scholarly journals Thermodynamic compatibility conditions of a new class of hysteretic materials

2021 ◽  
Author(s):  
Salvatore Sessa
Keyword(s):  
Constitutive Model ◽  
Dynamic Analysis ◽  
Closed Form ◽  
Iterative Procedure ◽  
Displacement Amplitude ◽  
Compatibility Conditions ◽  
Algebraic Functions ◽  
New Class ◽  
Thermodynamic Compatibility ◽  
Constitutive Parameters

AbstractThe thermodynamic compatibility defined by the Drucker postulate applied to a phenomenological hysteretic material, belonging to a recently formulated class, is hereby investigated. Such a constitutive model is defined by means of a set of algebraic functions so that it does not require any iterative procedure to compute the response and its tangent operator. In this sense, the model is particularly feasible for dynamic analysis of structures. Moreover, its peculiar formulation permits the computation of thermodynamic compatibility conditions in closed form. It will be shown that, in general, the fulfillment of the Drucker postulate for arbitrary displacement ranges requires strong limitations of the constitutive parameters. Nevertheless, it is possible to determine a displacement compatibility range for arbitrary sets of parameters so that the Drucker postulate is fulfilled as long as the displacement amplitude does not exceed the computed threshold. Numerical applications are provided to test the computed compatibility conditions.

Semi-Analytical Dynamic Analysis of Spiral-Grooved Mechanical Gas Face Seals

2003 ◽  
Vol 125 (2) ◽  
pp. 403-413 ◽  
Author(s):  
Brad A. Miller ◽  
Itzhak Green
Keyword(s):  
Constitutive Model ◽  
Dynamic Analysis ◽  
Closed Form ◽  
Prony Series ◽  
Closed Form Solutions ◽  
Face Seals ◽  
Mechanical Face Seal ◽  
Natural Response ◽  
Nonlinear Numerical Simulation ◽  
The Stability

A novel semi-analytical formulation is presented for the linearized dynamic analysis of spiral-grooved mechanical gas face seals. The linearized rotordynamic properties of the gas film are numerically computed and then represented analytically by a constitutive model consisting of a cosine modified Prony series. The cosine modification enables the Prony series to characterize the gas film properties of face seals in applications with large compressibility numbers. The gas film correspondence principle is then employed to couple the constitutive model to the dynamics of the mechanical face seal. Closed-form solutions are presented for the transient natural response to initial velocity conditions, the steady-state response to rotor runout and initial stator misalignment, the transmissibility ratios, and the stability threshold. Results from the closed-form solutions are all within a few percent of the results from a full nonlinear numerical simulation.

scholarly journals Multi-Scale Analyses and Modeling of Metallic Nano-Layers

Materials ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 450
Author(s):  
Zara Moleinia ◽  
David Bahr
Keyword(s):  
Experimental Data ◽  
Constitutive Model ◽  
Crystal Plasticity ◽  
Single Layer ◽  
Adaptive Boosting ◽  
Multi Scale ◽  
Nano Scale ◽  
Boosting Technique ◽  
Constitutive Parameters ◽  
Computational Processes

The current work centers on multi-scale approaches to simulate and predict metallic nano-layers’ thermomechanical responses in crystal plasticity large deformation finite element platforms. The study is divided into two major scales: nano- and homogenized levels where Cu/Nb nano-layers are designated as case studies. At the nano-scale, a size-dependent constitutive model based on entropic kinetics is developed. A deep-learning adaptive boosting technique named single layer calibration is established to acquire associated constitutive parameters through a single process applicable to a broad range of setups entirely different from those of the calibration. The model is validated through experimental data with solid agreement followed by the behavioral predictions of multiple cases regarding size, loading pattern, layer type, and geometrical combination effects for which the performances are discussed. At the homogenized scale, founded on statistical analyses of microcanonical ensembles, a homogenized crystal plasticity-based constitutive model is developed with the aim of expediting while retaining the accuracy of computational processes. Accordingly, effective constitutive functionals are realized where the associated constants are obtained via metaheuristic genetic algorithms. The model is favorably verified with nano-scale data while accelerating the computational processes by several orders of magnitude. Ultimately, a temperature-dependent homogenized constitutive model is developed where the effective constitutive functionals along with the associated constants are determined. The model is validated by experimental data with which multiple demonstrations of temperature effects are assessed and analyzed.

