This set of Composite Materials Multiple Choice Questions & Answers (MCQs) focuses on “Stress-Strain Relations for a Anisotropic Materials – String”.

1. What does the term “Anisotropic material” refers to?

a) A material that possess same properties in different directions

b) A material that possess different properties along different directions

c) A material that possess many axes of symmetry

d) A material that possess different properties in same direction

View Answer

Explanation: For a general anisotropic body, there won’t be any planes of symmetry. So, it has different properties along different directions when measured at a particular point. These material properties are directionally dependent. They always depend upon the crystal orientations in a body.

2. Which of the following is true regarding the anisotropic materials?

a) σ_{ij} & ε_{kl} are symmetric

b) σ_{ij} & ε_{kl} are not symmetric

c) σ_{ij} & ε_{kl} cannot be same at all

d) σ_{ij} & ε_{kl} do not dependent upon direction

View Answer

Explanation: In an anisotropic material, generally σ

_{ij}& ε

_{kl}are symmetric. This is the usual case when the body forces are absent. By the moment equilibrium concept, we can say that the shear stresses and the shear strains are same.

3. What is the best definition of Engineering Shear Strain (γ_{ij})?

a) It is the half of the angle of shearing under pure shear stress

b) It is half of the angle of shearing under pure shear strain

c) It is the total angle of shearing under a state of simple shear

d) They don’t have an accompanying rotation

View Answer

Explanation: The Engineering Shear Strain is defined as the total angle of the shearing under the state of simple shear. It implies that it is always accompanied with a rotation of an element. It differs from the tensor shear strain in the way that tensor shear strain doesn’t accompany any form of rotation.

4. The relation between Engineering Shear Strain (γ_{12}) and the Tensor Shear Strain (ε_{12}) is given by __________

a) 4γ_{12} = ε_{12}

b) γ_{12} = 4ε_{12}

c) 2γ_{12} = ε_{12}

d) γ_{12} = 2ε_{12}

View Answer

Explanation: The Engineering Shear Strain is given by the total angle of the shearing under the state of simple shear. Whereas, the Tensor Shear Strain is given by the half of the angle of shearing under the action of the simple shear. Hence, γ

_{12}= 2ε

_{12}.

5.The stiffness matrix (C_{ij}) of an anisotropic material will have 36 elastic constants.

a) True

b) False

View Answer

Explanation: Yes, According to the moment equilibrium concept, ij = ji => Τ

_{xy}= Τ

_{yx}. Also, as kl = lk, γ

_{xy}= γ

_{yx}Since σ

_{ij}& ε

_{kl}are symmetric for a material, the stiffness matrix is given by C

_{ijkl}= C

_{jilk}. Hence, 9*9 matrix converges to 6*6 stiffness matrix with 36 elastic constants.

6. The alternate name for characterizing anisotropic materials are ___________

a) monoclinic materials

b) symmetric materials

c) triclinic materials

d) orthotropic materials

View Answer

Explanation: For an anisotropic material, there won’t be any plane of symmetry for the material properties. Similarly, a triclinic material is a material in which the three axes of the material are all oblique to each other as in anisotropic materials. Hence, they are also called as triclinic materials.

7. Which of the following is not true about the monoclinic materials?

a) Monoclinic materials possess one plane of material property symmetry

b) Monoclinic material has 13 independent elastic constants

c) There will be 2 axes of symmetry

d) The plane of symmetry is about XY plane (Z=0)

View Answer

Explanation: If there are 2 orthotropic planes of material property symmetry for a material, symmetry will exist relative to the third mutually orthogonal plane. Then, they are said to be Orthotropic materials.

8. Which of the following is a wrong representation of compliance in terms of engineering constants?

a) S_{11} = 1/E_{1}

b) S_{22} = 1/E_{2}

c) S_{12} = -(γ_{21}/E_{2})

d) S_{66} = 1/G_{12}

View Answer

Explanation: The compliance term, S

_{12}in terms of Engineering constant is given by S

_{12}= -(γ21/E

_{2}) = -(γ

_{12}/E

_{1}). S

_{12}cannot be given in terms of E

_{2}.when Shear Strain is expressed as γ

_{21}.

9. What is the major objective in studying the stress – strain relations?

a) In order to conclude what deformation occurs because of a specific applied stress

b) In order to see the effect of only the anisotropic behavior of the body

c) In order to detect the properties of the material along only one direction

d) In order to know the behavior of materials when no load is applied

View Answer

Explanation: Stress–Strain relations gives us the idea about how the material is behaving towards the load that we are applying. It explains graphically when does the material goes into the plastic region from elastic zone. It elucidates when does the materials fail under the action of applied stresses and gives the corresponding elongations.

10. Which of the following is not true with respect to the orthotropic lamina?

a) It follows plane stress condition

b) Stress components in all out of plane conditions are zero

c) It has the reduced stiffness matrix from 3D to 2D

d) It doesn’t possess material symmetry at all

View Answer

Explanation: Orthotropic materials will have orthogonal symmetry to both XY and XZ plane. Hence, these materials where 3 mutually orthogonal symmetry exists are called as orthotropic elements. They will have 9 independent elastic constants.

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