scholarly journals A chemo-mechano-thermodynamical contact theory for adhesion, friction, and (de)bonding reactions

2021 ◽  
pp. 108128652110327
Author(s):  
Roger A. Sauer ◽  
Thang X. Duong ◽  
Kranthi K. Mandadapu
Keyword(s):  
Computational Models ◽  
Constitutive Relations ◽  
Thermal Contact ◽  
Irreversible Thermodynamics ◽  
Material Behavior ◽  
Mechanical Contact ◽  
Field Equations ◽  
Basic Principles ◽  
Analytical Test ◽  
Model Equations

This work presents a self-contained continuum formulation for coupled chemical, mechanical, and thermal contact interactions. The formulation is very general and, hence, admits arbitrary geometry, deformation, and material behavior. All model equations are derived rigorously from the balance laws of mass, momentum, energy, and entropy in the framework of irreversible thermodynamics, thus exposing all the coupling present in the field equations and constitutive relations. In the process, the conjugated kinematic and kinetic variables for mechanical, thermal, and chemical contact are identified, and the analogies between mechanical, thermal, and chemical contact are highlighted. Particular focus is placed on the thermodynamics of chemical bonding distinguishing between exothermic and endothermic contact reactions. Distinction is also made between long-range, non-touching surface interactions and short-range, touching contact. For all constitutive relations, examples are proposed and discussed comprehensively with particular focus on their coupling. Finally, three analytical test cases are presented that illustrate the thermo-chemo-mechanical contact coupling and are useful for verifying computational models. Although the main novelty is the extension of existing contact formulations to chemical contact, the presented formulation also sheds new light on thermo-mechanical contact, because it is consistently derived from basic principles using only a few assumptions.

scholarly journals Phase-field gradient theory

2021 ◽  
Vol 72 (2) ◽  
Author(s):  
Luis Espath ◽  
Victor Calo
Keyword(s):  
Free Energy ◽  
Field Equation ◽  
Field Gradient ◽  
Phase Field ◽  
Constitutive Relations ◽  
The Body ◽  
Second Grade ◽  
Gradient Theory ◽  
Boundary Edge ◽  
Field Equations

AbstractWe propose a phase-field theory for enriched continua. To generalize classical phase-field models, we derive the phase-field gradient theory based on balances of microforces, microtorques, and mass. We focus on materials where second gradients of the phase field describe long-range interactions. By considering a nontrivial interaction inside the body, described by a boundary-edge microtraction, we characterize the existence of a hypermicrotraction field, a central aspect of this theory. On surfaces, we define the surface microtraction and the surface-couple microtraction emerging from internal surface interactions. We explicitly account for the lack of smoothness along a curve on surfaces enclosing arbitrary parts of the domain. In these rough areas, internal-edge microtractions appear. We begin our theory by characterizing these tractions. Next, in balancing microforces and microtorques, we arrive at the field equations. Subject to thermodynamic constraints, we develop a general set of constitutive relations for a phase-field model where its free-energy density depends on second gradients of the phase field. A priori, the balance equations are general and independent of constitutive equations, where the thermodynamics constrain the constitutive relations through the free-energy imbalance. To exemplify the usefulness of our theory, we generalize two commonly used phase-field equations. We propose a ‘generalized Swift–Hohenberg equation’—a second-grade phase-field equation—and its conserved version, the ‘generalized phase-field crystal equation’—a conserved second-grade phase-field equation. Furthermore, we derive the configurational fields arising in this theory. We conclude with the presentation of a comprehensive, thermodynamically consistent set of boundary conditions.

RADIATING COLLAPSE WITH VANISHING WEYL STRESSES

2005 ◽  
Vol 14 (03n04) ◽  
pp. 667-676 ◽  
Author(s):  
S. D. MAHARAJ ◽  
M. GOVENDER
Keyword(s):  
Irreversible Thermodynamics ◽  
Temperature Profiles ◽  
Junction Conditions ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Extended Irreversible Thermodynamics ◽  
Recent Approach ◽  
Dust Solution ◽  
Limiting Case

In a recent approach in modeling a radiating relativistic star undergoing gravitational collapse the role of the Weyl stresses was emphasized. It is possible to generate a model which is physically reasonable by approximately solving the junction conditions at the boundary of the star. In this paper we demonstrate that it is possible to solve the Einstein field equations and the junction conditions exactly. This exact solution contains the Friedmann dust solution as a limiting case. We briefly consider the radiative transfer within the framework of extended irreversible thermodynamics and show that relaxational effects significantly alter the temperature profiles.

scholarly journals Aspects of Uncertainty Analysis for Large Nonlinear Computational Models

