Civil Engineering (CE) Exam > Civil Engineering (CE) Questions > The number of independent elastic constants r...
Start Learning for Free
The number of independent elastic constants required to express the stress strain relationship for a linearly elastic isotropic material is
- a)one
- b)two
- c)three
- d)four
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The number of independent elastic constants required to express the st...
If you consider the most generalized Hooke's law applied to an anisotropic elastic solid:
σij=Cijkl∗εkl
where Cijkl is the elastic stiffness tensor, which is a fourth rank tensor.
Upon expanding the above equation we would get nine equations, each with nine terms. Hence there are 81 constants in all.
But the stress and strain tensors are symmetric; which leads to:
Cijkl=Cjikl and Cijkl=Cijlk
Hence 36 terms of the elastic stiffness tensor are independent and distinct. But further reduction in the number of independent constants is possible.
Generally, Cij=Cji
Which means that of the 36 constants, there are 6 constants where i=j. This leaves 30 constants, but only half of them are independent. Therefore, for the general anisotropic linear elastic solid there are (30/2) + 6 = 21 independent elastic constants.
For an isotropic elastic material there are only 2 independent elastic constants.
Most Upvoted Answer
The number of independent elastic constants required to express the st...
Linearly Elastic Isotropic Material:
A material is said to be linearly elastic isotropic if it satisfies the following two conditions:
Stress-Strain Relationship:
The stress-strain relationship for a linearly elastic isotropic material can be expressed as follows:
σij = Cijkl εkl
where σij is the stress tensor, εkl is the strain tensor, and Cijkl is the stiffness tensor.
Number of Independent Elastic Constants:
The stiffness tensor Cijkl has 81 components, but due to symmetry, only 21 of these components are independent. Furthermore, due to the isotropic nature of the material, only 2 of these independent components are required to describe the material's elastic behavior.
Therefore, the number of independent elastic constants required to express the stress-strain relationship for a linearly elastic isotropic material is two. These two constants are typically denoted by E (Young's modulus) and ν (Poisson's ratio).
Conclusion:
In conclusion, for a linearly elastic isotropic material, only two independent elastic constants are needed to express the stress-strain relationship. This is due to the symmetry of the stiffness tensor and the isotropic nature of the material.
A material is said to be linearly elastic isotropic if it satisfies the following two conditions:
- It obeys Hooke's law, which states that the strain is directly proportional to the stress.
- It has the same elastic properties in all directions, which means it is isotropic.
Stress-Strain Relationship:
The stress-strain relationship for a linearly elastic isotropic material can be expressed as follows:
σij = Cijkl εkl
where σij is the stress tensor, εkl is the strain tensor, and Cijkl is the stiffness tensor.
Number of Independent Elastic Constants:
The stiffness tensor Cijkl has 81 components, but due to symmetry, only 21 of these components are independent. Furthermore, due to the isotropic nature of the material, only 2 of these independent components are required to describe the material's elastic behavior.
Therefore, the number of independent elastic constants required to express the stress-strain relationship for a linearly elastic isotropic material is two. These two constants are typically denoted by E (Young's modulus) and ν (Poisson's ratio).
Conclusion:
In conclusion, for a linearly elastic isotropic material, only two independent elastic constants are needed to express the stress-strain relationship. This is due to the symmetry of the stiffness tensor and the isotropic nature of the material.
|
Explore Courses for Civil Engineering (CE) exam
|
|
Similar Civil Engineering (CE) Doubts
Top Courses for Civil Engineering (CE)View all
The number of independent elastic constants required to express the stress strain relationship for a linearly elastic isotropic material isa)oneb)twoc)threed)fourCorrect answer is option 'B'. Can you explain this answer?
Question Description
The number of independent elastic constants required to express the stress strain relationship for a linearly elastic isotropic material isa)oneb)twoc)threed)fourCorrect answer is option 'B'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The number of independent elastic constants required to express the stress strain relationship for a linearly elastic isotropic material isa)oneb)twoc)threed)fourCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of independent elastic constants required to express the stress strain relationship for a linearly elastic isotropic material isa)oneb)twoc)threed)fourCorrect answer is option 'B'. Can you explain this answer?.
The number of independent elastic constants required to express the stress strain relationship for a linearly elastic isotropic material isa)oneb)twoc)threed)fourCorrect answer is option 'B'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The number of independent elastic constants required to express the stress strain relationship for a linearly elastic isotropic material isa)oneb)twoc)threed)fourCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of independent elastic constants required to express the stress strain relationship for a linearly elastic isotropic material isa)oneb)twoc)threed)fourCorrect answer is option 'B'. Can you explain this answer?.
Solutions for The number of independent elastic constants required to express the stress strain relationship for a linearly elastic isotropic material isa)oneb)twoc)threed)fourCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
Download more important topics, notes, lectures and mock test series for Civil Engineering (CE) Exam by signing up for free.
Here you can find the meaning of The number of independent elastic constants required to express the stress strain relationship for a linearly elastic isotropic material isa)oneb)twoc)threed)fourCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The number of independent elastic constants required to express the stress strain relationship for a linearly elastic isotropic material isa)oneb)twoc)threed)fourCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for The number of independent elastic constants required to express the stress strain relationship for a linearly elastic isotropic material isa)oneb)twoc)threed)fourCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of The number of independent elastic constants required to express the stress strain relationship for a linearly elastic isotropic material isa)oneb)twoc)threed)fourCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The number of independent elastic constants required to express the stress strain relationship for a linearly elastic isotropic material isa)oneb)twoc)threed)fourCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
|
|
Explore Courses for Civil Engineering (CE) exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup