics is considered a nonlocal method in which the equations of motion utilize integral form as opposed to the partial differential equations in the classical continuum mechanics. As a result, the enforcement of boundary conditions in solid mechanics analyses cannot follow the standard way as in a classical continuum theory. In this paper, a new approach for the boundary condition enforcement in the state-based peridynamic formulation is presented. The new method is first formulated based on a convex kernel approximation to restore the Kronecker-delta property on the boundary in 1-D case. The convex kernel approximation is further localized near the boundary to meet the condition that recovers the correct boundary particle forces. The new formulation is extended to the two-dimensional problem and is shown to reserve the conservation of linear momentum and angular momentum. Three numerical benchmarks are provided to demonstrate the effectiveness and accuracy of the proposed approach.

• Proceedings of the Korean Geotechical Society Conference
• /
• 2009.09a
• /
• pp.3-26
• /
• 2009

Superloading yield surface concept is newly introduced together with subloading yield surface conception in order to describe full gradation continuously of the mechanical behavior of soils from typical sand through intermediate soil to typical clay (All Soils). Finite deformation theory has been applied to the soil skeleton-pore water coupled continuum mechanics, which enables us to discuss things in a perpetual stream from stable state to unstable state like from deformation to failure and vice versa like from liquefaction to post liquefaction consolidation of sand (All States). Incremental form of the equation of motion has been employed in the continuum mechanics in order to incorporate a rate type constitutive equation, which is "All Round" enough to predict ground behavior under both static and dynamic conditions. The present paper is the shortened version of the lecture note delivered in 2008 Theoretical and Applied Mechanics Conference, Science Council Japan, but with newly developed application examples.

• Interaction and multiscale mechanics
• /
• v.7 no.1
• /
• pp.525-542
• /
• 2014

The state-based peridynamics is considered a nonlocal method in which the equations of motion utilize integral form as opposed to the partial differential equations in the classical continuum mechanics. As a result, the enforcement of boundary conditions in solid mechanics analyses cannot follow the standard way as in a classical continuum theory. In this paper, a new approach for the boundary condition enforcement in the state-based peridynamic formulation is presented. The new method is first formulated based on a convex kernel approximation to restore the Kronecker-delta property on the boundary in 1-D case. The convex kernel approximation is further localized near the boundary to meet the condition that recovers the correct boundary particle forces. The new formulation is extended to the two-dimensional problem and is shown to reserve the conservation of linear momentum and angular momentum. Three numerical benchmarks are provided to demonstrate the effectiveness and accuracy of the proposed approach.

• Structural Engineering and Mechanics
• /
• v.70 no.4
• /
• pp.445-455
• /
• 2019

Since the days of yore, plate's flexural analysis and formulation were dependent on the assumed coordinate system. In uncovering the coordinates-independent flexural interpretation, in this study, the plate bending analysis has been interpreted in terms of the tensor's components of curvatures and bending moments, in accordance with the continuum mechanics. The paper herein presents the theoretical formulations and conceptual perspectives of the Hydrostatic Method of Analysis (HM) that combines the continuum mechanics with the elasticity theory; the graphical statics and analysis; the theory of thin isotropic and orthotropic plates.

• Structural Engineering and Mechanics
• /
• v.77 no.6
• /
• pp.765-777
• /
• 2021

Recently, the plate bending analysis has been interpreted in terms of the tensor's components of curvatures and bending moments by presenting the conceptual perspectives of the Hydrostatic Method of Analysis (HM) and theoretical formulations that combine the continuum mechanics with the graphical statics analysis, the theory of thin orthotropic and isotropic plates, and the elasticity theory. In pursuance of uncovering a genuine formulation of the plate's flexural differential equations, that possess the general-covariance and coordinates-independency. This study had then, tackled various natural and structural problems in both solid and fluid branches of the continuum mechanics in a description of such theoretical and conceptual attainment in uncovering the dimensional independent diffeomorphism covariant partial differential laws.

• Structural Engineering and Mechanics
• /
• v.80 no.5
• /
• pp.625-643
• /
• 2021

In this paper, we present a new method to calculate interface warping functions for the analysis of beams with geometric and material discontinuities in the longitudinal direction. The classical Saint Venant torsion theory is extended to a three-dimensional domain by considering the longitudinal direction. The interface warping is calculated by considering both adjacent cross-sections of a given interface. We also propose a finite element procedure to simultaneously calculate the interface warping function and the corresponding twisting center. The calculated interface warping functions are employed in the continuum-mechanics based beam formulation to analyze arbitrary shape cross-section beams with longitudinal discontinuities. Compared to the previous work by Yoon and Lee (2014a), both geometric and material discontinuities are considered with fewer degrees of freedom and higher accuracy in beam finite element analysis. Through various numerical examples, the effectiveness of the proposed interface warping function is demonstrated.

• Multiscale and Multiphysics Mechanics
• /
• v.1 no.2
• /
• pp.171-188
• /
• 2016

Gradient enhanced theories of crystal plasticity enjoy great research interest. The focus of this work is on thermodynamically consistent modeling of grain size dependent hardening effects. In this contribution, we develop a model framework for damage coupled to gradient enhanced crystal thermoplasticity. The damage initiation is directly linked to the accumulated plastic slip. The theoretical setting is that of finite strains. Numerical results on single-crystalline metal showing the development of damage conclude the paper.

• Membrane and Water Treatment
• /
• v.13 no.4
• /
• pp.167-172
• /
• 2022

The analytical results are presented for the mass transfer in a cylindrical pore covering from the macroscale, multiscale to nanoscale owing to the variation of the inner diameter of the pore. When the thickness h_bf of the physically adsorbed layer potentially fully formed on the pore wall is comparable to but less than the inner radius R₀ of the pore, the multiscale flow occurs consisting of both the nanoscale non-continuum adsorbed layer flow and the macroscopic continuum liquid flow; When R₀ ≤ h_bf, the flow in the whole pore is essentially non-continuum; When R₀ is far greater than h_bf, the flow in the whole pore can be considered as macroscopic and continuum and the adsorbed layer effect is negligible.

• Structural Engineering and Mechanics
• /
• v.58 no.2
• /
• pp.231-242
• /
• 2016

To minimize the compliance of frame, a method to optimize the topology of bracing system in a frame is presented. The frame is first filled uniformly with a truss-like continuum, in which there are an infinite number of members. The frame and truss-like continuum are analysed by the finite element method altogether. By optimizing the distribution of members in the truss-like continuum over the whole design domain, the optimal bracing pattern is determined. As a result, the frame's lateral stiffness is enforced. Structural compliance and displacement are decreased greatly with a smaller increase in material volume. Since optimal bracing systems are described by the distribution field of members, rather than by elements, fewer elements are needed to establish the detailed structure. Furthermore, no numerical instability exists. Therefore it has high calculation effectiveness.