Material symmetry restrictions on non-polynomial constitutive equations

1963 ◽  
Vol 12 (1) ◽  
pp. 420-426 ◽  
Author(s):  
A. C. Pipkin ◽  
A. S. Wineman
Keyword(s):  
Constitutive Equations ◽  
Material Symmetry

Local material symmetry group for first- and second-order strain gradient fluids

2021 ◽  
pp. 108128652110216
Author(s):  
Victor A. Eremeyev
Keyword(s):  
Symmetry Group ◽  
Strain Gradient ◽  
Constitutive Equations ◽  
Strain Energy ◽  
Mass Density ◽  
Material Model ◽  
Second Order ◽  
Material Symmetry ◽  
Local Material ◽  
Current Mass

Using an unified approach based on the local material symmetry group introduced for general first- and second-order strain gradient elastic media, we analyze the constitutive equations of strain gradient fluids. For the strain gradient medium there exists a strain energy density dependent on first- and higher-order gradients of placement vector, whereas for fluids a strain energy depends on a current mass density and its gradients. Both models found applications to modeling of materials with complex inner structure such as beam-lattice metamaterials and fluids at small scales. The local material symmetry group is formed through such transformations of a reference placement which cannot be experimentally detected within the considered material model. We show that considering maximal symmetry group, i.e. material with strain energy that is independent of the choice of a reference placement, one comes to the constitutive equations of gradient fluids introduced independently on general strain gradient continua.

Material symmetry and constitutive equations

1980 ◽  
Vol 49 (5-6) ◽  
pp. 325-336 ◽  
Author(s):  
R. S. Rivlin
Keyword(s):  
Constitutive Equations ◽  
Material Symmetry

On the use of symmetry to simplify the constitutive equations of isotropic materials with memory

1968 ◽  
Vol 306 (1487) ◽  
pp. 449-476 ◽  
Keyword(s):  
Constitutive Equations ◽  
Material Symmetry ◽  
Materials With Memory ◽  
Material Response ◽  
Isotropic Materials ◽  
Frame Indifference ◽  
History Of ◽  
With Memory

This paper is concerned with general, compressible, isotropic materials, solid or fluid, characterized by functionals which give the stress when the history of the strain is specified. It is shown that for certain broad classes of motions the requirements of material symmetry and frame-indifference greatly simplify the form of constitutive equations. These simplifica­tions are derived without invoking integral expansions or other special hypotheses of smoothness for material response. Among the motions considered in detail are those which are locally equivalent to pure extensions and sheared extensions.

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.

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