Ramberg–Osgood material behavior expression and large deflections of Euler beams

2020 ◽  
pp. 108128652093236
Author(s):  
Ronald J Giardina ◽  
Dongming Wei
Keyword(s):  
Cross Sections ◽  
Nonlinear Behavior ◽  
Material Model ◽  
Material Behavior ◽  
Combined Loading ◽  
Elastic Behavior ◽  
Large Deflections ◽  
Euler Beam ◽  
Special Cases ◽  
Material Behaviors

Several assumptions are commonly made throughout the literature with regard to the mechanical expression of material behavior under a Ramberg–Osgood material model; specifically, the negligible effects of nonlinearity on the elastic behavior of the material. These assumptions do not reflect the complicated nonlinearity implied by the Ramberg–Osgood expression, which can lead to significant differences in the member model response from the true material behavior curve. With the proposed approach, new explicit results for Ramberg–Osgood materials are achieved without relying on these assumptions of material and model expression. The only assumptions present within the proposed model are the standard mechanical assumptions of an Euler beam. A general nonlinear moment–curvature relationship for monotone material behaviors is constructed. Large deflections of cantilever Euler beams with rectangular cross-sections under a combined loading are modeled. Numerical validation of this new method against results already given in the literature for the special cases of linear and power-law material behaviors are provided. An analysis is presented for three common material behavior relationships, with a focus on how these relationships are expressed through the deflection of members under the application of force within the model; this analysis clearly demonstrates that the sub-yield nonlinear behavior of the Ramberg–Osgood expression can be significant. The distinctions between material behavior expression demonstrated in this analysis have been long overlooked within the literature. This work addresses a gap between the modeling of Ramberg–Osgood material behaviors and the implementation of that model in mechanics.

Anisotropic and Inhomogeneous Tensile Behavior of the Human Anulus Fibrosus: Experimental Measurement and Material Model Predictions

2000 ◽  
Vol 123 (3) ◽  
pp. 256-263 ◽  
Author(s):  
Dawn M. Elliott ◽  
Lori A. Setton
Keyword(s):  
Tensile Modulus ◽  
Material Model ◽  
Material Behavior ◽  
Anulus Fibrosus ◽  
Linear Region ◽  
Material Behaviors ◽  
Model Predictions ◽  
Complete Set ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

The anulus fibrosus (AF) of the intervertebral disc exhibits spatial variations in structure and composition that give rise to both anisotropy and inhomogeneity in its material behaviors in tension. In this study, the tensile moduli and Poisson’s ratios were measured in samples of human AF along circumferential, axial, and radial directions at inner and outer sites. There was evidence of significant inhomogeneity in the linear-region circumferential tensile modulus (17.4±14.3 MPa versus 5.6±4.7 MPa, outer versus inner sites) and the Poisson’s ratio ν21 (0.67±0.22 versus 1.6±0.7, outer versus inner), but not in the axial modulus (0.8±0.9 MPa) or the Poisson’s ratios ν12 (1.8±1.4) or ν13 (0.6±0.7). These properties were implemented in a linear anisotropic material model of the AF to determine a complete set of model properties and to predict material behaviors for the AF under idealized kinematic states. These predictions demonstrate that interactions between fiber populations in the multilamellae AF significantly contribute to the material behavior, suggesting that a model for the AF as concentric and physically isolated lamellae may not be appropriate.

Analysis of crush-damaged carbon-fiber-reinforced-polymer (CFRP) composites with optimization-assisted post-peak-stress modeling

2020 ◽  
pp. 002199832095770
Author(s):  
Sheng Dong ◽  
Lars Gräning ◽  
Kelly Carney ◽  
Allen Sheldon
Keyword(s):  
Cross Sections ◽  
Peak Stress ◽  
Material Model ◽  
Material Behavior ◽  
Engineering Practice ◽  
Model Parameters ◽  
Optimization Strategy ◽  
Damage Models ◽  
Cfrp Composites ◽  
Force Time

In the presented effort, layered CFRP composites samples with differing thicknesses and cross-sections are manufactured and crushed under quasi-static loading conditions. Simulation of the crushes are conducted using traditional continuum mechanics damage models. Parameters are proposed to represent the post peak-stress material behavior including the residual strengths of the fiber and matrix, as well the ultimate strain for deletion of composite elements. This paper presents a systematic approach to identify optimal values for these post peak-stress parameters based on a methodology incorporating CAE models and numerical optimization. An adaptive meta-model based global optimization strategy, with the objective of matching the force-time characteristics of multiple crush experiments simultaneously, has been established to quantify the values of the CFRP’s post peak-stress degradation and erosion material model parameters through calibration. Using two separate test configurations for optimization, a set of values for those parameters are determined. This parameter set is shown to successfully predict the response of additional test cases, including matching of force-displacement curves and crushing modes. The resulting composite crush simulations show a good quantitative as well as qualitative agreement between simulations and experiments to a degree that is difficult to be achieved solely with previous engineering practice.