2010 ◽  
Vol 24-25 ◽  
pp. 25-41 ◽  
Author(s):  
Keith Worden ◽  
W.E. Becker ◽  
Manuela Battipede ◽  
Cecilia Surace
Keyword(s):  
Finite Element ◽  
Monte Carlo ◽  
Computational Models ◽  
Element Model ◽  
Finite Element Models ◽  
Bayesian Algorithm ◽  
Basic Principles ◽  
Structure Interaction ◽  
Output Uncertainty ◽  
Input Uncertainties

This paper concerns the analysis of how uncertainty propagates through large computational models like finite element models. If a model is expensive to run, a Monte Carlo approach based on sampling over the possible model inputs will not be feasible, because the large number of model runs will be prohibitively expensive. Fortunately, an alternative to Monte Carlo is available in the form of the established Bayesian algorithm discussed here; this algorithm can provide information about uncertainty with many less model runs than Monte Carlo requires. The algorithm also provides information regarding sensitivity to the inputs i.e. the extent to which input uncertainties are responsible for output uncertainty. After describing the basic principles of the Bayesian approach, it is illustrated via two case studies: the first concerns a finite element model of a human heart valve and the second, an airship model incorporating fluid structure interaction.

Implosion Analysis of Concrete Cylindrical Vessels

1979 ◽  
Vol 101 (1) ◽  
pp. 98-102
Author(s):  
H. Suzuki ◽  
W. F. Chen ◽  
T. Y. Chang
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Fracture Behavior ◽  
Constitutive Relations ◽  
Analysis Procedure ◽  
Material Behavior ◽  
Ultimate State ◽  
Element Analysis ◽  
Proposed Model ◽  
Effect Of Hydrostatic Pressure

Concrete constitutive relations which can simulate the overall material behavior up to and including its ultimate state under general triaxial loading conditions have been developed. The proposed constitutive relations include: 1) plastic deformation considering the effect of hydrostatic pressure, 2) a dual criterion predicting the fracture of concrete in terms of either stresses or strains, and 3) post-fracture behavior of concrete. Corresponding to the constitutive model, a finite element analysis procedure has also been utilized. Based on the proposed model, implosion pressures and load-deformation responses of several concrete vessels were obtained. The numerical results correlate quite well with the experimental data when the dual criterion was used.

Premetric representation of mechanics, electromagnetism and gravity

2018 ◽  
Vol 15 (supp01) ◽  
pp. 1840002 ◽  
Author(s):  
Yakov Itin
Keyword(s):  
Field Theory ◽  
Constitutive Relations ◽  
Classical Field Theory ◽  
Classical Field ◽  
Field Equations ◽  
Basic Field ◽  
Alternative Representation ◽  
Spacetime Metric ◽  
Underlying Manifold

The premetric formalism is an alternative representation of a classical field theory in which the field equations are formulated without the spacetime metric. Only the constitutive relations between the basic field variables can involve the metric of the underlying manifold. In this paper, we present a brief pedagogical review of the premetric formalism in mechanics, electromagnetism, and gravity.

scholarly journals Tolerance and asymptotic modelling of dynamic thermoelasticity problems for thin micro-periodic cylindrical shells

Meccanica ◽  
2020 ◽  
Vol 55 (12) ◽  
pp. 2391-2411 ◽  
Author(s):  
Barbara Tomczyk ◽  
Marcin Gołąbczak
Keyword(s):  
Cell Size ◽  
Constitutive Relations ◽  
Cylindrical Shells ◽  
Theory Of Elasticity ◽  
Asymptotic Model ◽  
Dynamic Thermoelasticity ◽  
Oscillating Coefficients ◽  
Stationary Action ◽  
A Cell ◽  
Model Equations

AbstractThe problem of linear dynamic thermoelasticity in Kirchhoff–Love-type circular cylindrical shells having properties periodically varying in circumferential direction (uniperiodic shells) is considered. In order to describe thermoelastic behaviour of such shells, two mathematical averaged models are proposed—the non-asymptotic tolerance and the consistent asymptotic models. Considerations are based on the known Kirchhoff–Love theory of elasticity combined with Duhamel-Neumann thermoelastic constitutive relations and on Fourier’s theory of heat conduction. The non-asymptotic tolerance model equations depending on a cell size are derived applying the tolerance averaging technique and a certain extension of the known stationary action principle. The consistent asymptotic model equations being independent on a microstructure size are obtained by means of the consistent asymptotic approach. Governing equations of both the models have constant coefficients, contrary to starting shell equations with periodic, non-continuous and oscillating coefficients. As examples, two special length-scale problems will be analysed in the framework of the proposed models. The first of them deals with investigation of the effect of a cell size on the shape of initial distributions of temperature micro-fluctuations. The second one deals with study of the effect of a microstructure size on the distribution of total temperature field approximated by sum of an averaged temperature and temperature fluctuations.

