A Viscoplastic Constitutive Theory for Monolithic Ceramics—I

1998 ◽  
Vol 120 (1) ◽  
pp. 155-161 ◽  
Author(s):  
L. A. Janosik ◽  
S. F. Duffy
Keyword(s):  
Potential Function ◽  
Constitutive Equations ◽  
Hydrostatic Stress ◽  
Functional Dependence ◽  
Threshold Function ◽  
Cauchy Stress ◽  
Creep Stress ◽  
Flow Potential ◽  
Tension And Compression ◽  
Monolithic Ceramics

This paper, which is the first of two in a series, provides an overview of a viscoplastic constitutive model that accounts for time-dependent material deformation (e.g., creep, stress relaxation, etc.) in monolithic ceramics. Using continuum principles of engineering mechanics, the complete theory is derived from a scalar dissipative potential function first proposed by Robinson (1978), and later utilized by Duffy (1988). Derivations based on a flow potential function provide an assurance that the inelastic boundary value problem is well posed, and solutions obtained are unique. The specific formulation used here for the threshold function (a component of the flow potential function) was originally proposed by Willam and Warnke (1975) in order to formulate constitutive equations for time-independent classical plasticity behavior observed in cement and unreinforced concrete. Here constitutive equations formulated for the flow law (strain rate) and evolutionary law employ stress invariants to define the functional dependence on the Cauchy stress and a tensorial state variable. This particular formulation of the viscoplastic model exhibits a sensitivity to hydrostatic stress, and allows different behavior in tension and compression.

scholarly journals A Viscoplastic Constitutive Theory for Monolithic Ceramics: I

1996 ◽  
Author(s):  
Lesley A. Janosik ◽  
Stephen F. Duffy
Keyword(s):  
Potential Function ◽  
Constitutive Equations ◽  
Hydrostatic Stress ◽  
Functional Dependence ◽  
Threshold Function ◽  
Cauchy Stress ◽  
Creep Stress ◽  
Flow Potential ◽  
Tension And Compression ◽  
Monolithic Ceramics

This paper, which is the first of two in a series, provides an overview of a viscoplastic constitutive model that accounts for time-dependent material deformation (e.g., creep, stress relaxation, etc.) in monolithic ceramics. Using continuum principles of engineering mechanics the complete theory is derived from a scalar dissipative potential function first proposed by Robinson (1978), and later utilized by Duffy (1988). Derivations based on a flow potential function provide an assurance that the inelastic boundary value problem is well posed, and solutions obtained are unique. The specific formulation used here for the threshold function (a component of the flow potential function) was originally proposed by Willam and Warnke (1975) in order to formulate constitutive equations for time-independent classical plasticity behavior observed in cement and unreinforced concrete. Here constitutive equations formulated for the flow law (strain rate) and evolutionary law employ stress invariants to define the functional dependence on the Cauchy stress and a tensorial state variable. This particular formulation of the viscoplastic model exhibits a sensitivity to hydrostatic stress, and allows different behavior in tension and compression.

A Viscoplastic Constitutive Theory for Monolithic Ceramics — II

1999 ◽  
Author(s):  
Lesley A. Janosik ◽  
Stephen F. Duffy
Keyword(s):  
Hydrostatic Stress ◽  
Rate Sensitivity ◽  
Time Dependent ◽  
Homogeneous State ◽  
Computer Algorithms ◽  
Load History ◽  
Deformation Response ◽  
Service Load ◽  
Tension And Compression ◽  
Monolithic Ceramics

This paper, which is the second of two in a series, exercises the viscoplastic constitutive model developed by the authors in the previous article (Janosik and Duffy, 1998). The model accounts for time-dependent phenomena (e.g., creep, rate sensitivity, and stress relaxation) in monolithic ceramics. Additionally, the formulation exhibits a sensitivity to hydrostatic stress, and allows different behavior in tension and compression. Here, the constitutive equations formulated for the flow law (i.e., the Strain rate) and the evolutionary law have been incorporated into computer algorithms for predicting the multiaxial inelastic (creep) response of a given homogeneous state of stress. Numerically simulated examples illustrate the model’s ability to capture the time-dependent phenomena suggested above. For each imposed service (load) history considered, creep curves and viscoplastic flow surfaces are examined to demonstrate the model’s ability to capture the inelastic creep deformation response. No attempt is made here to assess the accuracy of the model in comparison to experiment. A quantitative assessment is reserved for a later date, after the material constants have been suitably characterized for a specific ceramic material.