Application of a Smooth Approximation of the Schmid's Law to a Single Crystal Gas Turbine Blade

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Alessandro D. Ramaglia
Keyword(s):  
Single Crystal ◽  
Constitutive Models ◽  
Material Model ◽  
Research Literature ◽  
Material Behavior ◽  
Elastic Behavior ◽  
Full Potential ◽  
Smooth Approximation ◽  
Suitable Material ◽  
Von Mises

In industrial practice the choice of the most suitable material model does not solely rely on the ability of the model in describing the intended phenomena. Most of the choice is often based on a trade-off between a great variety of factors. Robustness, cost, and time for the minimum testing campaign necessary to identify the model and preexisting standard practices are only a few of them. This is particularly true in the case of nonlinear structural analyses because of their intrinsic difficulties and the higher level of skills needed to carefully exploit their full potential. So, despite the great progress in this field, in certain cases it is desirable to use plasticity models that are rate independent and possess very simple hardening terms. This is for example the case in which long term creep can be an issue or when the designer may want to treat separately different phenomena contributing to inelastic deformation. If the material to be modeled is isotropic, commercial finite element (FE) packages are able to deal with such problems in almost every case. On the contrary for anisotropic materials like Ni-based superalloys cast as single crystals, the choice of the designer is more limited and despite the large amount of research literature on the subject, single crystal constitutive models remain quite difficult to handle, to implement into FE codes, to calibrate, and to validate. Such difficulties, coupled with the unavoidable approximations introduced by any model, often force the practice of using oversimplifications of the material behavior. In what follows this problem is addressed by showing how single crystal plasticity modeling can be reduced to the adoption of an anisotropic elastic behavior with a sort of von Mises yield surface.

Imperfection Insensitivity of Thin Wavy Cylindrical Shells Under Axial Compression or Bending

2020 ◽  
Vol 87 (4) ◽  
Author(s):  
Kshitij Kumar Yadav ◽  
Simos Gerasimidis
Keyword(s):  
Axial Compression ◽  
Cross Sections ◽  
Cylindrical Shells ◽  
Decisive Role ◽  
High Sensitivity ◽  
Material Model ◽  
Material Behavior ◽  
Imperfection Sensitivity ◽  
Wave Parameters ◽  
Bending Load

Abstract The presence of imperfections significantly reduces the load carrying capacity of thin cylindrical shells due to the high sensitivity of thin shells to imperfections. To nullify this unfavorable characteristic, thin cylindrical shells are designed using a conservative knockdown factor method, which was developed by NASA in the late 1960s. Almost all the design codes, explicitly or implicitly, follow this approach. Recently, a new approach has emerged to significantly reduce the sensitivity of thin cylindrical shells. In this approach, wavy cross sections are used instead of circular cross sections for creating thin cylinders. Past studies have demonstrated the effectiveness of wavy cylinders to reduce imperfection sensitivity of thin cylinders under axial compression assuming linear elastic material behavior. These studies used eigenmode imperfections which do not represent realistic imperfections found in cylinders. In this paper, using a realistic dimple-like imperfection, new insights are presented into the response of wavy cylinders under uniform axial compression and bending. Furthermore, the effectiveness of the wavy cylinders to reduce imperfection sensitivity under bending load is investigated assuming a plastic Ramberg–Osgood material model. The effect of wave parameters, e.g., the amplitude and the number of waves, is also explored. This study reveals that wavy thin cylinders are insensitive to imperfections under bending in the inelastic range of the material. It is also found that the wave parameters play a decisive role in the response of thin wavy cylinders to imperfections under bending.

