The Proportional Anisotropic Elastic Invariants

1991 ◽  
Vol 58 (1) ◽  
pp. 50-57 ◽  
Author(s):  
A. M. Sadegh ◽  
S. C. Cowin
Keyword(s):  
Elastic Material ◽  
Hydrostatic Stress ◽  
Von Mises Stress ◽  
Stress And Strain ◽  
Fracture Criteria ◽  
Linear Elastic Material ◽  
Linear Elastic ◽  
Isotropic Elasticity ◽  
Anisotropic Elastic ◽  
Von Mises

There are two proportional invariants for a linear isotropic material, the hydrostatic invariant, and the deviatoric invariant. The former is proportional to the trace of the tensor and the latter is proportional to the trace of the square of the associated deviatoric tensor. The hydrostatic stress and strain and the von Mises stress and strain are directly related to the hydrostatic and deviatoric proportional invariants, respectively, for an isotropic, linear elastic material. For each anisotropic linear elastic material symmetry there are up to six proportional invariants. In this paper we illustrate the six proportional invariants of an orthotropic elastic material using the elastic constants for spruce as the numerical example. The proportional elastic invariants play a role in anisotropic linear elasticity similar to the roles played by the hydrostatic stress and strain and the von Mises stress and strain in isotropic elasticity. They are the unique parameters whose contours represent both the stress and the strain distributions. They also have potential for representing failure or fracture criteria.

scholarly journals Evaluation of Bone–Implant Interface Stress and Strain Using Heterogeneous Mandibular Bone Properties Based on Different Empirical Correlations

2021 ◽  
Author(s):  
Mostafa Omran Hussein ◽  
Mohammed Suliman Alruthea
Keyword(s):  
Finite Element ◽  
Group Iv ◽  
Von Mises Stress ◽  
Patient Specific ◽  
Dental Arch ◽  
Stress And Strain ◽  
Bone Implant ◽  
Bone Properties ◽  
Group I ◽  
Von Mises

Abstract Objective The purpose of this study was to compare methods used for calculating heterogeneous patient-specific bone properties used in finite element analysis (FEA), in the field of implant dentistry, with the method based on homogenous bone properties. Materials and Methods In this study, three-dimensional (3D) computed tomography data of an edentulous patient were processed to create a finite element model, and five identical 3D implant models were created and distributed throughout the dental arch. Based on the calculation methods used for bone material assignment, four groups—groups I to IV—were defined. Groups I to III relied on heterogeneous bone property assignment based on different equations, whereas group IV relied on homogenous bone properties. Finally, 150 N vertical and 60-degree-inclined forces were applied at the top of the implant abutments to calculate the von Mises stress and strain. Results Groups I and II presented the highest stress and strain values, respectively. Based on the implant location, differences were observed between the stress values of group I, II, and III compared with group IV; however, no clear order was noted. Accordingly, variable von Mises stress and strain reactions at the bone–implant interface were observed among the heterogeneous bone property groups when compared with the homogenous property group results at the same implant positions. Conclusion Although the use of heterogeneous bone properties as material assignments in FEA studies seem promising for patient-specific analysis, the variations between their results raise doubts about their reliability. The results were influenced by implants’ locations leading to misleading clinical simulations.

An optimized cross-linked network model to simulate the linear elastic material response of a smart polymer

2015 ◽  
Vol 27 (11) ◽  
pp. 1461-1475 ◽  
Author(s):  
Jinjun Zhang ◽  
Bonsung Koo ◽  
Nithya Subramanian ◽  
Yingtao Liu ◽  
Aditi Chattopadhyay
Keyword(s):  
Network Model ◽  
Elastic Material ◽  
Smart Polymer ◽  
Material Response ◽  
Linear Elastic Material ◽  
Linear Elastic

Simulation of Fatigue Crack Growth Using XFEM

2020 ◽  
Author(s):  
Durlabh Bartaula ◽  
Yong Li ◽  
Smitha Koduru ◽  
Samer Adeeb
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Elastic Material ◽  
Low Cycle Fatigue ◽  
Material Behavior ◽  
Plastic Behavior ◽  
Linear Elastic Material ◽  
Linear Elastic ◽  
Cyclic Approach

