Slip- and Time-dependent Fault Constitutive Law and its Significance in Earthquake Generation Cycles

2002 ◽  
pp. 2029-2044
Author(s):  
Hideo Aochi ◽  
Mitsuhiro Matsu’ura
Keyword(s):  
Constitutive Law ◽  
Time Dependent ◽  
Earthquake Generation

Unified Constitutive Modelling of Nonlinear Time-Dependent Materials

1989 ◽  
Vol 42 (11S) ◽  
pp. S78-S82
Author(s):  
P. G. Glockner ◽  
W. Szyszkowski
Keyword(s):  
Strain Softening ◽  
Strain Tensor ◽  
Damage Function ◽  
Constitutive Modelling ◽  
Constitutive Law ◽  
Time Dependent ◽  
Type Integral ◽  
Characteristic Features ◽  
Stress Dependent ◽  
Semi Empirical

A semi-empirical engineering constitutive law modelling in a unified and continuous manner the main characteristic features of time-dependent materials, including creep, strain softening, relaxation and recovery and tensile brittleness, is briefly reviewed. The model, which contains 13 parameters, is a hereditary single Volterra-type integral representation of material response with stress/strain nonlinearity assumed in the form of a power law, the strain tensor dependent on the entire stress history and the stress-anisotropy/brittleness feature handled by means of a tensile-stress dependent damage function. The capability/versatility of the model is illustrated by examples for several materials.

Analysis of a piezoelectric contact problem with subdifferential boundary condition

2014 ◽  
Vol 144 (5) ◽  
pp. 1007-1025 ◽  
Author(s):  
Stanisław Migórski ◽  
Anna Ochal ◽  
Mircea Sofonea
Keyword(s):  
Boundary Condition ◽  
Variational Formulation ◽  
Contact Process ◽  
Constitutive Law ◽  
Time Dependent ◽  
Hemivariational Inequalities ◽  
Material Behaviour ◽  
Nonlinear Integral Equations ◽  
Frictionless Contact ◽  
System Coupling

We consider a mathematical model which describes the frictionless contact between a piezoelectric body and a foundation. The contact process is quasi-static and the foundation is assumed to be insulated. The novelty of the model consists in the fact that the material behaviour is described with an electro-elastic–visco-plastic constitutive law and the contact is modelled with a subdifferential boundary condition. We derive a variational formulation of the problem which is in the form of a system coupling two nonlinear integral equations with a history-dependent hemivariational inequality and a time-dependent linear equation. We prove the existence of a weak solution to the problem and, under additional assumptions, its uniqueness. The proof is based on a recent result on history-dependent hemivariational inequalities obtained by Migórski, Ochal and Sofonea in 2011.

An Improved Analytical Model for Time-Dependent Shearing Deformation in Area-Array Interconnects

2004 ◽  
Vol 126 (1) ◽  
pp. 74-81
Author(s):  
S. Shakya ◽  
S. M. Heinrich ◽  
P. S. Lee
Keyword(s):  
Analytical Model ◽  
Elastic Solid ◽  
Step Function ◽  
Shear Displacement ◽  
Constitutive Law ◽  
Time Dependent ◽  
Correction Factors ◽  
Area Array ◽  
Linear Viscoelastic Material ◽  
Frequency Independent

An improved time-dependent analytical model is developed for predicting the maximum shearing displacement in an area-array electronic assembly under global thermal mismatch loading. The thermal loads are assumed to be uniform within the component and substrate, with both step-function and sinusoidal temperature histories being considered. The time-dependent effects in the array’s shear deformation are introduced in an approximate manner by modeling the interconnect material (solder) as a temperature-independent linear viscoelastic material. The viscoelastic constitutive law used for the solder is that of a three-parameter viscoelastic standard solid in distortion and an elastic solid in the hydrostatic mode. In the authors’ previous work the steady-state shear force in the joints was assumed to vary sinusoidally with a frequency-independent amplitude. This assumption has been relaxed in the present study, leading to improved accuracy. All results have been derived as closed-form correction factors to be applied to the easily calculated unconstrained shear displacement to obtain the maximum shear displacement. All the correction factors depend on prescribed geometric and material parameters of the component, substrate, and joints. The results have been presented in the form of dimensionless plots to aid in the analysis or design process, thereby providing convenient alternatives or supplements to time-consuming and expensive finite element analyses of entire assemblies.

