Performance of different stress-point algorithms for the integration of hypoplastic constitutive equations for geomaterials

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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Constitutive Equations of Soils: 4. Macro-Rheology

SOILS AND FOUNDATIONS ◽

10.3208/sandf1972.18.3_85 ◽

1978 ◽

Vol 18 (3) ◽

pp. 85-95

Author(s):

Hideo Sekiguchi

Keyword(s):

Constitutive Equations

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Shaping Microstructure and Mechanical Properties of High-Carbon Bainitic Steel in Hot-Rolling and Long-Term Low-Temperature Annealing

Materials ◽

10.3390/ma14020384 ◽

2021 ◽

Vol 14 (2) ◽

pp. 384

Author(s):

Tomasz Dembiczak ◽

Marcin Knapiński

Keyword(s):

Mathematical Models ◽

Hot Rolling ◽

Constitutive Equations ◽

Rolling Process ◽

Bainitic Steel ◽

Compression Tests ◽

High Carbon ◽

Bainite Steel ◽

Dilatometric Studies

Based on the research results, coefficients in constitutive equations, describing the kinetics of dynamic, meta-dynamic, and static recrystallization in high-carbon bainitic steel during hot deformation were determined. The developed mathematical model takes into account the dependence of the changing kinetics in the structural size of the preliminary austenite grains, the value of strain, strain rate, temperature, and time. Physical simulations were carried out on rectangular specimens. Compression tests with a flat state of deformation were carried out using a Gleeble 3800. Based on dilatometric studies, coefficients were determined in constitutive equations, describing the grain growth of the austenite of high-carbon bainite steel under isothermal annealing conditions. The aim of the research was to verify the developed mathematical models in semi-industrial conditions during the hot-rolling process of high-carbon bainite steel. Analysis of the semi-industrial studies of the hot-rolling and long-term annealing process confirmed the correctness of the predicted mathematical models describing the microstructure evolution.

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Rate Dependent Constitutive Equations of Cyclic Softening

Zeitschrift für Naturforschung A ◽

10.1515/zna-1985-0701 ◽

1985 ◽

Vol 40 (7) ◽

pp. 653-665

Author(s):

J. S. Mshana ◽

A. S. Krausz

Keyword(s):

Stress Relaxation ◽

Low Temperature ◽

Constitutive Equations ◽

Strain Softening ◽

Structural Characteristics ◽

High Stress ◽

Cyclic Strain ◽

Cyclic Stress ◽

Cyclic Softening ◽

Stress Softening

Constitutive equations of cyclic strain and stress softening for materials with low internal stress levels are derived from the rate theory. The study shows that over the high stress and low temperature range where the description of plastic flow in cyclic softening can be approximated with activation over a single energy barrier, cyclic strain softening is well related to stress relaxation process while cyclic stress softening is related to creep process. The material structural characteristics for cyclic strain softening, cyclic stress softening and stress relaxation are identical. Subsequently, it is shown that cyclic stress and strain softening within the high stress and low temperature range can be evaluated from the constitutive equations using the material structural characteristics measured from a simple stress relaxation test.

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

Mathematics and Mechanics of Solids ◽

10.1177/10812865211021640 ◽

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.

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