Abstract Pipelines carrying oil and gas are susceptible to fatigue failure (i.e., unstable fatigue crack propagation) due to fluctuating loading such as varying internal pressure and other external loadings. Fatigue crack growth (FCG) prediction through full-scale pipe tests can be expensive and time consuming, and experimental data is limited particularly in the face of large uncertainty involved. In contrast, numerical simulation techniques (e.g., XFEM) can be alternative to study the FCG, given that numerical models can be theoretically and/or experimentally validated with reasonable accuracy. In this study, capabilities and limitations of existing fatigue analysis code (e.g., direct cyclic approach with XFEM) in Abaqus for low cycle fatigue simulation are explored for compact-tension (CT) specimens and pipelines assuming linear elastic material behavior. The simulated FCG curve for a CT specimen is compared with that obtained from the analytical method using the stress intensity factor prescribed in ASTM E647. However, for real pipelines with elastic-plastic behavior, direct cyclic approach is not suitable, and an indirect cyclic approach is used based on the fracture energy parameters (e.g., J integral) calculated using XFEM in Abaqus. FCG law (e.g., power law relationship like Paris law) is used to generate the fatigue crack growth curve. For comparison, the FCG curve obtained through direct cyclic approach for pipelines assuming linear elastic material is also presented. The comparative studies here indicate that XFEM-based FCG simulation using appropriate techniques can be applied to pipelines for fatigue life prediction.

Effect of Housing Support on Bearing Dynamics

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Lijun Cao ◽  
Matthew D. Brouwer ◽  
Farshid Sadeghi ◽  
Lars-Erik Stacke
Keyword(s):  
Finite Element ◽  
Elastic Material ◽  
Contact Forces ◽  
Support Structure ◽  
Linear Elastic Material ◽  
Outer Race ◽  
Linear Elastic ◽  
Elastomeric Material ◽  
Bearing Dynamics ◽  
Element Method

The objective of this investigation was to determine the effect of housing support on bearing performance and dynamics. In order to achieve the objective, an existing dynamic bearing model (DBM) was coupled with flexible housing model to include the effect of support structure on bearing dynamics and performance. The DBM is based on the discrete element method, in which the bearing components are assumed to be rigid. To achieve the coupling, a novel algorithm was developed to detect contact conditions between the housing support and bearing outer race and then calculate contact forces based on the penalty method. It should be noted that although commercial finite element (FE) software such as abaqus is available to model flexible housings, combining these codes with a bearing model is quite difficult since the data transfer between the two model packages is time-consuming. So, a three-dimensional (3D) explicit finite element method (EFEM) was developed to model the bearing support structure for both linear elastic and nonlinear inelastic elastomeric materials. The constitutive relationship for elastomeric material is based on an eight chain model, which captures hyperelastic behavior of rubber for large strains. The viscoelastic property is modeled by using the generalized Maxwell-element rheological model to exhibit rate-dependent behaviors, such as creep and hysteresis on cyclic loading. The results of this investigation illustrate that elastomeric material as expected has large damping to reduce vibration and absorb energy, which leads to a reduction in ball–race contact forces and friction. A parametric study confirmed that the viscoelastic stress (VS) contributes significantly to the performance of the material, and without proper amount of viscoelasticity it loses its advantage in vibration reduction and exhibits linear elastic material characteristics. As expected, it is also demonstrated that housing supports made of linear elastic material provide minimal damping and rely on the bearing friction to dissipate energy. A study of housing support geometry demonstrates that bearing support plays a large role on the dynamic performance of the bearing. Motion of bearing outer race is closely related to the geometry and symmetry of the housing.

A Generalized von Mises Criterion for Yield and Fracture

1980 ◽  
Vol 47 (2) ◽  
pp. 297-300 ◽  
Author(s):  
W. H. Yang
Keyword(s):  
Bauschinger Effect ◽  
Hydrostatic Stress ◽  
Fracture Criteria ◽  
Deformation History ◽  
Von Mises Criterion ◽  
Effect On Yield ◽  
Von Mises ◽  
New Criterion ◽  
Physical Phenomena ◽  
Special Case

Yield and fracture criteria for real materials are to a varying degree affected by a state of hydrostatic stress. Some materials, after certain deformation history, exhibit different yield point when the direction of the stress is reversed, a behavior known as the Bauschinger effect. These physical phenomena are not represented by the von Mises criterion. Based on a convexity theorem of matrices, a generalization of the von Mises criterion is presented. The new criterion satisfies the convexity requirement of plasticity theory and, with two scalar functions of deformation history α and β, produces a class of hardening behavior. The current values of α and β account for the effect of hydrostatic stress and an aspect of the Bauschinger effect on yield and fracture. The generalized criterion reduces to the form of the von Mises criterion as a special case.

scholarly journals Comparison of Ortho-planar Spring design optimization based on Linear Elastic and Hyper Elastic Materials

