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Mooney-Rivlin is the most frequently used model from all models used for mechanical characterization of the hyperelestic materials. Simplicity, applicability in a large range of strains are the key reasons for regular use of this model. However, depending on the number of parameters, the Mooney model can take several forms. While, nine parameter being the highest order noticed, two parameter model is the most commonly found form in the current research domain. Since two parameter model used repetitively, we investigated the effect of incremental change in two material constant values one at a time, on model curve. As Drucker stability criterion is governing the extreme values of material parameters, changes in the model curves are discussed related to it. Resultant effects on stress-strain curves due to change in parameter values were examined and physical effect on the characterization is interpreted accordingly. © 2020 Trans Tech Publications Ltd, Switzerland.

Data fitting is an essential part of obtaining material constants for hyperelastic models. However, due to inadequate experimental data, a single-data set, i.e. uniaxial data, is often used for fitting. Despite a frequent use of this method, it is proven that it provides an inaccurate forecast for a characterization. Therefore, as an alternative method, combined-data fitting is usually recommended. In this research, material constants calculated through two different data-fitting methods were evaluated in terms of dispersion. First, material constants were obtained by taking the average of two single-data-set fitted constants (the uniaxial and biaxial data). The second method used the combined-data fitting to find the material constants. Using the constants found, biaxial and uniaxial curves were drawn for each case. For this purpose, three models, the Mooney, Ogden and Yeoh model, were selected. When considering the Mooney model, the averaged method seems not to show a sufficient improvement to the biaxial curve. The Yeoh model reacts equally to both methods, while the Ogden model seems not to be applicable to the averaged method. © 2020 Institute of Metals Technology.

Data fitting is an essential part of obtaining material constants for hyperelastic models. However, due to inadequate experimental data, a single-data set, i.e. uniaxial data, is often used for fitting. Despite a frequent use of this method, it is proven that it provides an inaccurate forecast for a characterization. Therefore, as an alternative method, combined-data fitting is usually recommended. In this research, material constants calculated through two different data-fitting methods were evaluated in terms of dispersion. First, material constants were obtained by taking the average of two single-data-set fitted constants (the uniaxial and biaxial data). The second method used the combined-data fitting to find the material constants. Using the constants found, biaxial and uniaxial curves were drawn for each case. For this purpose, three models, the Mooney, Ogden and Yeoh model, were selected. When considering the Mooney model, the averaged method seems not to show a sufficient improvement to the biaxial curve. The Yeoh model reacts equally to both methods, while the Ogden model seems not to be applicable to the averaged method. © 2020 Institute of Metals Technology.

Mooney-Rivlin is the most frequently used model from all models used for mechanical characterization of the hyperelestic materials. Simplicity, applicability in a large range of strains are the key reasons for regular use of this model. However, depending on the number of parameters, the Mooney model can take several forms. While, nine parameter being the highest order noticed, two parameter model is the most commonly found form in the current research domain. Since two parameter model used repetitively, we investigated the effect of incremental change in two material constant values one at a time, on model curve. As Drucker stability criterion is governing the extreme values of material parameters, changes in the model curves are discussed related to it. Resultant effects on stress-strain curves due to change in parameter values were examined and physical effect on the characterization is interpreted accordingly. © 2020 Trans Tech Publications Ltd, Switzerland.

In order to find hyperelastic material model constants, data fitting technique is often used. For this task, the data is collected through different laboratory tests, namely, the uniaxial, the biaxial and the pure shear. However, due to the difficulty in getting biaxial data, often only uniaxial data was used for the fitting. Despite frequent use, it was established that this practice creates erroneous results. With a view to improve the data fitting results and at the same time to overcome the difficulty of collecting primary biaxial data, uniaxial data was used to generate a secondary biaxial data set. The data derived through this method was then tested with four common models as to examine the compatibility of the method. Subsequently, real biaxial data was used to compare with the data fitting results obtained through the proposed method. As results indicated combined data fitting for both instances were very much identical with respect to all tested models. Cases where somewhat higher deviation observed between experimental curves and data fitted curves for biaxial data, gave similar results for adjusted data driven data fitting too. However, such deviation could be attributed to mismatch between models with the particular material behaviour rather than the generated data. © 2019 Trans Tech Publications Ltd, Switzerland.