scholarly journals FURTHER GENERALISATIONS OF THE KUMMER-SCHWARZ EQUATION: ALGEBRAIC AND SINGULARITY PROPERTIES

2017 ◽  
Vol 57 (6) ◽  
pp. 467 ◽  
Author(s):  
R Sinuvasan ◽  
K Krishnakumar ◽  
K M Tamizhmani ◽  
PGL Leach
Keyword(s):  
Closed Form ◽  
New Class ◽  
Schwarz Equation

The Kummer–Schwarz Equation, 2<em>y'y'''</em>− 3(<em>y''</em>)<sup>2</sup> = 0, has a generalisation, (<em>n</em> − 1)<em>y</em><sup>(<em>n</em>−2)</sup><em>y</em><sup>(<em>n</em>)</sup> − <em>ny</em><sup>(<em>n</em>−1)<sup>2</sup></sup> = 0, which shares many properties with the parent form in terms of symmetry and singularity. All equations of the class are integrable in closed form. Here we introduce a new class, (<em>n</em>+q−2)<em>y</em><sup>(<em>n</em>−2</sup>)<em>y</em><sup>(<em>n</em>)</sup> −(<em>n</em>+<em>q</em>−1)<em>y</em><sup>(<em>n</em>−1)<sup>2</sup></sup> = 0, which has different integrability and singularity properties.

A New Constitutive Model in the Theory of Plasticity—Part II: Examples

1995 ◽  
Vol 117 (4) ◽  
pp. 371-377 ◽  
Author(s):  
W. Jiang
Keyword(s):  
Plastic Strain ◽  
Constitutive Model ◽  
Closed Form ◽  
Hardening Model ◽  
Closed Form Solutions ◽  
Loading Paths ◽  
Theory Of Plasticity ◽  
Thin Walled Tube ◽  
Thin Walled

This part of the paper presents several examples to further demonstrate the hardening model proposed in the first part of the paper. Closed-form solutions are achieved for a thin-walled tube subjected to linear, rectangular, and circular loading paths, and the corresponding yield center loci and plastic strain trajectories are illustrated. The features of this model are further discussed.

scholarly journals A Continuum Theory of Crack Shielding in Ceramics

1987 ◽  
Vol 54 (1) ◽  
pp. 54-58 ◽  
Author(s):  
M. Ortiz
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Constitutive Model ◽  
Closed Form ◽  
Applied Stress ◽  
Continuum Theory ◽  
Displacement Fields ◽  
Stress Strain ◽  
Macroscopic Crack

A phenomenological constitutive model is proposed which aims at describing the overall effect of microfracture in ceramics. Based on this model, the asymptotic stress, strain, and displacement fields at the tip of a stationary macroscopic crack are determined in closed form. The near-tip stress-intensity factor is computed and observed to be significantly smaller than the applied stress-intensity factor even for moderate amounts of damage.

scholarly journals A closed-form orthotropic constitutive model for fused filament fabrication materials

2019 ◽  
Author(s):  
Ruiqi Chen ◽  
Debbie G. Senesky
Keyword(s):  
Constitutive Model ◽  
Closed Form ◽  
Elastic Constants ◽  
Complex Variable ◽  
Shape Parameter ◽  
Antiplane Shear ◽  
Fused Filament Fabrication ◽  
Effective Elastic Constants ◽  
Out Of Plane ◽  
Simulation Results

We model two common fused filament fabrication mesostructures, square and hexagonal, using an orthotropic constitutive model and derive closed-form expressions for all nine effective elastic constants. The periodic void shapes are modeled using three and four point hypotrochoid curves with a single shape parameter that controls the sharpness of the points. Using the complex variable method of elasticity, we derive the in-plane elastic constants (Exx, Eyy, Gxy, nuxy) as well as out-of-plane antiplane shear constants (Gzx and Gzy). The remaining out-of-plane elastic constants (Ezz, nuzx, nuzy) are derived by directly solving the linearelasticity equations. We compare our results by conducting unit cell simulations on both mesostructures and at various porosity values. The simulations match the closed-form expressions exactly for Ezz, nuzx, and nuzy. For the remaining elastic constants, the simulation results match the closed-form expressions better for the square mesostructure than the hexagonal mesostructure. Differences between simulation and closed-form expressions are less than 10% for porosity values less than 6% (hexagonal mesostructure) and 10% (square mesostructure) for any of the nine elastic constants.

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