scholarly journals Identification of the parameters of the quadratic model of the elastic anisotropic material

2021 ◽  
pp. 3-11
Author(s):  
Ши Тоан Нгуен ◽  
Дмитрий Викторович Христич
Keyword(s):  
Elastic Constants ◽  
Anisotropic Material ◽  
Orthotropic Material ◽  
Composite Plates ◽  
Anisotropic Materials ◽  
Second Order ◽  
Quadratic Model ◽  
Linearly Independent ◽  
Proposed Model ◽  
The Difference

Рассмотрена модель упругости второго порядка для ортотропного материала. Проведенный анализ показывает, что квадратичная часть предложенной модели содержит тринадцать упругих постоянных, из которых девять являются линейно независимыми. Параметры модели определены по данным экспериментов с композитными пластинами. Модель позволяет описывать наблюдаемые в экспериментах нелинейные зависимости между напряжениями и деформациями в процессах растяжения, сжатия и сдвига, а также разносопротивляемость анизотропных материалов. A second-order elasticity model for an orthotropic material is considered. The analysis shows that the quadratic part of the proposed model contains thirteen elastic constants, nine of which are linearly independent. The parameters of the model are determined from the data of experiments with composite plates. The model allows one to describe experimentally observed nonlinear dependences of stresses and strains in the processes of tension, compression, and shear, as well as the difference in resistance of anisotropic materials.

The Numerical Study on Errors of Stress in Anisotropic Linear Elastic Material when Simplified as Orthogonal one

2013 ◽  
Vol 275-277 ◽  
pp. 3-6
Author(s):  
Lin Li ◽  
Jin Yang ◽  
Xiu Qing Qian ◽  
Hai Xia Zhang ◽  
Zhi Cheng Liu
Keyword(s):  
Orthotropic Material ◽  
Numerical Study ◽  
Element Model ◽  
Anisotropic Materials ◽  
Orthotropic Materials ◽  
Maximum Relative Error ◽  
Linear Elastic ◽  
Extreme Stress ◽  
The Difference ◽  
Distribution Of Stress

Keywords: strain, stress, material constants, constitutive equation, anisotropy. Abstract. If the material is anisotropic, there are differences in stress distribution under the same boundary conditions when it was simplified as an orthotropic material. We established a simple finite element model for rectangular perforated planar material, in which one side was fixed, the opposite side was loaded with uniform force, and the other sides were set free. Based on this model we studied the difference of distribution of stress between anisotropic material and its simplified form, orthotropic material. The results showed differences in some cases quite large, the maximum relative error of extreme stress can reach 341%. In conclusions, this study does not support that the complex anisotropic materials are simplified to orthotropic materials. If researchers only concern the location of extreme stress, this study does not deny that the complex anisotropic materials can be simplified to orthotropic one.

Anisotropic Elasticity

1996 ◽  
Author(s):  
T. T. C. Ting
Keyword(s):  
Composite Materials ◽  
Elastic Constants ◽  
Piezoelectric Materials ◽  
Anisotropic Materials ◽  
Anisotropic Elasticity ◽  
Stress Singularities ◽  
Comprehensive Survey ◽  
The Subject ◽  
Key Topics ◽  
First Time

Anisotropic Elasticity offers for the first time a comprehensive survey of the analysis of anisotropic materials that can have up to twenty-one elastic constants. Focusing on the mathematically elegant and technically powerful Stroh formalism as a means to understanding the subject, the author tackles a broad range of key topics, including antiplane deformations, Green's functions, stress singularities in composite materials, elliptic inclusions, cracks, thermo-elasticity, and piezoelectric materials, among many others. Well written, theoretically rigorous, and practically oriented, the book will be welcomed by students and researchers alike.

Physical Ultrasonics of Composites

2011 ◽  
Author(s):  
Dale Chimenti ◽  
Stanislav Rokhlin ◽  
Peter Nagy
Keyword(s):  
Composite Laminates ◽  
Stiffness Matrix ◽  
Composite Plates ◽  
Anisotropic Media ◽  
Anisotropic Materials ◽  
Ultrasonic Waves ◽  
Laminated Plates ◽  
Structure Characteristic ◽  
Major Advance