This paper deals with effects of using different sets of material constants on the natural frequencies of laminated composite rectangular plates. The plate is symmetrically laminated by thin layers composed of recently developed carbon fiber reinforced plastic (CFRP) materials. Numerical experiments are conducted by using a semi-analytical solution based on the thin plate theory and the lamination theory. The displacements are assumed to accommodate any combination of classical boundary conditions. The material property is expressed by a set of four elastic constants, and some typical sets of values are cited from the recent literature. Furthermore, a new standard set of discretized constants is proposed to uncover the underlying characteristics of the existing constants. The convergence study is carried out first, and the lowest five natural frequencies are calculated for five sets of classical boundary conditions including totally free through totally clamped cases. Next, a new definition of frequency parameters is introduced to promote more physically meaningful comparison among the obtained results, and the effect of using slightly different constants is clarified for unified comparison and insights. It is also discussed to derive approximate frequency formulas by linear regression analysis and to test accuracy of the formulas.

This paper deals with effects of using different sets of material constants on the natural frequencies of laminated composite rectangular plates. The plate is symmetrically laminated by thin layers composed of recently developed carbon fiber reinforced plastic (CFRP) materials. Numerical experiments are conducted by using a semi-analytical solution based on the thin plate theory and the lamination theory. The displacements are assumed to accommodate any combination of classical boundary conditions. The material property is expressed by a set of four elastic constants, and some typical sets of values are cited from the recent literature. Furthermore, a new standard set of discretized constants is proposed to uncover the underlying characteristics of the existing constants. The convergence study is carried out first, and the lowest five natural frequencies are calculated for five sets of classical boundary conditions including totally free through totally clamped cases. Next, a new definition of frequency parameters is introduced to promote more physically meaningful comparison among the obtained results, and the effect of using slightly different constants is clarified for unified comparison and insights. It is also discussed to derive approximate frequency formulas by linear regression analysis and to test accuracy of the formulas.

In order to find hyperelastic material model constants, data fitting technique is often used. For this task, the data is collected through different laboratory tests, namely, the uniaxial, the biaxial and the pure shear. However, due to the difficulty in getting biaxial data, often only uniaxial data was used for the fitting. Despite frequent use, it was established that this practice creates erroneous results. With a view to improve the data fitting results and at the same time to overcome the difficulty of collecting primary biaxial data, uniaxial data was used to generate a secondary biaxial data set. The data derived through this method was then tested with four common models as to examine the compatibility of the method. Subsequently, real biaxial data was used to compare with the data fitting results obtained through the proposed method. As results indicated combined data fitting for both instances were very much identical with respect to all tested models. Cases where somewhat higher deviation observed between experimental curves and data fitted curves for biaxial data, gave similar results for adjusted data driven data fitting too. However, such deviation could be attributed to mismatch between models with the particular material behaviour rather than the generated data. © 2019 Trans Tech Publications Ltd, Switzerland.

The risk of error in using only uniaxial data for fitting constitutive model curves is emphasized by many hyperelastic material researchers over the years. Unfortunately, despite these indications, often the method is utilized in finding material constants for mathematical models. The reason behind this erroneous practice is the difficulty in obtaining biaxial data. Therefore, as a remedial measure, in this research work we suggest a method of forecasting biaxial data from uniaxial data with a reasonable accuracy. Initially, a set of data is collected through standard uniaxial test. A predefined generalized function is then used to generate a set of values which subsequently used as multiplication factors in order to get biaxial tension data. Eventually, with availability of two data sets, Mooney-Rivlin two parameter model was used for combined data fitting. Material constants were then obtained through least squares approach and thereby theoretical load curves namely uniaxial, equi-biaxial tension and pure shear were drawn. The results of this work suggest a definite improvement related to three curves when compared with only uniaxial test data fitted outcomes. For validation of secondary biaxial data, separate eqi-biaxial test was done and resulting curves were compared. Biaxial primary data curve and forecasted data driven curve show identical data distribution pattern though there is a shift and therefore provide a basis for further research in this direction. © 2018 Trans Tech Publications, Switzerland.

The risk of error in using only uniaxial data for fitting constitutive model curves is emphasized by many hyperelastic material researchers over the years. Unfortunately, despite these indications, often the method is utilized in finding material constants for mathematical models. The reason behind this erroneous practice is the difficulty in obtaining biaxial data. Therefore, as a remedial measure, in this research work we suggest a method of forecasting biaxial data from uniaxial data with a reasonable accuracy. Initially, a set of data is collected through standard uniaxial test. A predefined generalized function is then used to generate a set of values which subsequently used as multiplication factors in order to get biaxial tension data. Eventually, with availability of two data sets, Mooney-Rivlin two parameter model was used for combined data fitting. Material constants were then obtained through least squares approach and thereby theoretical load curves namely uniaxial, equi-biaxial tension and pure shear were drawn. The results of this work suggest a definite improvement related to three curves when compared with only uniaxial test data fitted outcomes. For validation of secondary biaxial data, separate eqi-biaxial test was done and resulting curves were compared. Biaxial primary data curve and forecasted data driven curve show identical data distribution pattern though there is a shift and therefore provide a basis for further research in this direction. © 2018 Trans Tech Publications, Switzerland.

This paper presents a numerical procedure for the analysis of complex laminate structures. The procedure is based on the application of reduced stiffness of complex laminate. Introduction of reduced stiffness of composite facilitates both linear and nonlinear numerical integration, i.e. the tangential stiffness matrix is translated in the classical plate theory problem. The formulated numerical procedure was implemented in the program system KOMIPS. Special subroutine REDKRUT that calculates reduced stiffness of the laminate was written, and its application in numerical verification of experiments conducted on chairs was presented in (Nestorovic, 2010). At the end of this work, for 3D stress and strain analysis of veneer composites, recommendations were given for experimental determination of all nine independent material constants E-x, E-y, E-z, v(xy), v(xz), G(xy), G(xz), G(yz), five of which were determined in the previous paper of the author (Nestorovic, 2010).

The paper deals with an elastomer body having a random 3D-distribution of ellipsoidal mutually parallel voids. By making use of Levin’s formulae effective stiffness as well as thermal expansion tensors are found numerically. Slight disorder case differs insignificantly from parallel voids. For such a disorder these effective material features are found. Subsequently, the energy release rate is used as a triggering tool for opening and closing of existing cracks. The accomplished results make possible a further application to kinetic equations., U radu se razmatra elastomer kao deformabilno telo sa slučajnom 3D-raspodelom paralelnih elipsoidnih šupljina. Korišćenjem Levinovih formula numerički se dobija efektivna krutost kao i tenzor koeficijenata termičkog širenja. Slučaj male neuređenosti se malo razlikuje od paralelnih šupljina. Za takvu neuređenost su nađene ove efektivne karakteristike. Zatim se brzina oslobađanja energije koristi kao uslov otvaranja i zatvaranja postojećih prslina. Dobijeni rezultati daju mogućnost primene kod rešavanja kinetičkih jednačina.

The paper deals with an elastomer body having a random 3D-distribution of ellipsoidal mutually parallel voids. By making use of Levin’s formulae effective stiffness as well as thermal expansion tensors are found numerically. Slight disorder case differs insignificantly from parallel voids. For such a disorder these effective material features are found. Subsequently, the energy release rate is used as a triggering tool for opening and closing of existing cracks. The accomplished results make possible a further application to kinetic equations., U radu se razmatra elastomer kao deformabilno telo sa slučajnom 3D-raspodelom paralelnih elipsoidnih šupljina. Korišćenjem Levinovih formula numerički se dobija efektivna krutost kao i tenzor koeficijenata termičkog širenja. Slučaj male neuređenosti se malo razlikuje od paralelnih šupljina. Za takvu neuređenost su nađene ove efektivne karakteristike. Zatim se brzina oslobađanja energije koristi kao uslov otvaranja i zatvaranja postojećih prslina. Dobijeni rezultati daju mogućnost primene kod rešavanja kinetičkih jednačina.

A large part of Sweden is located within the Taiga Area and hence most of the wood species growing there are included in the division of Coniferales. This has also led to major research activities on the needle-leaved types in the Pinaceae family. There are, however, many broad-leaved trees, but because of their relatively low economic importance only a few researchers have had the opportunity to study such woods. For certain branches of the Swedish wood manufacturing industry the Angiosperms are of vital importance, e.g. the furniture factories. In this paper the mechanical properties of two Swedish hard wood genera, namely Betula and Alnus, are revealed. These findings are also compared with those found in the literature.

The report describes studies of the deformation and failure behavior of Ti-6Al-4V titanium and 2024-T3 aluminum. This work was accomplished by the Lawrence Livermore National Laboratory under an Interagency Agreement between the Federal Aviation Administration (FAA) William J. Hughes Technical Center and the Department of Energy (DOE). The work was accomplished under the FAA's Aircraft Catastrophic Failure Prevention Program as part of its research into the turbine engine uncontainment event. Data was obtained at high strain rates and large strains using the split Hopkinson pressure bar method. This information, plus additional data from the literature, were used to critically evaluate the ability of the Johnson-Cook material model to represent the deformation and failure response of Ti-6Al-4V and 2024-T3 under conditions relevant to simulations of engine containment and the influence of uncontained engine debris on aircraft structures. This model is being used in the DYNA3D finite element code, which is being developed/validated for evaluating aircraft/engine designs relative to the federal airworthiness standards and for improving mitigation/containment technology. The results of this experimental work were used to define a new set of material constants for the strength component of the Johnson-Cook model for Ti-6Al-4V and 2024-T3.