An Analytical Framework for the Solution of Autofrettaged Tubes Under Constant Axial Strain Condition

2008 ◽  
Author(s):  
E. Hosseinian ◽  
G. H. Farrahi ◽  
M. R. Movahhedy
Keyword(s):  
Numerical Methods ◽  
Analytical Method ◽  
Numerical Solutions ◽  
Yield Criterion ◽  
Axial Strain ◽  
Material Model ◽  
Analytical Framework ◽  
Material Behavior ◽  
Perfectly Plastic ◽  
Special Cases

Autofrettage is a technique for introducing beneficial residual stresses into cylinders. Both analytical and numerical methods are used for analysis of the autofrettage process. Analytical methods have been presented only for special cases of autofrettage. In this work, an analytical framework for the solution of autofrettaged tubes with constant axial strain conditions is developed. Material behavior is assumed to be incompressible and two different quadratic polynomials are used for strain hardening in loading and unloading. Clearly, elastic-perfectly plastic and linear hardening materials are special cases of this general model. This material model is convenient for description of the behavior of a class of pressure vessel steels such as A723. The Bauschinger effect is assumed fixed and total deformation theory based upon von-Mises yield criterion is used. An explicit solution for the constant axial strain conditions and its special cases such as plane strain and closed-end conditions is obtained. For open-end condition for which axial force is zero the presented analytical method leads to a simple numerical solution. Finally, results of the new method are compared with those obtained from other analytical and numerical methods and excellent agreement is observed. Since the presented method is a general analytical method, it is believed that it could be used for validation of numerical solutions or analytical solutions for special loading cases.

An Analytical Framework for the Solution of Autofrettaged Tubes Under Constant Axial Strain Condition

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
E. Hosseinian ◽  
G. H. Farrahi ◽  
M. R. Movahhedy
Keyword(s):  
Numerical Methods ◽  
Analytical Method ◽  
Numerical Solutions ◽  
Yield Criterion ◽  
Axial Strain ◽  
Material Model ◽  
Analytical Framework ◽  
Material Behavior ◽  
Perfectly Plastic ◽  
Special Cases

Autofrettage is a technique for introducing beneficial residual stresses into cylinders. Both analytical and numerical methods are used for the analysis of the autofrettage process. Analytical methods have been presented only for special cases of autofrettage. In this work, an analytical framework for the solution of autofrettaged tubes with constant axial strain conditions is developed. Material behavior is assumed to be incompressible, and two different quadratic polynomials are used for strain hardening in loading and unloading. Clearly, elastic perfectly plastic and linear hardening materials are the special cases of this general model. This quadratic material model is convenient for the description of the behavior of a class of pressure vessel steels such as A723. The Bauschinger effect is assumed fixed, and the total deformation theory based on the von Mises yield criterion is used. An explicit solution for the constant axial strain conditions and its special cases such as plane strain and closed-end conditions is obtained. For an open-end condition, for which the axial force is zero, the presented analytical method leads to a simple numerical solution. Finally, results of the new method are compared with those obtained from other analytical and numerical methods, and excellent agreement is observed. Since the presented method is a general analytical method, it could be used for validation of numerical solutions or analytical solutions for special loading cases.

scholarly journals Confinement effects for rubberised concrete in tubular steel cross-sections under combined loading

2021 ◽  
Vol 21 (2) ◽  
Author(s):  
A. Mujdeci ◽  
D. V. Bompa ◽  
A. Y. Elghazouli
Keyword(s):  
Axial Compression ◽  
Cross Section ◽  
Cross Sections ◽  
Image Correlation ◽  
Combined Loading ◽  
Test Results ◽  
Compression Tests ◽  
Confinement Effects ◽  
Rubber Content ◽  
Dependent Modification

AbstractThis paper describes an experimental investigation into confinement effects provided by circular tubular sections to rubberised concrete materials under combined loading. The tests include specimens with 0%, 30% and 60% rubber replacement of mineral aggregates by volume. After describing the experimental arrangements and specimen details, the results of bending and eccentric compression tests are presented, together with complementary axial compression tests on stub-column samples. Tests on hollow steel specimens are also included for comparison purposes. Particular focus is given to assessing the confinement effects in the infill concrete as well as their influence on the axial–bending cross-section strength interaction. The results show that whilst the capacity is reduced with the increase in the rubber replacement ratio, an enhanced confinement action is obtained for high rubber content concrete compared with conventional materials. Test measurements by means of digital image correlation techniques show that the confinement in axial compression and the neutral axis position under combined loading depend on the rubber content. Analytical procedures for determining the capacity of rubberised concrete infilled cross-sections are also considered based on the test results as well as those from a collated database and then compared with available recommendations. Rubber content-dependent modification factors are proposed to provide more realistic representations of the axial and flexural cross-section capacities. The test results and observations are used, in conjunction with a number of analytical assessments, to highlight the main parameters influencing the behaviour and to propose simplified expressions for determining the cross-section strength under combined compression and bending.