2018 ◽  
Vol 166 ◽  
pp. 01004
Author(s):  
Ruetai Graipaspong ◽  
Teeranoot Chanthasopeephan
Keyword(s):  
Topology Optimization ◽  
Elastic Material ◽  
Maximum Stress ◽  
Nonlinear Material ◽  
Small Displacement ◽  
Linear Elastic Material ◽  
Output Displacement ◽  
Linear Elastic ◽  
Hyper Elastic ◽  
Matlab Programming

In this paper, compliant Ortho-planar spring was designed based on a three-dimensional topology optimization method. The computation was developed using MATLAB programming. The objective of this work was to apply dual method to design an Ortho-planar spring while the design should have minimum mass and at the same time satisfy a set of constrained displacement. Throughout this paper, we analyzed a method for designing an Ortho-planar spring using linear elastic material and hyperelastic material. The results showed that under small displacement conditions, the output displacement, maximum stress magnitude, and the maximum stress of linear elastic assumption and hyper-elastic material were relatively close to each other. However, the mass fraction and the layout as the result of the optimization process was different. As for larger displacement, the maximum stress of linear elastic material appeared 2.59 times higher than the maximum stress of the hyper-elastic material model. The topology optimization output based on linear material was invalid because the topology of the computed Ortho-planar spring was not appeared as a one-piece layout while the design based on nonlinear material looked promising.

Simulation of Shock Wave Assisted Free and Shape Forming of Metallic Plates in a Shock Tube

2015 ◽  
Vol 813-814 ◽  
pp. 586-591 ◽  
Author(s):  
Kottakota Kalasagarreddi ◽  
Prem Sai Koppuravuri Sobhan ◽  
Vinay Kumar Gundu ◽  
S.R. Nagaraja
Keyword(s):  
Shock Wave ◽  
Shock Tube ◽  
Metal Forming ◽  
Von Mises Stress ◽  
Stress And Strain ◽  
Shock Strength ◽  
Engineering Problems ◽  
Experimental Values ◽  
Von Mises ◽  
Metallic Plates

Due to their complexity, certain engineering problems like finding shock strength, Mach number etc. and the interaction of shock wave with a structure in free and restricted metal forming techniques cannot be achieved in a single experimentation, these can be obtained only through a number of trials and that leads to increase in cost and time. In such cases both cost and time can be reduced by adopting numerical simulations. In this projectcommercial software ANSYS is used to simulate the propagation shock wave through a shock tube, free and shape forming of metallic plates subjected to this shock wave. Shock Mach numbers up to 2.12 have been generated by varying the driver to driven pressure ratios. Thin copper plates of diameter 60mm and thickness of 0.5mm and 0.3mm are subjected to shock wave loadingin order to form into dies.These dies,madeof structural steel are modelled with pre-defined shapes. The plate peakoverpressures ranging from 9 to 20bar have been generated.The midpoint deflection, Von Mises stress and strain are calculated for free forming copper plates. The simulated results are compared with the experimental values available in literature. The simulated results match well with the experimental values.

scholarly journals Strength and stiffness analyses of standard and double mortise and tenon joints

BioResources ◽  
2020 ◽  
Vol 15 (4) ◽  
pp. 8249-8267
Author(s):  
Seid Hajdarevic ◽  
Murco Obucina ◽  
Elmedin Mesic ◽  
Sandra Martinovic
Keyword(s):  
Bending Moment ◽  
Von Mises Stress ◽  
Elastic Model ◽  
Proportional Limit ◽  
Linear Elastic ◽  
Mortise And Tenon ◽  
Strength And Stiffness ◽  
Experimental Values ◽  
Maximal Moment ◽  
Von Mises

This paper investigated the effect of the tenon length on the strength and stiffness of the standard mortise and tenon joints, as well of the double mortise and tenon joints, that were bonded by poly(vinyl acetate) (PVAc) and polyurethane (PU) glues. The strength was analyzed by measuring applied load and by calculating ultimate bending moment and bending moment at the proportional limit. Stiffness was evaluated by measuring displacement and by calculating the ratio of applied force and displacement along the force line. The results were compared with the data obtained by the simplified static expressions and numerical calculation of the orthotropic linear-elastic model. The results indicated that increasing tenon length increased the maximal moment and proportional moment of the both investigated joints types. The analytically calculated moments were increased more than the experimental values for both joint types, and they had generally lower values than the proportional moments for the standard tenon joints, as opposed to the double tenon joints. The Von Mises stress distribution showed characteristic zones of the maximum and increased stress values. These likewise were monitored in analytical calculations. The procedures could be successfully used to achieve approximate data of properties of loaded joints.

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