scholarly journals Isotropic and anisotropic elastic scatterers of underwater sound

2021 ◽  
Vol 4 (398) ◽  
pp. 138-147
Author(s):  
Alexandr Kleschev ◽  
Keyword(s):  
Anisotropic Body ◽  
Diffraction Theory ◽  
Physical Parameters ◽  
Underwater Sound ◽  
Boundary Problems ◽  
Angular Scattering ◽  
Transversally Isotropic ◽  
Anisotropic Bodies ◽  
Anisotropic Elastic ◽  
Isotropic Bodies

Object and purpose of research. This paper discusses diffraction parameters of isotropic and anisotropic elastic scatterers, demonstrating that transversally isotropic bodies with a certain orientation of their planes of isotropy might be regarded as isotropic scatterers with similar size, shape and physical parameters. Materials and methods. Diffraction theory methods in solution of boundary problems and equations of dynamic elasticity theory for isotropic and anisotropic bodies. Main results. Calculation of moduli for angular parameters, as well as of relative back-scattering sections for isotropic and anisotropic scatterers of various shapes. Conclusion. The studies demonstrated that if transversally isotropic bodies of various shapes have a certain orientation of their planes of isotropy and a certain vector of a plane wave falling onto them, their reflection parameters, like relative backscattering sections and angular scattering characteristic of an anisotropic body are the same as those for isotropic bodies of similar size, shape and elasticity.

3D Phase Field Modeling of Martensitic Microstructure Evolution in Steels

2011 ◽  
Vol 172-174 ◽  
pp. 1066-1071 ◽  
Author(s):  
Hemantha Kumar Yeddu ◽  
John Ågren ◽  
Annika Borgenstam
Keyword(s):  
Elastic Material ◽  
Microstructure Evolution ◽  
Phase Field ◽  
Plastic Material ◽  
Elastic Strain Energy ◽  
Physical Parameters ◽  
Perfectly Plastic ◽  
Martensitic Microstructure ◽  
Anisotropic Elastic ◽  
Elastic Perfectly Plastic

Complex martensitic microstructure evolution in steels generates enormous curiosity among the materials scientists and especially among the Phase Field (PF) modeling enthusiasts. In the present work PF Microelasticity theory proposed by A.G. Khachaturyan coupled with plasticity is applied for modeling the Martensitic Transformation (MT) by using Finite Element Method (FEM). PF simulations in 3D are performed by considering different cases of MT occurring in a clamped system, i.e. simulation domain with fixed boundaries, of (a) pure elastic material with dilatation (b) pure elastic material without dilatation (c) elastic perfectly plastic material with dilatation having (i) isotropic as well as (ii) anisotropic elastic properties. As input data for the simulations the thermodynamic parameters corresponding to Fe - 0.3% C alloy as well as the physical parameters corresponding to steels acquired from experimental results are considered. The results indicate that elastic strain energy, dilatation and plasticity affect MT whereas anisotropy affects the microstructure.

scholarly journals Stability of mathematical models of the main problems of the anisotropic theory of elasticity

2020 ◽  
Vol 30 (1) ◽  
pp. 112-124
Author(s):  
A.V. Yudenkov ◽  
A.M. Volodchenkov
Keyword(s):  
Boundary Value Problems ◽  
Analytic Functions ◽  
Boundary Value ◽  
Research Result ◽  
Theory Of Elasticity ◽  
Boundary Problems ◽  
Main Research ◽  
Contour Shape ◽  
Variable Function ◽  
Anisotropic Bodies

The boundary problems of the complex-variable function theory are effectively used while investigating equilibrium of homogeneous elastic mediums. The most complicated systems of the boundary value problems correspond to the case when an elastic body exhibits anisotropic properties. Anisotropy of the medium results in the drift of boundary conditions of the function that in general disrupts analyticity of the functions of interest. The paper studies systems of the boundary value problems with drift for analytic vectors corresponding to the primal elastic problems (first, second and mixed problems). Systems of analytic vectors with drift are reduced to equivalent systems of Hilbert boundary value problems for analytic functions with weak singularity integrators. The obtained general solution of the primal boundary value problems for the anisotropic theory of elasticity allows us to check the above problems for stability with respect to perturbations of boundary value conditions and contour shape. The research is relevant as there is necessity to apply approximate numerical methods to the boundary value problems with drift. The main research result comes to be a proof of stability of the systems of the vector boundary value problems with drift for analytic functions on the Hölder space corresponding to the primal problems of the elastic theory for anisotropic bodies in the case of change in the boundary value conditions and contour shape.

