• Computers and Concrete
• /
• v.7 no.4
• /
• pp.365-386
• /
• 2010

This paper presents the physical formulation of a 1D material model suitable for seismic applications. It is written within the framework of thermodynamics with internal variables that is, especially, very efficient for the phenomenological representation of material behaviors at macroscale: those of the representative elementary volume. The model can reproduce the main characteristics observed for concrete, that is nonsymetric loading rate-dependent (viscoelasticity) behavior with appearance of permanent deformations and local hysteresis (continuum plasticity), stiffness degradation (continuum damage), cracking due to displacement localization (discrete plasticity or damage). The parameters have a clear physical meaning and can thus be easily identified. Although this point is not detailed in the paper, this material model is developed to be implemented in a finite element computer program. Therefore, for the benefit of the robustness of the numerical implementation, (i) linear state equations (no local iteration required) are defined whenever possible and (ii) the conditions in which the presented model can enter the generalized standard materials class - whose elements benefit from good global and local stability properties - are clearly established. To illustrate the capabilities of this model - among them for Earthquake Engineering applications - results of some numerical applications are presented.

• Computers and Concrete
• /
• v.1 no.2
• /
• pp.131-150
• /
• 2004

We present in this work a coupled phenomenological chemo-mechanical model that represents the degradation of concrete-like materials. The chemical behaviour is described by the nowadays well known simplified calcium leaching approach. And the mechanical damage behaviour is described by a continuum damage model which involves the gradient of the damage quantity. The coupled nonlinear problem at hand is addressed within the context of the finite element method. For the equation governing the calcium dissolution-diffusion part of the problem, special care is taken to treat the highly nonlinear calcium conductivity and solid calcium functions. The algorithmic design is based on a Newton-type iterative scheme where use is made of a recently proposed relaxed linearization procedure. And for the equation governing the damage part of the problem, an augmented Lagrangian formulation is used to take into account the damage irreversibility constraint. Finally, numerical simulations are compared with experimental results on cement paste.

• Journal of the Korean Chemical Society
• /
• v.17 no.5
• /
• pp.324-331
• /
• 1973

We study a mixture of ideal gases by use of recently developed methods in continuum thermodynamics of irreversible processes. A complete form of the free energy function and the gas law for each component are derived directly from an entropy production inequality by assuming that: (1) Constitutive functions depend on the mass densities, the diffusion velocities, the temperature and its gradient only. (2) Phenomenological coefficients appearing in an extra entropy flux are material constants. (3) The internal energy density per unit mass is independent of the total mass density (Joule).

• Proceedings of the Korea Concrete Institute Conference
• /
• 2006.05b
• /
• pp.633-636
• /
• 2006

Impact damage modeling of concrete under high strain rate loading conditions is investigated. A phenomenological penetration model that can account for complicated impact and penetration process such as the rate and loading history response of concrete, the microstructure-penetration interaction etc. is discussed. Constitutive law compatible with Second Law of thermodynamics and coupled damage and plasticity modelling based on continuum damage mechanics are also examined. The purpose of this paper is preliminarily to study with respect to impact and penetration models for concrete before the development of that model.

• Journal of the Korean Society for Heat Treatment
• /
• v.7 no.4
• /
• pp.233-243
• /
• 1994

Constitutive relation of thermoelasto-plastic material undergoing phase transformation during quenching process were developed on the basic of continuum thermodynamics. The metallic structure, temperature and residual stresses distributions were numerically calculated by the finite element technique. The metallic structure were defined by transformation from austenite to pearlite and characterized as a fuction of thermal history and mixture rule of phase. On the distribution of thermal stress along the radial direction, axial and tangential stresses are compressive in the surface, and tential in the inner part. Radial stress is tensile in the whole body. The reversion of residual stress takes plase at 11.5~15.5mm from the center.

• Coupled systems mechanics
• /
• v.7 no.1
• /
• pp.5-25
• /
• 2018

A fully-coupled thermodynamic-based transient finite element formulation is proposed in this article for electric, magnetic, thermal and mechanic fields interactions limited to the linear case. The governing equations are obtained from conservation principles for both electric and magnetic flux, momentum and energy. A full-interaction among different fields is defined through Helmholtz free-energy potential, which provides that the constitutive equations for corresponding dual variables can be derived consistently. Although the behavior of the material is linear, the coupled interactions with the other fields are not considered limited to the linear case. The implementation is carried out in a research version of the research computer code FEAP by using 8-node isoparametric 3D solid elements. A range of numerical examples are run with the proposed element, from the relatively simple cases of piezoelectric, piezomagnetic, thermoelastic to more complicated combined coupled cases such as piezo-pyro-electric, or piezo-electro-magnetic. In this paper, some of those interactions are illustrated and discussed for a simple geometry.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2002.05a
• /
• pp.796-801
• /
• 2002

