Enabling Integrated Material and Product Design Under Uncertainty Through Stochastic Constitutive Relations

2010 ◽  
Author(s):  
M. Steven Greene ◽  
Yu Liu ◽  
Wei Chen ◽  
Wing Kam Liu ◽  
Hong-Zhong Huang
Keyword(s):  
Product Design ◽  
Constitutive Relation ◽  
Material Properties ◽  
Constitutive Relations ◽  
High Strength ◽  
Material Behavior ◽  
Constitutive Law ◽  
Copula Functions ◽  
Computational Framework ◽  
Uncertainty Sources

This paper presents a computational framework that mathematically propagates material microstructure uncertainties to coarser system resolutions for use in multiscale design frameworks. The computational framework uses a homogenized stochastic constitutive relation that links microstructure uncertainty with stochastic material properties. The stochastic constitutive relation formulated in this work serves as the critical link between the material and product domains in integrated material and product design. Ubiquitous fine resolution uncertainty sources influencing prediction of material properties based on their structures are categorized, and stochastic cell averaging is achieved by two advanced uncertainty quantification methods: random process polynomial chaos expansion and statistical copula functions. Both methods confront the mathematical difficulty in randomizing constitutive law parameters by capturing the marked correlation among them often seen in complex materials, thus the results proffer a more accurate probabilistic estimation of constitutive material behavior. The method put forth in this research, though quite general, is applied to a plastic, high strength steel alloy for demonstration.

Common nonlocal elastic constitutive relation and material-behavior modeling of nanostructures

2017 ◽  
Vol 231 (2) ◽  
pp. 83-87
Author(s):  
A Naderi ◽  
AR Saidi
Keyword(s):  
Constitutive Relation ◽  
Constitutive Relations ◽  
Surface Effects ◽  
Mechanical Analysis ◽  
Material Behavior ◽  
Constitutive Law ◽  
Behavior Modeling ◽  
Infinite Body ◽  
Beam Columns ◽  
Special Cases

This article reviews conventional nonlocal elasticity constitutive relation which is frequently used for mechanical analyses of nanostructures. It is shown here that since this constitutive relation has been essentially derived based on infinite-body assumption, it cannot consider the nonlocal effects at all points of a nanoscale body accurately. Also, it is shown that although the nonlocal constitutive relations can potentially consider the surface effects, that constitutive relation has been obtained substantially by ignoring those effects. So, it cannot also consider the surface effects accurately. Therefore, the conventional nonlocal constitutive relation generally is not accurate for material-behavior modeling and consequently mechanical analysis of nanostructures. Furthermore, common nonlocal constitutive law is examined in buckling problem of Timoshenko beam-columns to show another limitation of that constitutive law. Finally, some special cases for which that constitutive relation can be used more accurately are proposed.

Constitutive Equations and Finite Element Implementation of Isochronous Nonlinear Viscoelastic Behavior

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Hossein Sepiani ◽  
Maria Anna Polak ◽  
Alexander Penlidis
Keyword(s):  
Finite Element ◽  
Material Properties ◽  
Constitutive Relations ◽  
Viscoelastic Behavior ◽  
Material Behavior ◽  
Constitutive Law ◽  
Nonlinear Viscoelastic ◽  
Nonlinear Viscoelastic Behavior ◽  
Stress Dependent

We present a phenomenological three-dimensional (3D) nonlinear viscoelastic constitutive model for time-dependent analysis. Based on Schapery's single integral constitutive law, a solution procedure has been provided to solve nonlinear viscoelastic behavior. This procedure is applicable to 3D problems and uses time- and stress-dependent material properties to characterize the nonlinear behavior of material. The equations describing material behavior are chosen based on the measured material properties in a short test time frame. This estimation process uses the Prony series material parameters, and the constitutive relations are based on the nonseparable form of equations. Material properties are then modified to include the long-term response of material. The presented model is suitable for the development of a unified computer code that can handle both linear and nonlinear viscoelastic material behavior. The proposed viscoelastic model is implemented in a user-defined material algorithm in abaqus (UMAT), and the model validity is assessed by comparison with experimental observations on polyethylene for three uniaxial loading cases, namely short-term loading, long-term loading, and step loading. A part of the experimental results have been conducted by (Liu, 2007, “Material Modelling for Structural Analysis of Polyethylene,” M.Sc. thesis, University of Waterloo, Waterloo, ON Canada), while the rest are provided by an industrial partner. The research shows that the proposed finite element model can reproduce the experimental strain–time curves accurately and concludes that with proper material properties to reflect the deformation involved in the mechanical tests, the deformation behavior observed experimentally can be accurately predicted using the finite element simulation.