On the Efficiency of Analyzing 3D Anisotropic, Transversely Isotropic, and Isotropic Bodies in BEM

2010 ◽  
Vol 26 (4) ◽  
pp. 483-491
Author(s):  
Y. C. Shiah ◽  
W. X. Sun
Keyword(s):  
Closed Form ◽  
Computational Efficiency ◽  
Transverse Isotropy ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Fundamental Solutions ◽  
Engineering Practice ◽  
Closed Form Solutions ◽  
Anisotropic Bodies ◽  
Isotropic Bodies

ABSTRACTDue to a lack of closed-form solutions for three dimensional anisotropic bodies, the computational burden of evaluating the fundamental solutions in the boundary element method (BEM) has been a research focus over the years. In engineering practice, transversely isotropic material has gained popularity in the use of composites. As a degenerate case of the generally anisotropic material, transverse isotropy still needs to be treated separately to ease the computations. This paper aims to investigate the computational efficiency of the BEM implementations for 3D anisotropic, transversely isotropic, and isotropic bodies. For evaluating the fundamental solutions of 3D anisotropy, the explicit formulations reported in [1,2] are implemented. For treating transversely isotropic materials, numerous closed form solutions have been reported in the literature. For the present study, the formulations presented by Pan and Chou [3] are particularly employed. At the end, a numerical example is presented to compare the computational efficiency of the three cases and to demonstrate how the CPU time varies with the number of meshes.

scholarly journals Identifying Elastic Constants for PPS Technical Material When Designing and Printing Parts Using FDM Technology

Materials ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1123
Author(s):  
Jone Retolaza ◽  
Rubén Ansola ◽  
Jose Luis Gómez ◽  
Gorka Díez
Keyword(s):  
Elastic Constants ◽  
Fused Deposition Modeling ◽  
Moisture Absorption ◽  
Image Correlation ◽  
Fused Deposition ◽  
Environmental Aging ◽  
Transversally Isotropic ◽  
Correlation System ◽  
Technical Material ◽  
Anisotropic Elastic

This paper introduces a methodology to study the anisotropic elastic constants of technical phenylene polysulfide thermoplastic (PPS), printed using fused deposition modeling (FDM) in order to provide designers with a guide to achieve the required mechanical properties in a printed part. The properties given by the manufacturer are usually taken from injected samples and these are not the real properties for printed parts. Compared to other plastic materials, PPS offers higher mechanical and thermal resistance, lower moisture absorption, higher dimensional stability, is highly resistant to chemical attacks and environmental aging, and its fireproof performance is good. One of the main difficulties presented when calculating and designing for FDM printing is that printed parts present anisotropic behavior i.e., they do not have the same properties in different directions. Haltera-type samples were printed in the three manufacturing directions according to optimum parameters for material printing, aimed at calculating the anisotropic matrix of the material. The samples were tested in order to meet standards and values for elastic modulus, shear modulus and tensile strength were obtained, using Digital Image Correlation System to measure the deformations. An approximated transversally isotropic matrix was defined using the obtained values. The fracture was analyzed using SEM microscopy to check whether the piece was printed correctly. Finally, the obtained matrix was validated by a flexural test and a finite element simulation.

Branched Cracks in Anisotropic Elastic Solids

1989 ◽  
Vol 56 (4) ◽  
pp. 858-864 ◽  
Author(s):  
Makoto Obata ◽  
Siavouche Nemat-Nasser ◽  
Yoshiaki Goto
Keyword(s):  
Hilbert Problem ◽  
Anisotropic Body ◽  
Singular Integral Equations ◽  
Isotropic Case ◽  
Density Functions ◽  
Intensity Factors ◽  
Elastic Solids ◽  
Variable Approach ◽  
Crack Problems ◽  
Anisotropic Elastic

Branched crack problems are analyzed in two-dimensional, anisotropically elastic homogeneous solids. The method of analysis is based on the complex variable approach of Savin and Lekhnitskii. The Hilbert problem in an anisotropic body is defined, and a pair of singular integral equations are derived for dislocation density functions associated with a branched crack. For both symmetric and nonsymmetric geometries, and under symmetric and antisymmetric loads, the stress intensity factors and the energy release rate are computed numerically by extrapolation for infinitesimally small lengths of branched cracks. The results are compared with those of the isotropic case given in the literature and the effects of anisotropy are discussed.

