what is tenser quantity as per graduation level?
Answers
Answe Tensor is a mathematical object that can be used to describe physical properties Like Scalar and Vector. Which are often used in physics and engineering applications.
Magnitude define the Scalar Completely. Example Mass.
Direction is required with Magnitude to define a Vector
Plane on which its acting is required with Magnitude and direction to Define a Tensor Completely. Example: Stress, Strain, Electrical
Explanation:
Answer:
Tensor is a mathematical object that can be used to describe physical properties Like Scalar and Vector. Which are often used in physics and engineering applications.
Magnitude define the Scalar Completely. Example Mass.
Direction is required with Magnitude to define a Vector
Plane on which its acting is required with Magnitude and direction to Define a Tensor Completely. Example: Stress, Strain, Electrical
Scalar - (Zero Order tensor Quantity)
Vector - (1st Order Tensor)
Stress - (2nd Order Tensor)
Piezoelectricity - (3rd Order tensor Quantity)
Stiffness - (4th Order tensor Quantity)
So, you need to recall scalar and Vector which will helps you to Understand Tensor.
Just for Recall:
Scalar - Physical quantity that only has magnitude and no other characteristics, often accompanied by units of measurement.
i.e. Magnitude define the Scalar Completely. Example Mass.
Scalar which is Zero Order Tensor.
Vector- is also a Physical quantity. To define any Vector Apart from magnitude, one more Additional data is required.
ie. Direction is required with Magnitude to define a Vector Completely. Example: Force, Velocity
Vector is a first Order Tensor.
Tensor - Tensor is a mathematical object that can be used to describe physical properties.
To define any Tensor, Apart from magnitude and direction one more Additional data is required.
i.e. Plane on which its acting is required with Magnitude and direction to Define a Tensor Completely. Example: Stress, Strain, Electrical conductivity in aeolotropic materials.
So, Magnitude, Direction and Plane of action is required to define a Tensor quantity Completely.
σ11, σ22, σ33 - Which are normal stresses, rest of the stresses are Shear stresses
First suffix indicates the Direction of stress, Second Suffix indicates direction of normal to the area on which stress is acting.
Tensors of higher Order are required to fully describe properties that relate two second Order tensors (e.g. Stiffness (4th Order): stress and strain) or a second Order tensor and a vector (e.g. Piezoelectricity (3rd Order): stress and polarisation).
Orders in Tensors:
The order (or rank) of a tensor is defined by the number of directions required to describe Tensor.
Properties that require one direction (first order) can be described completely is First Order Tensors.
Properties that require Two direction (second order) can be described completely is Second Order Tensors.
The need for second order tensors comes when we need to consider more than one direction to describe one of these physical properties.
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