Constitutive equations involving functional dependence of one vector on another

1961 ◽  
Vol 12 (5) ◽  
pp. 447-452 ◽  
Author(s):  
Ronald S. Rivlin
Keyword(s):  
Constitutive Equations ◽  
Functional Dependence

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.

HIV-Associated Prospective Memory Deficits Predict Functional Dependence

2007 ◽  
Author(s):  
Steven P. Woods ◽  
Jennifer E. Iudicello ◽  
Matthew S. Dawson ◽  
Lisa M. Moran ◽  
Catherine L. Carey ◽  
...  
Keyword(s):  
Prospective Memory ◽  
Functional Dependence ◽  
Memory Deficits

Prediction of Tread Pattern Wear by an Explicit Finite Element Model3

2007 ◽  
Vol 35 (4) ◽  
pp. 276-299 ◽  
Author(s):  
J. C. Cho ◽  
B. C. Jung
Keyword(s):  
Finite Element ◽  
Wear Rate ◽  
Tangential Stress ◽  
Rate Equation ◽  
Constitutive Equations ◽  
Slip Velocity ◽  
Test Results ◽  
Explicit Finite Element ◽  
Driving Condition ◽  
Driving Conditions

Abstract Tread pattern wear is predicted by using an explicit finite element model (FEM) and compared with the indoor drum test results under a set of actual driving conditions. One pattern is used to determine the wear rate equation, which is composed of slip velocity and tangential stress under a single driving condition. Two other patterns with the same size (225/45ZR17) and profile are used to be simulated and compared with the indoor wear test results under the actual driving conditions. As a study on the rubber wear rate equation, trial wear rates are assumed by several constitutive equations and each trial wear rate is integrated along time to yield the total accumulated wear under a selected single cornering condition. The trial constitutive equations are defined by independently varying each exponent of slip velocity and tangential stress. The integrated results are compared with the indoor test results, and the best matching constitutive equation for wear is selected for the following wear simulation of two other patterns under actual driving conditions. Tens of thousands of driving conditions of a tire are categorized into a small number of simplified conditions by a suggested simplification procedure which considers the driving condition frequency and weighting function. Both of these simplified conditions and the original actual conditions are tested on the indoor drum test machines. The two results can be regarded to be in good agreement if the deviation that exists in the data is mainly due to the difference in the test velocity. Therefore, the simplification procedure is justified. By applying the selected wear rate equation and the simplified driving conditions to the explicit FEM simulation, the simulated wear results for the two patterns show good match with the actual indoor wear results.

Evaluation of the accuracy indicators in determination of the coating thickness by crater grinding method

2020 ◽  
Vol 86 (7) ◽  
pp. 39-44
Author(s):  
K. V. Gogolinsky ◽  
A. E. Ivkin ◽  
V. V. Alekhnovich ◽  
A. Yu. Vasiliev ◽  
A. E. Tyurnina ◽  
...  
Keyword(s):  
Coating Thickness ◽  
Functional Dependence ◽  
Measurement Procedure ◽  
Metrological Certification ◽  
Measuring Instruments ◽  
Properties Of Coatings ◽  
Special Equipment ◽  
Grinding Method ◽  
Accuracy Of Measurements ◽  
Wide Range

Thickness is one of the key indicators characterizing the quality and functional properties of coatings. Various indirect methods (electromagnetic, radiation, optical) most often used in practice to measure thickness are based on the functional dependence of a particular physical parameter of the system «base – coating» on the coating thickness. The sensitivity of these procedures to the certain properties of coatings imposes the main restriction to the accuracy of measurements. Therefore, the development and implementation of the approaches based on direct measurements of geometric parameters of the coating appears expedient. These methods often belong to the class of «destructive» and, in addition to measuring instruments, require the use of special equipment. To ensure the uniformity of measurements in the laboratory or technological control, these methods are isolated as a separate procedure (method) and must undergo metrological certification in accordance with GOST R 8.563–2009. We present implementation, metrological certification and practical application of the method for measuring thickness of coatings by crater-grinding method. The principles of technical implementation of test equipment, measurement procedure and calculation formulas are described. The results of evaluating the accuracy indicators of the proposed procedure by calculation and experimental methods are presented. In both cases, the relative error did not exceed 6%. The applicability of the developed technique is shown for a wide range of coating materials (from soft metals to superhard ceramics) of different thickness (with from units to hundreds of micrometers). Apart from the goals of process control and outgoing inspection, the method can be recommended as a reference measurement procedure for calibration of measures and adjusting samples for various types of thickness gauges.

