What Is a Quad Strain?

Shear strain means that when an object is deformed by force, the degree of deformation at different points in the body is generally not the same. The mechanical quantity used to describe the degree of deformation at a point is the strain at that point. Simply put, it is the amount of change in the angle between two mutually perpendicular surfaces in radians after deformation.

Shear modulus, material constant, is the ratio of shear stress to strain. Also known as trimming modulus or rigid modulus, one of the mechanical properties of materials. It is the material under the action of shear stress that

With the continuous development of science and technology and the increasingly wide application fields, mechanics has developed many branch disciplines, such as solid mechanics, elastic mechanics, plastic mechanics, viscous mechanics, material mechanics,

Review of Shear Strain Concept

Although the concept of shear strain has been elaborated in different disciplines of applied mechanics, there are obvious differences in terms of its wording. There are two main types:

The first describes the concept of shear strain as: the characteristic of shear deformation is that small rectangles become skewed parallelograms, which is equivalent to the original rectangular ABCD becoming skewed parallelograms. The skew angle is called shear strain. This is one of the ways in which the concept of shear strain is explained in material mechanics.

The second type expresses the concept of shear strain as: the value of the change in the angle between two tiny line segments on an object after deformation is called the shear strain there. Similar expressions are generally used in the applied mechanics literature. The specific expressions are different, most of them are written narratives, and a few are expressed by mathematical formulas. In addition, it can be seen that the concept of shear strain that is similar to this expression but slightly different in content is that half the amount of angle change between two perpendicular lines is called angular strain.

Uncertainty of Shear Strain Concept

Seen literally, the concepts of shear strain expressed by the above two methods seem to be completely the same, but careful analysis is different.

In the first description, the "skewed angle" of a rectangle is called a shear strain. There are literally two ways to understand it. One is to understand "skewed" from a right angle in a rectangle to a non-right angle in a parallelogram ( Obtuse angle or acute angle), then, "skewed angle" is also the change amount of right angle . In this way, the meaning of the first description and the second description are consistent, but the former is a special case of the latter (right angle It only skews in one direction instead of two directions); The second is to understand "skew" as the change of the angle of the line segment before and after deformation, that is, the deflection of the line segment after deformation, and the "skew angle" is the deflection angle . From the relationship between shear strain and shear stress, it can be clearly seen that this description reflects the concept of shear strain that is skewed in one direction only under the "unidirectional shear stress state" in which shear stress exists in one direction.

The shear strain in the second description refers to the amount of change in the right angle. As we all know, the change in the angle of any corner is caused by the deflection of the two sides of the corner alone or together. There are infinitely many groups of and values that satisfy the condition that is a fixed value, that is, the values of and are uncertain. In terms of geometric relationship, as long as the shape of the quadrilateral is kept unchanged, any rotation around the fixed point can satisfy the connotation of the concept of shear strain expressed in the second description. From this point of view, this description only specifies the deformed shape of the object, and does not specify the direction in which the deformation occurs, that is, the direction of the shear strain is uncertain. However, as mentioned earlier, the reciprocity theorem of shear stress does not actually hold. From the above analysis, it can be seen that the shear strain concept expressed in both ways has obvious uncertainty or multiple solutions. ^[3]

Modification of the existing shear strain concept

From the previous discussion and analysis, it can be seen that the connotation of the existing shear strain concept is uncertain, so it must be modified. As we all know, shear strain is the result of shear stress. The concept of shear strain should also reflect the relationship between shear strain and shear stress. In this way, the concept of shear strain can be modified as follows: the relative displacement (distortion distance) of the two ends of a tiny line segment on an object in the vertical direction of the line segment (also the direction of the shear stress) is the same as the original length of the line segment. The ratio is called the shear strain. When the shear deformation is not large, the deflection angle of the line segment before and after the deformation can also be used to represent the shear strain.

The similarities and differences between the revised concept of the new shear strain and the original concept of the shear strain are: the shear strain concept in the original first description is equivalent to the unidirectional shear stress state of the new shear strain concept; the shear in the second description The strain concept is equivalent to the plane (two-way) stress state of the new shear strain concept. That is, the shear strain in the original second description is equal to the sum of the shear strains in two directions in the new concept. When two mutually perpendicular shear stresses are equal, the newly defined shear strain value is only half of the original definition. The original concept of shear strain specifies a change in angle at right angles, and the modified concept of shear strain specifies a change in angle of a line segment. The two values are sometimes equal in value. ^[1]