scholarly journals Material Behavior Description for a Large Range of Strain Rates from Low to High Temperatures: Application to High Strength Steel

Metals ◽  
2018 ◽  
Vol 8 (10) ◽  
pp. 795 ◽  
Author(s):  
Pierre Simon ◽  
Yaël Demarty ◽  
Alexis Rusinek ◽  
George Voyiadjis
Keyword(s):  
High Strength Steel ◽  
Constitutive Relations ◽  
High Strength ◽  
Numerical Approach ◽  
Complex Stress ◽  
Material Behavior ◽  
Experimental Results ◽  
Large Field ◽  
Strain Rates ◽  
Behavior Description

Current needs in the design and optimization of complex protective structures lead to the development of more accurate numerical modelling of impact loadings. The aim of developing such a tool is to be able to predict the protection performance of structures using fewer experiments. Considering only the numerical approach, the most important issue to have a reliable simulation is to focus on the material behavior description in terms of constitutive relations and failure model for high strain rates, large field of temperatures and complex stress states. In this context, the present study deals with the dynamic thermo-mechanical behavior of a high strength steel (HSS) close to the Mars® 190 (Industeel France, Le Creusot, France). For the considered application, the material can undergo both quasi-static and dynamic loadings. Thus, the studied strain rate range is varying from 10−3–104 s−1. Due to the fast loading time, the local temperature increase during dynamic loading induces a thermal softening. The temperature sensitivity has been studied up to 473 K under quasi-static and dynamic conditions. Low temperature measurements (lower than the room temperature) are also reported in term of σ − ε | ε ˙ , T curves. Experimental results are then used to identify the parameters of several constitutive relations, such as the model developed initially by Johnson and Cook; Voyiadjis and Abed; and Rusinek and Klepaczko respectively termed Johnson–Cook (JC), Voyiadjis–Abed (VA), and Rusinek–Klepaczko (RK). Finally, comparisons between experimental results and model predictions are reported and compared.

Verification of a Thermoviscoplastic Constitutive Relation for Brass Material Using Taylor's Test

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Farid Abed ◽  
Tomasz Jankowiak ◽  
Alexis Rusinek
Keyword(s):  
Strain Rate ◽  
Dynamic Behavior ◽  
Constitutive Relation ◽  
Split Hopkinson Pressure Bar ◽  
Constitutive Relations ◽  
Strain Curve ◽  
Material Behavior ◽  
Experimental Results ◽  
Face Centered Cubic ◽  
Test Technique

This paper presents a methodology to define and verify the dynamic behavior of materials based on Taylor's test. A brass alloy with a microstructure composed mainly of two pure metals that have two different crystal structures, copper (face-centered cubic (fcc)) and zinc (hexagonal closed-packed (hcp)), is used in this study. A combined approach of different principal mechanisms controlled by the emergence and evolution of mobile dislocations as well as the long-range intersections between forest dislocations is, therefore, adopted to develop accurate definition for its flow stress. The constitutive relation is verified against experimental results conducted at low and high strain rates and temperatures using compression screw machine and split Hopkinson pressure bar (SHPB), respectively. The present model predicted results that compare well with experiments and was capable of simulating the low strain rate sensitivity that was observed during the several static and dynamic tests. The verified constitutive relations are further integrated and implemented in a commercial finite element (FE) code for three-dimensional (3D) Taylor's test simulations. A Taylor's test enables the definition of only one point on the stress–strain curve for a given strain rate using the initial and final geometry of the specimen after impact into a rigid surface. Thus, it is necessary to perform several tests with different geometries to define the complete material behavior under dynamic loadings. The advantage of using strain rate independent brass in this study is the possibility to rebuild the complete process of strain hardening during Taylor's tests by using the same specimen geometry. Experimental results using the Taylor test technique at a range of velocity impacts between 70 m/s and 200 m/s are utilized in this study to validate the constitutive model of predicting the dynamic behavior of brass at extreme conditions.

A modified physical model of high-strength water hydraulic artificial muscles considering the effects of geometry and material properties

2021 ◽  
pp. 095440622199907
Author(s):  
Zengmeng Zhang ◽  
Jinkai Che ◽  
Peipei Liu ◽  
Yunrui Jia ◽  
Yongjun Gong
Keyword(s):  
Physical Model ◽  
Relative Error ◽  
Wall Thickness ◽  
Material Properties ◽  
High Strength ◽  
Artificial Muscles ◽  
Operating Pressure ◽  
Rubber Tube ◽  
Contraction Ratio ◽  
Water Hydraulic

Compared with pneumatic artificial muscles (PAMs), water hydraulic artificial muscles (WHAMs) have the advantages of high force/weight ratio, high stiffness, rapid response speed, large operating pressure range, low working noise, etc. Although the physical models of PAMs have been widely studied, the model of WHAMs still need to be researched for the different structure parameters and work conditions between PAMs and WHAMs. Therefore, the geometry and the material properties need to be considered in models, including the wall thickness of rubber tube, the geometry of ends, the elastic force of rubber tube, the elongation of fibers, and the friction among fiber strands. WHAMs with different wall thickness and fiber materials were manufactured, and static characteristic experiments were performed when the actuator is static and fixed on both ends, which reflects the relationship between contraction force and pressure under the different contraction ratio. The deviations between theoretical values and experimental results were analyzed to investigate the effect of each physical factor on the modified physical model accuracy at different operating pressures. The results show the relative error of the modified physical model was 7.1% and the relative error of the ideal model was 17.4%. When contraction ratio is below 10% and operating pressure is 4 MPa, the wall thickness of rubber tube was the strongest factor on the accuracy of modified model. When the WHAM contraction ratio from 3% to 20%, the relative error between the modified physical model and the experimental data was within ±10%. Considering the various physical factors, the accuracy of the modified physical model of WHAM is improved, which lays a foundation of non-linear control of the high-strength, tightly fiber-braided and thick-walled WHAMs.

scholarly journals Impact of residual stress evoked by pyramidal embossing on the magnetic material properties of non-oriented electrical steel

2021 ◽  
Author(s):  
Ines Gilch ◽  
Tobias Neuwirth ◽  
Benedikt Schauerte ◽  
Nora Leuning ◽  
Simon Sebold ◽  
...  
Keyword(s):  
Magnetic Material ◽  
Residual Stress ◽  
Magnetic Flux ◽  
Material Properties ◽  
Electrical Steel ◽  
Maximum Energy ◽  
Material Behavior ◽  
Electrical Machine ◽  
Element Analysis ◽  
Steel Sheets

AbstractTargeted magnetic flux guidance in the rotor cross section of rotational electrical machines is crucial for the machine’s efficiency. Cutouts in the electrical steel sheets are integrated in the rotor sheets for magnetic flux guidance. These cutouts create thin structures in the rotor sheets which limit the maximum achievable rotational speed under centrifugal forces and the maximum energy density of the rotating electrical machine. In this paper, embossing-induced residual stress, employing the magneto-mechanical Villari effect, is studied as an innovative and alternative flux barrier design with negligible mechanical material deterioration. The overall objective is to replace cutouts by embossings, increasing the mechanical strength of the rotor. The identification of suitable embossing geometries, distributions and methodologies for the local introduction of residual stress is a major challenge. This paper examines finely distributed pyramidal embossings and their effect on the magnetic material behavior. The study is based on simulation and measurements of specimen with a single line of twenty embossing points performed with different punch forces. The magnetic material behavior is analyzed using neutron grating interferometry and a single sheet tester. Numerical examinations using finite element analysis and microhardness measurements provide a more detailed understanding of the interaction of residual stress distribution and magnetic material properties. The results reveal that residual stress induced by embossing affects magnetic material properties. Process parameters can be applied to adjust the magnetic material deterioration and the effect of magnetic flux guidance.

Development and Application of New Design Method by High-Strength Composite Material - Fusing of Optimum Strength Evaluation and Product Design

2013 ◽  
Vol 372 ◽  
pp. 17-20 ◽  
Author(s):  
Haruhiko Iida ◽  
Hidetoshi Sakamoto ◽  
Yoshifumi Ohbuchi
Keyword(s):  
Composite Material ◽  
Carbon Fiber ◽  
Product Design ◽  
Design Method ◽  
Target Material ◽  
High Strength ◽  
Fiber Glass ◽  
Strength Evaluation ◽  
Fiber Reinforced Materials ◽  
Manufacturing Methods

The purpose of this research is the development of new design method for integrating the optimum strength evaluation and the product design which can make the best use of material's characteristics obtained by the experiment and the analysis. Further we do design using high-strength composite material with this developed concept which is different from conventional design. First, to establish this design method of high-strength materials, we examined these materials characteristics and manufacturing methods and the commercialized products. As this research target material, we focus the fiber reinforced materials such as composite with carbon fiber, glass fiber and aramid fiber. Above all, we marked the carbon fiber which has the high specific tensile strength, wear resistance, heat conductivity and conductance. Here, we introduce the fundamental design concept which makes the best use of the design with enough strength.

