In the deformed body in three-dimensional stress state, does the direction of normal stress necessarily produce normal strain? According to the total quantity theory, there should be no necessity!

This theory was very correct in the past, and we all think so,
It wasn't until an American scientist came up with a material that was not stretched but shortened
Therefore, it is impossible to say whether the direction of normal stress necessarily produces normal strain

In mechanics of materials, the relationship between true stress and engineering stress is true stress = engineering stress * (1 + engineering strain),

Ao = initial cross section area;
Lo = starting length;
1 + engineering strain = 1 + (l-lo) / Lo = L / Lo; (1)
The volume is constant, i.e. AO * Lo = a * l (2)
L/Lo=Ao/A (3)
From (1), (3)
1 + engineering strain = AO / A
P / AO * (1 + engineering strain) = P / A
Engineering stress * (1 + engineering strain) = true stress

In mechanics of materials, how to understand "the continuity of matter determines that the stress and strain in matter are continuous functions"?
The total feeling stress can change suddenly. This sentence is a thinking question in the book of material mechanics of Tongji University
But when drawing stress diagram, such as axial diagram, there is a sudden change. If the stress is continuous, isn't it contradictory to the stress diagram?
Third floor: I understand what you said about the stress diagram. Please tell me the first question again, why "deformation remains continuous = > strain is continuous"
Imagine: there are many discrete points that produce different degrees of strain, one of which is not continuous with the surrounding strain, and the other points are continuous with the surrounding strain. In this case, all points produce strain, but the size is different. Why can the point of strain mutation judge the material discontinuity of the point?

My understanding is this
Continuity of material = > material remains continuous after deformation = > both elastic and plastic strains are continuous = > two constants of elastic modulus and Poisson's ratio = > stress must also be continuous
Note that this sentence is very strict, and the restriction of "in matter" ensures the correctness of this sentence. The point where the external force acts can produce stress mutation, but the external force can only act on the surface of the object, and the mutation occurs on the surface
This is my understanding 4 years ago. It hasn't changed. I don't know right or wrong. Let's discuss it
In fact, the bar can not be a line segment, and the loading can not be carried out inside the bar. In fact, the position where the stress mutation occurs is only on the surface, and the internal part is continuous. The mutation of the average stress of the section is caused by the surface mutation
Explain the problem you added. Strain discontinuity (or sudden change of strain) means that the displacement of all points in the material is discontinuous. That is to say, the complete object has been destroyed here. If it is a point, it is this point that is free. Take the broken object as another new object again, and all the stress and strain in the new object are still continuous

The relationship among external force, internal force and stress in mechanics of materials

The problem is very simple: external force is the force exerted on an object by an external object, specifically including surface force (force acting on the surface) and physical force (some also call it mass force, such as gravity, magnetic force, etc.)
Internal force, needless to say, is the force relative to external force, the force generated by the interaction between the internal body
Stress, which is different from internal force, is the internal force acting on the unit area. The definition formula is: the internal force when s tends to 0

Explanation of mechanical terms: straight beam, internal force, stress

In mechanics, according to its stress, it can be divided into simply supported beam and statically indeterminate beam: simply supported beam means that both ends of the beam are built on two supports, one end is hinged and the other end is fixed. When a continuous beam has three or more supports, it is called statically indeterminate structural beam
Internal force refers to the internal material force, relative to the external force. Stress refers to the internal force per unit area

Seeking strain effect

The phenomenon that the resistance value of metal conductor changes with the mechanical deformation (tension or compression) caused by the force is called resistance strain effect of metal

Difference between compressive stress and tensile stress

Compressive stress if a cylinder is compressed at both ends, the stress along its axis is compressive stress. Compressive stress refers to the stress that makes the object tend to compress. It is not only the compressive stress caused by the force on the object, but also any compression deformation will occur, including the expansion of the object

What is the condition for applying the formula of tension compression normal stress σ = f / a? Is the stress less than the proportional limit, or is the stress less than the elastic limit?

Is less than the scale limit,
The premise of the study of tension compression normal stress is that the tension compression bar is in steady state. For slender compression bar, in addition to considering its strength, its stability must be checked by Euler formula. The premise of Euler formula must conform to Hooke's law, that is, the stress is less than the proportional limit

The allowable tensile stress and compressive stress of aluminum, and the allowable tensile stress and compressive stress of aluminum alloy

The tensile strength of pure aluminum is 590kg, and the stress of alloy 300 is close to its tensile strength

The maximum normal stress on the section plane of plane bending beam occurs at

Two section maximum

In the deformed body in three-dimensional stress state, does the direction of normal stress necessarily produce normal strain? According to the total quantity theory, there should be no necessity!