scholarly journals Anisotropic and age-dependent elastic material behavior of the human costal cartilage

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Matthias Weber ◽  
Markus Alexander Rothschild ◽  
Anja Niehoff
Keyword(s):  
Costal Cartilage ◽  
Indentation Test ◽  
Biomechanical Properties ◽  
Material Behavior ◽  
Cartilage Tissue ◽  
Elastic Behavior ◽  
Unconfined Compression ◽  
Unconfined Compression Test ◽  
Young’S Moduli ◽  
Age Related

AbstractCompared to articular cartilage, the biomechanical properties of costal cartilage have not yet been extensively explored. The research presented addresses this problem by studying for the first time the anisotropic elastic behavior of human costal cartilage. Samples were taken from 12 male and female cadavers and unconfined compression and indentation tests were performed in mediolateral and dorsoventral direction to determine Young’s Moduli EC for compression and Ei5%, Ei10% and Eimax at 5%, 10% and maximum strain for indentation. Furthermore, the crack direction of the unconfined compression samples was determined and histological samples of the cartilage tissue were examined with the picrosirius-polarization staining method. The tests revealed mean Young’s Moduli of EC = 32.9 ± 17.9 MPa (N = 10), Ei5% = 11.1 ± 5.6 MPa (N = 12), Ei10% = 13.3 ± 6.3 MPa (N = 12) and Eimax = 14.6 ± 6.6 MPa (N = 12). We found that the Young’s Moduli in the indentation test are clearly anisotropic with significant higher results in the mediolateral direction (all P = 0.002). In addition, a dependence of the crack direction of the compressed specimens on the load orientation was observed. Those findings were supported by the orientation of the structure of the collagen fibers determined in the histological examination. Also, a significant age-related elastic behavior of human costal cartilage could be shown with the unconfined compression test (P = 0.009) and the indentation test (P = 0.004), but no sex effect could be detected. Those results are helpful in the field of autologous grafts for rhinoplastic surgery and for the refinement of material parameters in Finite Element models e.g., for accident analyses with traumatic impact on the thorax.

A Viscoelastic Correspondence Principle for Plane Membranes Subjected to Lateral Pressure

1983 ◽  
Vol 50 (4a) ◽  
pp. 740-742 ◽  
Author(s):  
B. Stora˚kers
Keyword(s):  
Time Dependence ◽  
Viscoelastic Material ◽  
Lateral Pressure ◽  
Correspondence Principle ◽  
Material Model ◽  
Material Behavior ◽  
Linear Elastic Material ◽  
First Order ◽  
Linear Elastic ◽  
Consistent Approximation

The classical Fo¨ppl equations, governing the deflection of plane membranes, constitute the first-order consistent approximation in the case of linear elastic material behavior. It is shown that despite the static and kinematic nonlinearities present, for arbitrary load histories a correspondence principle for viscoelastic material behavior exists if all relevant relaxation moduli are of uniform time dependence. Application of the principle is illustrated by means of a popular material model.

A Simple and Accurate Method for Determining Large Deflections in Compliant Mechanisms Subjected to End Forces and Moments

1998 ◽  
Vol 120 (3) ◽  
pp. 392-400 ◽  
Author(s):  
A. Saxena ◽  
S. N. Kramer
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Elliptic Integral ◽  
Beam Equation ◽  
Large Deflections ◽  
Euler Beam ◽  
Body Model ◽  
Rigid Body Model ◽  
Analysis And Synthesis

Compliant members in flexible link mechanisms undergo large deflections when subjected to external loads. Because of this fact, traditional methods of deflection analysis do not apply. Since the nonlinearities introduced by these large deflections make the system comprising such members difficult to solve, parametric deflection approximations are deemed helpful in the analysis and synthesis of compliant mechanisms. This is accomplished by representing the compliant mechanism as a pseudo-rigid-body model. A wealth of analysis and synthesis techniques available for rigid-body mechanisms thus become amenable to the design of compliant mechanisms. In this paper, a pseudo-rigid-body model is developed and solved for the tip deflection of flexible beams for combined end loads. A numerical integration technique using quadrature formulae has been employed to solve the large deflection Bernoulli-Euler beam equation for the tip deflection. Implementation of this scheme is simpler than the elliptic integral formulation and provides very accurate results. An example for the synthesis of a compliant mechanism using the proposed model is also presented.

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