Constitutive Equations of Soils: 4. Macro-Rheology

1978 ◽  
Vol 18 (3) ◽  
pp. 85-95
Author(s):  
Hideo Sekiguchi
Keyword(s):  
Constitutive Equations

Improved Outcomes after Reperfusion Therapies for Ischemic Stroke: A “Real-world” Study in a Developing Country

2020 ◽  
Vol 17 (4) ◽  
pp. 361-375
Author(s):  
Victor C. Schulz ◽  
Pedro S.C. de Magalhaes ◽  
Camila C. Carneiro ◽  
Julia I.T. da Silva ◽  
Vivian N. Silva ◽  
...  
Keyword(s):  
Ischemic Stroke ◽  
Real World ◽  
Time Window ◽  
Functional Dependence ◽  
Developed Countries ◽  
First Year ◽  
Middle Income ◽  
Probability Of Survival ◽  
Stroke Center ◽  
Cerebral Reperfusion

Background: It is unknown if improvements in ischemic stroke (IS) outcomes reported after cerebral reperfusion therapies (CRT) in developed countries are also applicable to the “real world” scenario of low and middle-income countries. We aimed to measure the long-term outcomes of severe IS treated or not with CRT in Brazil. Methods: Patients from a stroke center of a state-run hospital were included. We compared the survival probability and functional status at 3 and 12 months in patients with severe IS treated or not with CRT. From 2010 to 2011, we performed intravenous reperfusion when patients arrived within 4.5 h time-window (IVT group) and after 2011, mechanical thrombectomy (MT) combined or not with intravenous alteplase (IAT group). Those who arrived >4.5 h in 2010-2011 and >6 h in 2012-2017 did not undergo CRT (NCRT group). Results: From 2010 to 2017, we registered 917 patients: 74% (677/917) in the NCRT group, 19% (178/917) in the IVT group and 7% (62/917) in the IAT group. Compared to the NCRT group, IVT patients had a 28% higher (HR: 0.72; 95% CI 0.53-0.96) 3-month adjusted probability of survival and risk of functional dependence was 19% lower (adjusted RR: 0.81; 95% CI 0.73-0.91). For those who underwent MT, the adjusted probability of survival was 59 % higher (HR: 0.41; 95% CI 0.21-0.77) and the risk of functional dependence was 21% lower (adjusted RR: 0.79; 95% CI 0.66-094). These outcomes remained significantly better throughout the first year. Conclusion: CRT led to better outcomes in patients with severe IS in Brazil.

The impact of duration observations on precision of results GNSS measurements

2017 ◽  
Vol 921 (3) ◽  
pp. 7-13 ◽  
Author(s):  
S.V. Grishko
Keyword(s):  
Measurement Accuracy ◽  
Functional Dependence ◽  
Observation Time ◽  
Satellite Networks ◽  
Satellite Measurements ◽  
Proposed Model ◽  
Actual Error ◽  
Gnss Measurements ◽  
The Impact ◽  
Qualitative Characteristics

This paper shows that the accuracy of relative satellite measurements depend not only on the length of the baseline, as it is regulated by the rating formula of accuracy of GNSS equipment, but also on the duration of observations. As a result of the strict adjustment much redundant satellite networks with different duration of observations obtained covariance matrix of baselines, the most realistic reflecting the actual error of satellite observations. Research of forms of communication of these errors from length of the baseline and duration of its measurement is executed. A significant influence of solar activity on accuracy of satellite measurements, in general, leads to unequal similar series of measurements made at different periods, for example, in the production of monitoring activities. The model of approximation of the functional dependence of accuracy of the baseline from its length and duration of observations having good qualitative characteristics is offered. Based on the proposed model, we analyzed the dynamics of changes in measurement accuracy with an increase in observation time.

Sign in / Sign up

Export Citation Format

Share Document