Physical Ultrasonics of Composites is a rigorous introduction to the characterization of composite materials by means of ultrasonic waves. Composites are treated here not simply as uniform media, but as inhomogeneous layered anisotropic media with internal structure characteristic of composite laminates. The objective here is to concentrate on exposing the singular behavior of ultrasonic waves as they interact with layered, anisotropic materials, materials which incorporate those structural elements typical of composite laminates. This book provides a synergistic description of both modeling and experimental methods in addressing wave propagation phenomena and composite property measurements. After a brief review of basic composite mechanics, a thorough treatment of ultrasonics in anisotropic media is presented, along with composite characterization methods. The interaction of ultrasonic waves at interfaces of anisotropic materials is discussed, as are guided waves in composite plates and rods. Waves in layered media are developed from the standpoint of the "Stiffness Matrix", a major advance over the conventional, potentially unstable Transfer Matrix approach. Laminated plates are treated both with the stiffness matrix and using Floquet analysis. The important influence on the received electronic signals in ultrasonic materials characterization from transducer geometry and placement are carefully exposed in a dedicated chapter. Ultrasonic wave interactions are especially susceptible to such influences because ultrasonic transducers are seldom more than a dozen or so wavelengths in diameter. The book ends with a chapter devoted to the emerging field of air-coupled ultrasonics. This new technology has come of age with the development of purpose-built transducers and electronics and is finding ever wider applications, particularly in the characterization of composite laminates.

scholarly journals Generalization of intrinsic ductile-to-brittle criteria by Pugh and Pettifor for materials with a cubic crystal structure

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
O. N. Senkov ◽  
D. B. Miracle
Keyword(s):  
Crystal Structure ◽  
Shear Modulus ◽  
Bulk Modulus ◽  
Single Crystal ◽  
Elastic Constants ◽  
Mechanical Analysis ◽  
Quantum Mechanical ◽  
Modulus Ratio ◽  
Cubic Crystal ◽  
The Difference

AbstractTwo classical criteria, by Pugh and Pettifor, have been widely used by metallurgists to predict whether a material will be brittle or ductile. A phenomenological correlation by Pugh between metal brittleness and its shear modulus to bulk modulus ratio was established more than 60 years ago. Nearly four decades later Pettifor conducted a quantum mechanical analysis of bond hybridization in a series of intermetallics and derived a separate ductility criterion based on the difference between two single-crystal elastic constants, C12–C44. In this paper, we discover the link between these two criteria and show that they are identical for materials with cubic crystal structures.

scholarly journals Antiplane–inplane shear mode delamination between two second-order shear deformable composite plates

2016 ◽  
Vol 22 (3) ◽  
pp. 259-282 ◽  
Author(s):  
András Szekrényes
Keyword(s):  
Plate Theory ◽  
Plate Thickness ◽  
State Space Model ◽  
Boundary Surface ◽  
Plate Boundary ◽  
Composite Plates ◽  
Second Order ◽  
Shear Mode ◽  
Mode Iii ◽  
Double Plate System

The second-order laminated plate theory is utilized in this work to analyze orthotropic composite plates with asymmetric delamination. First, a displacement field satisfying the system of exact kinematic conditions is presented by developing a double-plate system in the uncracked plate portion. The basic equations of linear elasticity and Hamilton’s principle are utilized to derive the system of equilibrium and governing equations. As an example, a delaminated simply supported plate is analyzed using Lévy plate formulation and the state-space model by varying the position of the delamination along the plate thickness. The displacements, strains, stresses and the J-integral are calculated by the plate theory solution and compared with those by linear finite-element calculations. The comparison of the numerical and analytical results shows that the second-order plate theory captures very well the mechanical fields. However, if the delamination is separated by only a relatively thin layer from the plate boundary surface, then the second-order plate theory approximates badly the stress resultants and so the mode-II and mode-III J-integrals and thus leads to erroneous results.

scholarly journals High temperature and pressure effects on the elastic properties of B2 intermetallics AgRE

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Lili Liu ◽  
Xiaozhi Wu ◽  
Weiguo Li ◽  
Rui Wang ◽  
Qing Liu
Keyword(s):  
High Temperature ◽  
Intermetallic Compounds ◽  
Elastic Properties ◽  
Elastic Constants ◽  
Second Order ◽  
Pressure Effects ◽  
High Temperature And Pressure ◽  
Normal Behavior ◽  
Temperature And Pressure ◽  
Temperature And Pressure Effects

AbstractThe high temperature and pressure effects on the elastic properties of the AgRE (RE=Sc, Tm, Er, Dy, Tb) intermetallic compounds with B2 structure have been performed from first principle calculations. For the temperature range 0-1000 K, the second order elastic constants for all the AgRE intermetallic compounds follow a normal behavior: they decrease with increasing temperature. The pressure dependence of the second order elastic constants has been investigated on the basis of the third order elastic constants. Temperature and pressure dependent elastic anisotropic parameters A have been calculated based on the temperature and pressure dependent elastic constants.

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