The goal of this research is the shape design of the valve using a computer simulation. For an analysis a basic mathematical model describing compression cycle is considered as consisting of five sets of coupled equations. These are the volume equation (kinematics), valve dynamic equation (dynamics), ideal gas equation (thermodynamics), Bernoulli equation (fluid dynamics), and dynamic equation of fluid particle based on Helmholtz equation (acoustics). Valve motion is made by the superposition of free vibration modes obtained by the finite element method. That is, the eigenvalues and eigenvectors are the sufficient modeling factors fur the valve in the simulation program. Thus, to design a shape of the valve, shape design sensitivity through chain-ruled derivatives is considered from two sensitivity coefficients, one is the design sensitivity of the capability of compressor with respect to the eigenvalues of the valve, and the other is the design sensitivity of the eigenvalue with respect to the shape change of the valve. In this research, the continuum design sensitivity analysis concepts are used for the latter.

• Transactions of Materials Processing
• /
• v.33 no.1
• /
• pp.18-35
• /
• 2024

In the present work, the evolution rules for the internal variables including continuum damage factors are obtained using the thermodynamic framework, which are in turn facilitated to derive the elastic-plastic constitutive relation for the particulate composites. Using the Mori-Tanaka scheme, the homogenization on state and internal variables such as back-stress and damage factors is carried out to procure the rate independent plasticity relations. Moreover, the degradation of mechanical properties of constituents is depicted by the distinctive damages such that the phase and interfacial damages are treated individually accordingly, whereas the kinematic hardening is depicted by combining the Armstrong-Frederick and Phillips' back-stress evolutions. On the other hand, the present constitutive relation for each phase is expressed in terms of the respective damage-free effective quantities, then, followed by transformation into the damage affected overall nominal relations using the aforementioned homogenization concentration factors. An emphasis is placed on the qualitative analyses for strain localization by observing the perturbation growth instead of the conventional bifurcation analyses. It turns out that the proposed constitutive model offers a wide range of strain localization behavior depending on the evolution of various internal variable descriptions.

• Membrane Journal
• /
• v.10 no.3
• /
• pp.139-147
• /
• 2000

Non-Fickian (or anomalous) diffusion was observed in transient sorption of aromatic solvents(such as benzene, toluene, and chlorobenzene) in fluoropolymers (such as ETFE, ECTFE and PVDF). In this study, five other transient sorption models (Crank, Long ＆ Richman, Berens ＆ Hopfenberg, Neogi, Li) based on Fick's law were employed to fit the anomalous sorption data for aromatic solvents. The adjustable parameters were determined by least square analysis of the measured and predicted fractional uptake. For ETFE sorption data slightly deviating from Fickian behavior, all the models exhibited satisfactory results in fitting the anomalous sorption data. In particular, Neogj model predicted intrinsic diffusivity (0.4～0.8$\times$10$^{-5}$ $\textrm{cm}^2$/day) and equilibrium diffusivity (0.13～0.31$\times$10$^{-4}$ $\textrm{cm}^2$/day) as well as relaxation kinetics related to non-Fickain diffusion. For a typical sigmoidal sorption behavior in PVDF, only Crank's model could give the reasonable evaluation on transport properties. The ratio of intial diffusivity (D$_{i}$) to final equilibrium diffusivity (D$_{\infty}$) was ranged from 80 to 200. For the final stage of uptake In ECTFE with drastic acceleration, all the models exhibited significant deviations from the sorption data. New diffusion models based on thermodynamics and continuum mechanics should be employed to get valuable information on transport properties as well as relaxation kinetics coupled with non-Fickian diffusion.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.31 no.4
• /
• pp.191-197
• /
• 2018

This paper details the development of an isotropic elastic-damage constitutive model for polymeric foam based on irreversible thermodynamics to consider the growth and coalescence of voids. The constitutive equations describe the material behavior sustaining unilateral damage. To facilitate finite element analysis, the material properties for specific types of polymeric foams are applied to the developed model; the model is then implemented in ABAQUS as a user-defined material subroutine. To validate the developed damage model, the simulated results are compared to the results of a series of tensile tests on various polymeric foams. The proposed damage model can be utilized to further research on continuum damage mechanics and finite element analysis of polymeric foams in computational engineering.