On the Linear Constitutive Equations of Transversely Isotropic Incompressible Elastic Materials

1972 ◽  
Vol 45 (4) ◽  
pp. 1104-1110
Author(s):  
H. Demiray ◽  
M. Levinson
Keyword(s):  
Stress Concentration ◽  
Stress Analysis ◽  
Circular Hole ◽  
Elastic Material ◽  
Constitutive Equations ◽  
Transversely Isotropic ◽  
Elastic Materials ◽  
Rubber Composites ◽  
Limiting Case ◽  
Compressible Materials

Abstract The linear constitutive equations of a transversely isotropic, incompressible, elastic material are derived in this paper as a limiting case of the constitutive equations for the corresponding compressible materials. These equations should be appropriate for the stress analysis of products fabricated from certain laminated, reinforced rubber composites. Some details of a problem concerned with the stress concentration around a circular hole are also given.

scholarly journals Reciprocity, passivity and causality in Willis materials

2016 ◽  
Vol 472 (2194) ◽  
pp. 20160604 ◽  
Author(s):  
Michael B. Muhlestein ◽  
Caleb F. Sieck ◽  
Andrea Alù ◽  
Michael R. Haberman
Keyword(s):  
Elastic Material ◽  
Time Domain ◽  
Material Properties ◽  
Constitutive Equations ◽  
Wave Motion ◽  
Constitutive Relations ◽  
Alternative Formulation ◽  
Elastic Materials ◽  
Order Dispersion ◽  
Insight Into

Materials that require coupling between the stress–strain and momentum–velocity constitutive relations were first proposed by Willis (Willis 1981 Wave Motion 3 , 1–11. ( doi:10.1016/0165-2125(81)90008-1 )) and are now known as elastic materials of the Willis type, or simply Willis materials. As coupling between these two constitutive equations is a generalization of standard elastodynamic theory, restrictions on the physically admissible material properties for Willis materials should be similarly generalized. This paper derives restrictions imposed on the material properties of Willis materials when they are assumed to be reciprocal, passive and causal. Considerations of causality and low-order dispersion suggest an alternative formulation of the standard Willis equations. The alternative formulation provides improved insight into the subwavelength physical behaviour leading to Willis material properties and is amenable to time-domain analyses. Finally, the results initially obtained for a generally elastic material are specialized to the acoustic limit.

Stress Analysis of Holes in Thick Plates

2004 ◽  
Vol 1-2 ◽  
pp. 153-158 ◽  
Author(s):  
S. Quinn ◽  
Janice M. Dulieu-Barton
Keyword(s):  
Stress Concentration ◽  
Stress Analysis ◽  
Uniaxial Tension ◽  
Plane Stress ◽  
Plate Surface ◽  
Flat Plates ◽  
Thick Plates ◽  
Concentration Factors ◽  
Stress Concentration Factors

A review of the Stress Concentration Factors (SCFs) obtained from normal and oblique holes in thick flat plates loaded in uniaxial tension has been conducted. The review focuses on values from the plate surface and discusses the ramifications of making a plane stress assumption.

scholarly journals Non-local criteria for the borehole problem: Gradient Elasticity versus Finite Fracture Mechanics

Meccanica ◽  
2021 ◽  
Author(s):  
A. Sapora ◽  
G. Efremidis ◽  
P. Cornetti
Keyword(s):  
Stress Concentration ◽  
Fracture Mechanics ◽  
Elastic Material ◽  
Fracture Criterion ◽  
Biaxial Loading ◽  
Gradient Elasticity ◽  
Energy Conditions ◽  
Material Behaviour ◽  
Finite Fracture Mechanics ◽  
Non Local

AbstractTwo nonlocal approaches are applied to the borehole geometry, herein simply modelled as a circular hole in an infinite elastic medium, subjected to remote biaxial loading and/or internal pressure. The former approach lies within the framework of Gradient Elasticity (GE). Its characteristic is nonlocal in the elastic material behaviour and local in the failure criterion, hence simply related to the stress concentration factor. The latter approach is the Finite Fracture Mechanics (FFM), a well-consolidated model within the framework of brittle fracture. Its characteristic is local in the elastic material behaviour and non-local in the fracture criterion, since crack onset occurs when two (stress and energy) conditions in front of the stress concentration point are simultaneously met. Although the two approaches have a completely different origin, they present some similarities, both involving a characteristic length. Notably, they lead to almost identical critical load predictions as far as the two internal lengths are properly related. A comparison with experimental data available in the literature is also provided.

The Stress Analysis and Experimental Research of Tubular K-Joints With Overlap

1987 ◽  
Vol 109 (4) ◽  
pp. 375-380
Author(s):  
Tie-yun Chen ◽  
Wei-min Chen
Keyword(s):  
Experimental Data ◽  
Stress Concentration ◽  
Variational Method ◽  
Stress Analysis ◽  
Experimental Research ◽  
Hot Spot ◽  
Intersection Point ◽  
Tubular Joints ◽  
Photoelastic Experiment ◽  
Intersection Curves

The geometry of overlapping tubular joints, the equations of intersection curves and the coordinate of the intersection point are introduced first. The variational method for simple tubular joints is extended to the stress analysis of tubular K-joints with overlap. The computer program is compiled. The stress concentration factor and the position of the hot spot of an overlapping joint are found. For the sake of proving the feasibility of our analysis and program, the computed results are compared with experimental data of our photoelastic experiment and other experiments.

Stress Analysis and Structure Optimization for the Opening Flat Cover of Pressure Vessels

2012 ◽  
Vol 538-541 ◽  
pp. 3253-3258 ◽  
Author(s):  
Jun Jian Xiao
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Stress Concentration ◽  
Stress Analysis ◽  
Structure Optimization ◽  
Pressure Vessels ◽  
Secondary Stress ◽  
Element Analysis ◽  
Primary Stress ◽  
Flat Cover

According to the results of finite element analysis (FEA), when the diameter of opening of the flat cover is no more than 0.5D (d≤0.5D), there is obvious stress concentration at the edge of opening, but only existed within the region of 2d. Increasing the thickness of flat covers could not relieve the stress concentration at the edge of opening. It is recommended that reinforcing element being installed within the region of 2d should be used. When the diameter of openings is larger than 0.5D (d>0.5D), conical or round angle transitions could be employed at connecting location, with which the edge stress decreased remarkably. However, the primary stress plus the secondary stress would be valued by 3[σ].

Sign in / Sign up

Export Citation Format

Share Document