Strain-Rate Effect on the Tensile Behaviour of High Strength Alloys

2011 ◽  
Vol 82 ◽  
pp. 124-129 ◽  
Author(s):  
Ezio Cadoni ◽  
Matteo Dotta ◽  
Daniele Forni ◽  
Stefano Bianchi
Keyword(s):  
Strain Rate ◽  
Rate Sensitivity ◽  
High Strength ◽  
Constitutive Law ◽  
Tensile Behaviour ◽  
Strain Rates ◽  
Cross Sectional ◽  
Split Hopkinson Tensile Bar ◽  
Wide Range ◽  
First Results

In this paper the first results of the mechanical characterization in tension of two high strength alloys in a wide range of strain rates are presented. Different experimental techniques were used for different strain rates: a universal machine, a Hydro-Pneumatic Machine and a JRC-Split Hopkinson Tensile Bar. The experimental research was developed in the DynaMat laboratory of the University of Applied Sciences of Southern Switzerland. An increase of the stress at a given strain increasing the strain-rate from 10-3 to 103 s-1, a moderate strain-rate sensitivity of the uniform and fracture strain, a poor reduction of the cross-sectional area at fracture with increasing the strain-rate were shown. Based on these experimental results the parameters required by the Johnson-Cook constitutive law were determined.

A convenient formulation of Sadowsky's model for elastic ribbons

2021 ◽  
Vol 477 (2255) ◽  
Author(s):  
Sébastien Neukirch ◽  
Basile Audoly
Keyword(s):  
Differential Equations ◽  
Constitutive Relation ◽  
Classical Problem ◽  
Constitutive Law ◽  
System Of Differential Equations ◽  
Dimensional Model ◽  
Simple Method ◽  
One Dimensional ◽  
Aspect Ratios ◽  
Nonlinear Constitutive Relation

Elastic ribbons are elastic structures whose length-to-width and width-to-thickness aspect ratios are both large. Sadowsky proposed a one-dimensional model for ribbons featuring a nonlinear constitutive relation for bending and twisting: it brings in both rich behaviours and numerical difficulties. By discarding non-physical solutions to this constitutive relation, we show that it can be inverted; this simplifies the system of differential equations governing the equilibrium of ribbons. Based on the inverted form, we propose a natural regularization of the constitutive law that eases the treatment of singularities often encountered in ribbons. We illustrate the approach with the classical problem of the equilibrium of a Möbius ribbon, and compare our findings with the predictions of the Wunderlich model. Overall, our approach provides a simple method for simulating the statics and the dynamics of elastic ribbons.

Simulation on the Life Expectancy of Fine Blanking Tool Punch for High-Strength Automobile Start Motor Flange

2014 ◽  
Vol 607 ◽  
pp. 612-615
Author(s):  
Jong Deok Kim ◽  
Hyun Jun Ko
Keyword(s):  
Life Expectancy ◽  
Material Properties ◽  
High Strength ◽  
Manufacturing Cost ◽  
Working Process ◽  
Product Cost ◽  
Fine Blanking ◽  
Stamping Process ◽  
Cutting Surface ◽  
Secondary Operations

Fine blanking is a press-working process that permits the production of precise, finished components which are cleanly sheared through the whole cutting surface. The manufacturing cost can be reduced because the secondary operations such as milling and broaching can be eliminated and the multistage combined stamping process can be added. The product cost can increase, however, while the precise fine blanking tool and high cost fine blanking press are required. Therefore it is important to design the fine blanking tool in view of the life expectancy of the punch. In this paper the fatigue simulation of fine blanking tool punch for automobile start motor flange was conducted using the commercial FEA software ANSYS. Initially, the material properties were tested and the fine blanking tool was designed for production experiments. The modelling of tool elements and the fatigue simulation according to repeated loads were conducted. As a result of fatigue simulation, the fine blanking tool punch for start motor flange had been fractured with 3,981 strokes. In the fine blanking production experiments, the fine blanking tool punch had to be regrinded after it was used with 3,425 strokes. It was also found that the fatigue simulation of fine blanking tool punch was conducted with an error of 14%.

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