Constitutive Model of a Transversely Isotropic Bingham Fluid

2002 ◽  
Vol 69 (5) ◽  
pp. 641-648 ◽  
Author(s):  
D. N. Robinson ◽  
K. J. Kim ◽  
J. L. White
Keyword(s):  
Viscous Flow ◽  
Potential Function ◽  
Flow Characteristics ◽  
Transversely Isotropic ◽  
Bingham Fluid ◽  
Threshold Function ◽  
Isotropic Model ◽  
Flow Potential ◽  
Characterization Procedure

A constitutive theory is presented for a transversely isotropic, viscoplastic (Bingham) fluid. The theory accounts for threshold (yield) and viscous flow characteristics through inclusion of a potential function serving the dual role of a threshold function and a viscous flow potential. The arguments and form of the potential function derive from the theory of tensorial invariants. The model reduces to a transversely isotropic model of perfect plasticity in the limit of vanishing viscosity. In the limit of isotropy, it reduces to the Hohenemser-Prager generalization of Bingham’s model. A characterization procedure is prescribed based on correlation with experiments conducted under simple states of stress. Application is made to polymer melts filled with talc particles.

Internal Variable Theory Formulated by One Extended Potential Function

2020 ◽  
Vol 45 (3) ◽  
pp. 311-318
Author(s):  
Qiang Yang ◽  
Zhuofu Tao ◽  
Yaoru Liu
Keyword(s):  
Potential Function ◽  
Internal Variable ◽  
The State ◽  
Internal Variables ◽  
State Variables ◽  
Kinetic Rate ◽  
Variable Theory ◽  
Rate Laws ◽  
Flow Potential ◽  
Internal Variable Theory

AbstractIn the kinetic rate laws of internal variables, it is usually assumed that the rates of internal variables depend on the conjugate forces of the internal variables and the state variables. The dependence on the conjugate force has been fully addressed around flow potential functions. The kinetic rate laws can be formulated with two potential functions, the free energy function and the flow potential function. The dependence on the state variables has not been well addressed. Motivated by the previous study on the asymptotic stability of the internal variable theory by J. R. Rice, the thermodynamic significance of the dependence on the state variables is addressed in this paper. It is shown in this paper that the kinetic rate laws can be formulated by one extended potential function defined in an extended state space if the rates of internal variables do not depend explicitly on the internal variables. The extended state space is spanned by the state variables and the rate of internal variables. Furthermore, if the rates of internal variables do not depend explicitly on state variables, an extended Gibbs equation can be established based on the extended potential function, from which all constitutive equations can be recovered. This work may be considered as a certain Lagrangian formulation of the internal variable theory.

On a class of non-dissipative materials that are not hyperelastic

2008 ◽  
Vol 465 (2102) ◽  
pp. 493-500 ◽  
Author(s):  
K.R Rajagopal ◽  
A.R Srinivasa
Keyword(s):  
Physical Meaning ◽  
Constitutive Equations ◽  
Mechanical Response ◽  
Mass Density ◽  
Cauchy Stress ◽  
Response Functions ◽  
State Variables ◽  
Hyperelastic Materials ◽  
Current Mass ◽  
Helmholtz Potential

The purpose of this brief note is to develop fully Eulerian, implicit constitutive equations for the mechanical response of a class of materials that do not dissipate mechanical work in any process. We show that such materials can be modelled by obtaining a form for the Helmholtz potential as a function of the current mass density, the Cauchy stress and certain other parameters that capture anisotropic response. The resulting constitutive equations are of the form , where and are functions of the state variables of the system. The class of materials that can be obtained from such a constitutive relation is considerably more general than conventional Green-elastic hyperelastic materials. Such response functions may be suitable for the modelling of biological tissue where, due to the constant remodelling that takes place, there may be no physical meaning to a ‘reference configuration’.

Constitutive equations that describe creep stress relaxation for 316H stainless steel at 550°C

2011 ◽  
Vol 28 (3) ◽  
pp. 155-164 ◽  
Author(s):  
Bo Chen ◽  
David J. Smith ◽  
Peter E.J. Flewitt ◽  
Michael W. Spindler
Keyword(s):  
Stainless Steel ◽  
Stress Relaxation ◽  
Constitutive Equations ◽  
Creep Stress

THE STABILITY OF FCC CRYSTAL Cu UNDER UNIAXIAL LOADING IN [001] DIRECTION

2009 ◽  
Vol 23 (15) ◽  
pp. 1871-1880 ◽  
Author(s):  
X. M. LIU ◽  
Z. L. LIU ◽  
X. C. YOU ◽  
J. F. NIE ◽  
Z. ZHUANG
Keyword(s):  
Hydrostatic Stress ◽  
Element Model ◽  
Uniaxial Loading ◽  
Ideal Strength ◽  
Anisotropic Character ◽  
Tension And Compression ◽  
Loading Tests ◽  
The Stability ◽  
Critical Resolved Shear Stress ◽  
The Ideal

Uniaxial loading tests of copper with inter-atomic potential finite-element model are carried out to determine the corresponding ideal tension and compression strength using the modified Born stability criteria. The influence of biaxial stresses applied perpendicularly to the [100] loading axis, on the ideal strength is investigated, and tension-compression asymmetry in ideal strength under [100] loading is also studied. The results suggest that asymmetry for yielding strength of [100] nanowires may result from anisotropic character of crystal instability. Moreover, the results also reveal that the critical resolved shear stress in the direction of slip is not an accurate criterion for the ideal strength since it cannot capture the dependence on the loading conditions and hydrostatic stress components for the ideal strength.

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