On Characterization of Anisotropic Elastomeric Materials for Structural Analysis

2004 ◽  
Vol 77 (1) ◽  
pp. 115-130 ◽  
Author(s):  
Mark R. Gurvich
Keyword(s):  
Structural Analysis ◽  
Biaxial Tension ◽  
Composite Layer ◽  
Anisotropic Body ◽  
Test Results ◽  
Material Stiffness ◽  
Computational Implementation ◽  
Elastomeric Materials ◽  
Anisotropic Elastic

Abstract Existing efforts in constitutive modeling of elastomers are primarily focused on isotropic materials. On the other hand, anisotropic elastic models were successfully developed for traditional composites with relatively small strains, where geometrical non-linearity of deformation may be ignored. There are, however, certain materials where neither large deformation and incompressibility nor anisotropy of material stiffness may be neglected. This study proposes a general constitutive approach to model both hyperelasticity (including incompressibility) and full anisotropy of material deformation in structural analysis. According to the proposed approach, an original hyperelastic anisotropic body is modeled as a combination of two hypothetical components (hyperelastic isotropic and elastic anisotropic ones). The proposed approach shows simplicity and convenience of practical application along with high accuracy of analysis. It may be easily implemented in computational analysis of 2- and 3-D problems using commercially available FEA codes without additional programming efforts. Analytical and computational implementation of the approach is considered on representative examples of elastomeric structures and rubber-based composites. Analytical solutions are shown for examples of biaxial tension of composites and inflation of a toroidal anisotropic tube. FEA solutions are discussed on examples of an inflated anisotropic sphere and non-uniform deformation of a composite layer. Obtained results are discussed to emphasize benefits of the proposed approach. Finally, a methodology to evaluate material parameters using corresponding test results is considered according to the proposed approach.

Green’s Functions for Generalized Plane Problems of Anisotropic Bodies With a Hole or a Rigid Inclusion

1993 ◽  
Vol 60 (3) ◽  
pp. 583-588 ◽  
Author(s):  
Yung-Ming Wang ◽  
Jiann-Quo Tarn
Keyword(s):  
Conformal Mapping ◽  
Edge Dislocation ◽  
Rigid Inclusion ◽  
Green's Functions ◽  
Green’S Functions ◽  
Anisotropic Elastic Medium ◽  
Mapping Functions ◽  
Anisotropic Bodies ◽  
Anisotropic Elastic

Green’s function solutions are presented for the generalized plane problems of a point force and an edge dislocation located in the general anisotropic elastic medium with a hole or with a rigid inclusion. The Lekhnitskii’s complex potential approach is used and a general expression of the solutions is obtained. Particular attention is paid to the determination of appropriate mapping functions that map the exterior of the hole or the inclusion onto the exterior of a unit circle. The conditions under which the conformal mapping is possible are explored. Examples using the Green’s functions for the solution of notch problem are given.

Anisotropic Elastic Field of 3D Prismatic Dislocation Loops in Bounded and Voided Single Crystal Films

2016 ◽  
Vol 725 ◽  
pp. 195-201
Author(s):  
Jia Pei Guo ◽  
Ying Ying Cai ◽  
Yi Ping Chen
Keyword(s):  
Thin Films ◽  
Elastic Field ◽  
Elastic Cylinder ◽  
Physical Parameters ◽  
Dislocation Loops ◽  
Principle Of Superposition ◽  
Elastic Fields ◽  
Crystal Films ◽  
Finite Medium ◽  
Anisotropic Elastic

Dislocations in a finite medium bring about image stresses. These image stresses play important roles in the dislocation behavior in finite sized systems such as thin films. Since the ratio of surface to volume is higher for thin films than for bulk materials, dislocation behaviors in thin films are greatly different from those in a corresponding infinite medium, which make it necessary to take into account the effects of free surfaces on the evolution of dislocations in thin films. In the investigations[4, 5], image stresses in an elastic cylinder and thin films are calculated by employing a Fourier transform (FFT) approach and isotropically elastic fields due to dislocations are adopted in their formulation. However, most crystals are anisotropic, and the anisotropic ratio changes with environment physical parameters, such as the temperature, moisture, electron field, magnetic field. A theorem based on anisotropic Stroh’s formula for calculating the image stress of infinite straight dislocations in anisotropic bicrystals has been developed by Barnett and Lothe[6]. Wu et al.[3] recently also make use of the FFT technique to investigate the general dislocation image stresses of cubic thin films, thus extending the formalism by Weinberger et al.[4,5] from isotropic to anisotropic thin films. It is clear that for the assumed in-plane elastic fields to be periodically defined within an unbounded region is an essential and indispensable prerequisite for the above FFT-based approach to be effectively implemented, thus ruling out the possibility of its being employed to analyse image stresses in bounded and/or voided thin cubic films. Our motivation here is then to make an further extension by first calculating the anisotropic elastic fields of dislocation loops in an unbounded thin film with cavities and then invoking FEM and the principle of superposition to seek the image stress solution.

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