Optimal recovery of the elasticity tensor of general anisotropic materials from ultrasonic velocity data

1997 ◽  
Vol 101 (2) ◽  
pp. 813-833 ◽  
Author(s):  
Christophe Aristégui ◽  
Stéphane Baste
Keyword(s):  
Ultrasonic Velocity ◽  
Anisotropic Materials ◽  
Optimal Recovery ◽  
Elasticity Tensor ◽  
Velocity Data

Stochastic Properties of Anisotropic Materials

2001 ◽  
Author(s):  
Michael “Mick” Peterson ◽  
Miao Sun
Keyword(s):  
Elastic Properties ◽  
Anisotropic Materials ◽  
Optimal Recovery ◽  
Growth Patterns ◽  
Curvilinear Coordinates ◽  
Natural Material ◽  
Materials Properties ◽  
Damping Characteristics ◽  
Different Types ◽  
Stochastic Properties

Abstract Extensive research has been directed toward the development of methods for the optimal recovery of elastic properties from ultrasonic measurements. For a number of applications both the elastic and damping characteristics of the materials are required in design. The use of the optimal recovery does present challenges when applied to either man-made or natural anisotropic materials. In many cases manufacturing variability results in a need for a statistical description of the elastic and damping properties. In addition, errors in material lay-up or growth patterns may result in mis-orientation of the principle materials axes with respect to the geometrical axes. In this work, an examples is shown that demonstrates the recovery of the elastic properties of a natural material when stochastic properties are required. Statistical descriptions of the materials properties are obtained for wood of two different types of material. Results are shown assuming a nominally orthotropic orientation, although the existence of curvilinear coordinates is acknowledged.

scholarly journals FINITE STRAINS OF NONLINEAR ELASTIC ANISOTROPIC MATERIALS

2021 ◽  
pp. 103-116
Author(s):  
M.Yu. Sokolova ◽  
◽  
D.V. Khristich ◽  
Keyword(s):  
Coordinate System ◽  
Elastic Properties ◽  
Mutual Influence ◽  
Strain Tensor ◽  
Anisotropic Materials ◽  
Elasticity Tensor ◽  
Finite Strains ◽  
Cubic Materials ◽  
Elasticity Tensors ◽  
Nonlinear Elastic

Anisotropic materials with the symmetry of elastic properties inherent in crystals of cubic syngony are considered. Cubic materials are close to isotropic ones by their mechanical properties. For a cubic material, the elasticity tensor written in an arbitrary (laboratory) coordinate system, in the general case, has 21 non-zero components that are not independent. An experimental method is proposed for determining such a coordinate system, called canonical, in which a tensor of elastic properties includes only three nonzero independent constants. The nonlinear model of the mechanical behavior of cubic materials is developed, taking into account geometric and physical nonlinearities. The specific potential strain energy for a hyperelastic cubic material is written as a function of the tensor invariants, which are projections of the Cauchy-Green strain tensor into eigensubspaces of the cubic material. Expansions of elasticity tensors of the fourth and sixth ranks in tensor bases in eigensubspaces are determined for the cubic material. Relations between stresses and finite strains containing the second degree of deformations are obtained. The expressions for the stress tensor reflect the mutual influence of the processes occurring in various eigensubspaces of the material under consideration.

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