Creep Analysis of Beams and Arches Based on a Hereditary Visco-Elastic-Plastic Constitutive Law

1990 ◽  
Vol 112 (2) ◽  
pp. 210-217 ◽  
Author(s):  
J. M. Stubstad ◽  
G. J. Simitses
Keyword(s):  
Thermal Cycling ◽  
Temperature Gradients ◽  
Constitutive Law ◽  
Time Dependent ◽  
Temperature Dependent ◽  
Hastelloy X ◽  
Ambient Temperatures ◽  
Creep Analysis ◽  
Highly Nonlinear ◽  
Temperature Dependent Properties

An analytic study of planar beams and arches subjected to significant thermal cycling from ambient temperatures up to 800°C is presented. The study employs a recently unified nonlinear hereditary type of viscoelastoplastic constitutive law to characterize the time- and temperature-dependent properties of Hastelloy X, a typical aerospace alloy. The results demonstrate a strong interaction between the backstress variable of the constitutive law and the time-dependent stress distribution produced by the deformation. This interaction tends to control, in a highly nonlinear manner, the creep ratchetting response of the beam or arch. Moreover, temperature gradients in the thickness direction tend to exert an important influence during thermal cycling.

Development of Time Dependent Stress-Strain Simulation of Clay

2009 ◽  
Vol 25 (1) ◽  
pp. 27-40 ◽  
Author(s):  
C.-Y. Ou ◽  
C.-C. Liu ◽  
C.-K. Chin
Keyword(s):  
Constitutive Law ◽  
Time Dependent ◽  
Soil Behavior ◽  
Creep Tests ◽  
Clay Model ◽  
Model Sets ◽  
Dependent Behavior ◽  
Modified Cam Clay ◽  
Parametric Studies ◽  
Cam Clay

AbstractThe objective of this study is to derive a time dependent effective based constitutive law on the basis of framework of the Modified Cam-Clay model. This model takes into account the anisotropic characteristics and creep behavior, based on the theory of viscoplasticity. The model sets the initial yield surface symmetric to the Ko line for modeling the initial Ko condition. A method is then developed to compute the gyration and expansion of the loading surface to simulate the anisotropic behavior due to the principal stress gyration after shear. The creep or time dependent behavior is considered in the model by adopting Kutter and Sathialingam's model, which was derived from Taylor's secondary consolidation theory and Bjerrum's delayed compression model. Compared with the Modified Cam-Clay model, the model requires five additional parameters to describe the soil behavior. All of the additional parameters can be obtained through conventional soil tests or parametric studies. The model is evaluated through a series of simulation of undrained shear tests and undrained creep tests.

On Transient Thermal Stresses in Viscoelastic Materials With Temperature-Dependent Properties

1961 ◽  
Vol 28 (2) ◽  
pp. 193-207 ◽  
Author(s):  
Rokuro Muki ◽  
Eli Sternberg
Keyword(s):  
Thermal Stresses ◽  
Constitutive Law ◽  
Time Dependent ◽  
Temperature Dependent ◽  
Infinite Extent ◽  
Temperature Dependent Properties ◽  
Transient Thermal ◽  
Temperature Time ◽  
Symmetric Temperature ◽  
Actual Test

This paper deals with the quasi-static analysis of transient thermal stresses in the linear theory of viscoelastic solids with temperature-dependent properties. The underlying constitutive law rests on the temperature-time equivalence hypothesis. Following an exposition of the theoretical framework exact solutions to two specific problems are deduced: The first concerns the thermal stresses in a slab of infinite extent, generated by a temperature field that depends arbitrarily on the thickness co-ordinate and time; the second application concerns the stresses produced in a sphere by an arbitrary time-dependent radially symmetric temperature distribution. The numerical illustrations of the results obtained include a quantitative study based on actual test data for a polymethyl methacrylate.

