On controllable states of stress for every compressible, isotropic, elastic material

2003 ◽  
Vol 161 (1-2) ◽  
pp. 127-129
Author(s):  
V. K. Agarwal
Keyword(s):  
Elastic Material ◽  
Isotropic Elastic Material

General theory of small elastic deformations superposed on finite elastic deformations

1952 ◽  
Vol 211 (1104) ◽  
pp. 128-154 ◽  
Keyword(s):  
General Theory ◽  
Elastic Material ◽  
Finite Deformation ◽  
Plane Surface ◽  
Thin Sheet ◽  
Potential Functions ◽  
Homogeneous Deformation ◽  
Infinitesimal Deformation ◽  
Elastic Deformations ◽  
Isotropic Elastic Material

Using tensor notations a general theory is developed for small elastic deformations, of either a compressible or incompressible isotropic elastic body, superposed on a known finite deformation, without assuming special forms for the strain-energy function. The theory is specialized to the case when the finite deformation is pure homogeneous. When two of the principal extension ratios are equal the changes in displacement and stress due to the small superposed deformation are expressed in terms of two potential functions in a manner which is analogous to that used in the infinitesimal deformation of hexagonally aeolotropic materials. The potential functions are used to solve the problem of the infinitesimally small indentation, by a spherical punch, of the plane surface of a semi-infinite body of incompressible isotropic elastic material which is first subjected to a finite pure homogeneous deformation symmetrical about the normal to the force-free plane surface. The general theory is also applied to the infinitesimal deformation of a thin sheet of incompressible isotropic elastic material which is first subjected to a finite pure homogeneous deformation by forces in its plane. A differential equation is obtained for the small deflexion of the sheet due to small forces acting normally to its face. This equation is solved completely in the case of a clamped circular sheet subjected to a pure homogeneous deformation having equal extension ratios in the plane of the sheet, the small bending force being uniformly distributed over a face of the sheet. Finally, equations are obtained for the homogeneously deformed sheet subjected to infinitesimal generalized plane stress, and a method of solution by complex variable technique is indicated.

Optimum Elastic Restraint for Pressurised Circular Plates

1963 ◽  
Vol 67 (632) ◽  
pp. 525-526
Author(s):  
Charles W. Bert
Keyword(s):  
Effective Stress ◽  
Elastic Material ◽  
Unit Volume ◽  
List Type ◽  
Maximum Deflection ◽  
Type Number ◽  
Circular Plates ◽  
Uniform Thickness ◽  
Isotropic Elastic Material ◽  
Elastically Restrained

SummaryFor uniform-thickness, solid circular plates made of isotropic elastic material and elastically restrained at the edge, expressions are derived for the optimum support stiffness to minimise the following quantities: 1.The largest effective stress based on several different strength theories.2.The largest effective stress per unit of maximum deflection or per unit volume displaced.

Sensitivities of Medial Meniscal Motion and Deformation to Material Properties of Articular Cartilage, Meniscus and Meniscal Attachments Using Design of Experiments Methods

2005 ◽  
Vol 128 (3) ◽  
pp. 399-408 ◽  
Author(s):  
Jiang Yao ◽  
Paul D. Funkenbusch ◽  
Jason Snibbe ◽  
Mike Maloney ◽  
Amy L. Lerner
Keyword(s):  
Experimental Data ◽  
Articular Cartilage ◽  
Elastic Material ◽  
Material Properties ◽  
Cruciate Ligament ◽  
Transverse Isotropy ◽  
Experimental Studies ◽  
Critical Material ◽  
Isotropic Elastic Material ◽  
Meniscal Attachments

This study investigated the role of the material properties assumed for articular cartilage, meniscus and meniscal attachments on the fit of a finite element model (FEM) to experimental data for meniscal motion and deformation due to an anterior tibial loading of 45N in the anterior cruciate ligament-deficient knee. Taguchi style L18 orthogonal arrays were used to identify the most significant factors for further examination. A central composite design was then employed to develop a mathematical model for predicting the fit of the FEM to the experimental data as a function of the material properties and to identify the material property selections that optimize the fit. The cartilage was modeled as isotropic elastic material, the meniscus was modeled as transversely isotropic elastic material, and meniscal horn and the peripheral attachments were modeled as noncompressive and nonlinear in tension spring elements. The ability of the FEM to reproduce the experimentally measured meniscal motion and deformation was most strongly dependent on the initial strain of the meniscal horn attachments (ε1H), the linear modulus of the meniscal peripheral attachments (EP) and the ratio of meniscal moduli in the circumferential and transverse directions (Eθ∕ER). Our study also successfully identified values for these critical material properties (ε1H=−5%, EP=5.6MPa, Eθ∕ER=20) to minimize the error in the FEM analysis of experimental results. This study illustrates the most important material properties for future experimental studies, and suggests that modeling work of meniscus, while retaining transverse isotropy, should also focus on the potential influence of nonlinear properties and inhomogeneity.

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