Conjugate Heat Transfer and Estimation of Thermal State of Elements of the Thermal Protection Shield Package

2019 ◽  
pp. 44-57
Author(s):  
V.A. Tovstonog
Keyword(s):  
Heat Transfer ◽  
Thermal Deformation ◽  
Conjugate Heat Transfer ◽  
Computational Models ◽  
Thermal Protection ◽  
Thermal State ◽  
Mechanical Contact ◽  
Thermal Insulating ◽  
Temperature State ◽  
Radiation Shields

This article presents the physical and computational models of heat transfer and the high-temperature flow path thermal protection with the use of radiation shields package. The analysis of the thermal insulating ability and temperature state of a multi-element radiation shields package was performed. It is shown that the distribution the temperature of the package elements is uneven, which can cause different thermal deformation of elements, the distortion of the shield, the possibility of mechanical contact of neighboring elements and the deterioration of the heat insulating ability.

A Fully Coupled Theory and Variational Principle for Thermal–Electrical–Chemical–Mechanical Processes

2014 ◽  
Vol 81 (11) ◽  
Author(s):  
Pengfei Yu ◽  
Shengping Shen
Keyword(s):  
Variational Principle ◽  
Electrostatic Potential ◽  
Constitutive Relations ◽  
Irreversible Thermodynamics ◽  
Electrochemical Reactions ◽  
Mechanical Coupling ◽  
Field Diffusion ◽  
Chemical And Biological Systems ◽  
Fully Coupled ◽  
Large Research

Thermal–electrical–chemical–mechanical coupling controls the behavior of many transport and electrochemical reactions processes in physical, chemical and biological systems. Hence, advanced understanding of the coupled behavior is crucial and attracting a large research interest. However, most of the existing coupling theories are limited to the partial coupling or particular process. In this paper, on the basis of irreversible thermodynamics, a variational principle for the thermal electrical chemical mechanical fully coupling problems is proposed. The complete fully coupling governing equations, including the heat conduction, mass diffusion, electrochemical reactions and electrostatic potential, are derived from the variational principle. Here, the piezoelectricity, conductivity, and electrochemical reactions are taken into account. Both the constitutive relations and evolving equations are fully coupled. This theory can be used to deal with coupling problems in solids, including conductors, semiconductors, piezoelectric and nonpiezoelectric dielectrics. As an application of this work, a developed boundary value problem is solved numerically in a mixed ion-electronic conductor (MIEC). Numerical results show that the coupling between electric field, diffusion, and chemical reactions influence the defect distribution, electrostatic potential and mechanical stress.

Study on Non-Local Damage Constitutive Model of Concrete under Freeze-Thaw Action

2010 ◽  
Vol 452-453 ◽  
pp. 133-136 ◽  
Author(s):  
Zong Min Liu ◽  
Ji Ze Mao ◽  
Hai Yan Song
Keyword(s):  
Constitutive Model ◽  
Internal State ◽  
Constitutive Relations ◽  
Irreversible Thermodynamics ◽  
Local Damage ◽  
Variable Theory ◽  
Freeze Thaw ◽  
Adjacent Point ◽  
Damage Constitutive Model ◽  
Non Local

Concrete is multi-phase composites. Due to the inhomogeneity of mechanical properties and complexity of physical properties, constitutive relations of concrete are more complicated. Starting from irreversible thermodynamics theory, internal state variable theory and nonlocal field theory, non-local damage constitutive model of concrete under freeze-thaw action is established in this paper. In the model, non-local influence functions are discussed which are used to describe interplay of damage between adjacent point.

Stiffness Comparisons Between Adventitia, Media and Full Thickness Specimens From Human Atherosclerotic Carotid Arteries

2009 ◽  
Author(s):  
Allen H. Hoffman ◽  
Zhongzhao Teng ◽  
Calvin Mui ◽  
Jie Zheng ◽  
Pamela K. Woodard ◽  
...  
Keyword(s):  
Material Properties ◽  
Computational Models ◽  
Carotid Arteries ◽  
Layered Composite ◽  
Material Behavior ◽  
Full Thickness ◽  
Paired Samples ◽  
Highly Nonlinear ◽  
Deductive Method ◽  
The Media

Arteries display highly nonlinear, anisotropic material behavior and can be considered to be a layered composite of fiber oriented materials composed of three layers: intima, media and adventitia. The intima does not affect the material properties of the artery. Thus, the mechanical properties of an artery result from the combined interaction of the media and adventitia with each layer displaying different material properties. It has been widely accepted that atherosclerosis changes the material properties of the arterial wall. However, little experimental data exists relating the properties of the media and adventitia of atherosclerotic vessels to the overall properties of the artery. Knowledge of the properties of human atherosclerotic tissues is essential for an improved understanding the effects of atherosclerosis and also for creating more accurate computational models for predicting the effects of the disease [1]. A prior study of bovine carotid arteries determined the properties of the adventitia and media using a deductive method [2]. This paper focuses on directly measuring and comparing the stiffness of paired samples of adventitia, media and full thickness specimens from human atherosclerotic carotid arteries.

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