Further Results on the Stability of Viscoelastic Columns

1987 ◽  
Vol 11 (3) ◽  
pp. 179-194
Author(s):  
W. Szyszkowski ◽  
P.G. Glockner
Keyword(s):  
Element Model ◽  
Static Stability ◽  
Model Material ◽  
Constitutive Law ◽  
Time Dependent ◽  
Closed Form Expression ◽  
Solution Technique ◽  
Arbitrary Boundary ◽  
Post Buckling ◽  
The Stability

Recent results published by the authors on the stability behaviour of columns made of time-dependent materials are extended in a number of ways. Firstly, the closed-form expression obtained for the safe load limit of a simply supported column made of a linear three-element model material, is generalized for an arbitrary linearly viscoelastic constitutive law. The result, obtained by means of the static stability approach, is confirmed by an asymptotic solution of the dynamic stability equations. The same solution technique is used to generalize this expression for columns with arbitrary boundary conditions. Even though columns as structural members exhibit stable post-buckling behaviour, there are structural configurations, involving compression members, the overall load deflection behaviour of which indicate unstable post-buckling characteristics. A simple example is used to alert the designer to the possibility of encountering such configurations and the danger associated with such post-buckling behaviour in the case of structures made of time-dependent materials.

Multi-Scale Modelling of Long-Term Mechanical Behaviour in Polymer Composite Laminates with Woven Fibre Architecture

2001 ◽  
Vol 9 (5) ◽  
pp. 297-317 ◽  
Author(s):  
V. Gupta ◽  
S. Roy ◽  
L. R. Dharani
Keyword(s):  
Polymer Matrix ◽  
Constitutive Law ◽  
Time Dependent ◽  
Woven Fabric ◽  
Creep Model ◽  
Elastic Behaviour ◽  
Multi Scale ◽  
Out Of Plane ◽  
Scale Modelling

A comprehensive analytical model for predicting the long-term durability of polymers and polymer matrix composites should in general take into account polymer viscoelastic/viscoplastic creep, hygrothermal effects, and the effects of physical and chemical ageing on material response. These effects, in turn are influenced by a multitude of factors such as polymer morphology, service temperature, ambient relative humidity, internal moisture concentrations, stacking sequence, fibre volume fraction, fibre architecture, applied stress level, degree of damage and ageing time. The primary objective of this paper is to present a multi-scale modelling methodology to simulate the long-term interlaminar properties in polymer matrix woven composites and then predict the critical regions where failure is most likely to occur. A micro-mechanics approach towards modelling the out-of-plane viscoelastic behaviour of a five-harness satin woven-fibre cross-ply composite laminate is presented, taking into consideration the weave architecture and time-dependent effects. In-plane properties are assumed to be dominated by the carbon fibres and are hence deemed elastic. The classical lamination theory model proposed by Raju and Wang is adapted to include the in-plane elastic behaviour of woven fibre composites. For the matrixdominated out-of-plane response, a viscoelastic creep model is employed to model the resin, based on Schapery's nonlinear viscoelastic constitutive law. In addition, physical ageing of the matrix has been included in the model, using the effective time theory proposed by Struik. Furthermore, the effect of large deflections and rotations on the time dependent out-of-plane behaviour is also investigated using the micro-mechanics model. The homogenized in-plane and out-of-plane compliance obtained using the proposed micro-mechanics methodology could be applied within the framework of a structural finite element code to model the macro-scale long-term behaviour of a woven fabric composite structure.

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