Aditivní výrobní technologie umožňují výrobu tvarově komplexních struktur, které jsou běžnými postupy vyrobitelné jen velmi obtížně. Jednou z těchto struktur je i mikroprutová struktura složená z periodicky se opakujících prutových buněk. Tato práce se zabývá shrnutím dosavadních poznatků v oblasti mechanických vlastností mikroprutových struktur vyrobených metodou Selective Laser Melting a jejich testování. Dalším cílem bylo nalezení vhodných kritérií pro porovnání strukturovaného materiálu. Z hodnot získaných při materiálových testech reálných těles byly získány veličiny nutné k výpočtu hledaných materiálových konstant. Pro tento účel byl vytvořen skript v programu MS Excel. Provedeným výzkumem byly zjištěny hlavní faktory ovlivňující mechanické vlastnosti mikroprutových struktur. Na základě údajů a závislostí prezentovaných v této práci je možné porovnání strukturovaného materiálu., Additive manufacturing technologies allow manufacturing of complex structures which are near impossible to manufacture by other more conventional technologies. A fine example of these complex structures is a periodic metallic micro-cellular structure This bachelor thesis is focused on summarization of known mechanical behaviour of lattice structures manufactured via Selective Laser Melting. This study also investigates suitable comparison criteria for lattice structures. Required values for determination of material constants were obtained from mechanical testing of real specimens. For faster evaluation of mechanical testing, automatic script in MS Excel was created. Research showed up some of the major parameters characterising the mechanical behaviours of lattice structures. It is possible to compare qualities of lattice structures based on criteria presented in this work.

Aditivní výrobní technologie umožňují výrobu tvarově komplexních struktur, které jsou běžnými postupy vyrobitelné jen velmi obtížně. Jednou z těchto struktur je i mikroprutová struktura složená z periodicky se opakujících prutových buněk. Tato práce se zabývá shrnutím dosavadních poznatků v oblasti mechanických vlastností mikroprutových struktur vyrobených metodou Selective Laser Melting a jejich testování. Dalším cílem bylo nalezení vhodných kritérií pro porovnání strukturovaného materiálu. Z hodnot získaných při materiálových testech reálných těles byly získány veličiny nutné k výpočtu hledaných materiálových konstant. Pro tento účel byl vytvořen skript v programu MS Excel. Provedeným výzkumem byly zjištěny hlavní faktory ovlivňující mechanické vlastnosti mikroprutových struktur. Na základě údajů a závislostí prezentovaných v této práci je možné porovnání strukturovaného materiálu., Additive manufacturing technologies allow manufacturing of complex structures which are near impossible to manufacture by other more conventional technologies. A fine example of these complex structures is a periodic metallic micro-cellular structure This bachelor thesis is focused on summarization of known mechanical behaviour of lattice structures manufactured via Selective Laser Melting. This study also investigates suitable comparison criteria for lattice structures. Required values for determination of material constants were obtained from mechanical testing of real specimens. For faster evaluation of mechanical testing, automatic script in MS Excel was created. Research showed up some of the major parameters characterising the mechanical behaviours of lattice structures. It is possible to compare qualities of lattice structures based on criteria presented in this work.

Aditivní výrobní technologie umožňují výrobu tvarově komplexních struktur, které jsou běžnými postupy vyrobitelné jen velmi obtížně. Jednou z těchto struktur je i mikroprutová struktura složená z periodicky se opakujících prutových buněk. Tato práce se zabývá shrnutím dosavadních poznatků v oblasti mechanických vlastností mikroprutových struktur vyrobených metodou Selective Laser Melting a jejich testování. Dalším cílem bylo nalezení vhodných kritérií pro porovnání strukturovaného materiálu. Z hodnot získaných při materiálových testech reálných těles byly získány veličiny nutné k výpočtu hledaných materiálových konstant. Pro tento účel byl vytvořen skript v programu MS Excel. Provedeným výzkumem byly zjištěny hlavní faktory ovlivňující mechanické vlastnosti mikroprutových struktur. Na základě údajů a závislostí prezentovaných v této práci je možné porovnání strukturovaného materiálu., Additive manufacturing technologies allow manufacturing of complex structures which are near impossible to manufacture by other more conventional technologies. A fine example of these complex structures is a periodic metallic micro-cellular structure This bachelor thesis is focused on summarization of known mechanical behaviour of lattice structures manufactured via Selective Laser Melting. This study also investigates suitable comparison criteria for lattice structures. Required values for determination of material constants were obtained from mechanical testing of real specimens. For faster evaluation of mechanical testing, automatic script in MS Excel was created. Research showed up some of the major parameters characterising the mechanical behaviours of lattice structures. It is possible to compare qualities of lattice structures based on criteria presented in this work.