sabato 20 gennaio 2024

Why does the stress strain curve in Abaqus of my concrete model look like this?A question posed (2024, Jan 11, ) by Hanif Hanif on ResearchGate

 







It is a stress-strain diagram. Let’s divide the diagram into 3 different zones: 1, 2, 3, each characterized by its own typical trend.

ZONE 1: Linear law between stress and strain (Hook’s Law). The slope of such a line is a measure of the elastic module of the material. If during this phase you stop applying the force, the preserved elasticity of the material brings it back to the original dimension from which you started (i.e. the origin of the axes). Elastic modulus, also known as Young's modulus, is a fundamental property of materials that measures their stiffness or resistance to elastic deformation under stress. This property is essential in engineering and materials science, as it determines a material's ability to support loads and maintain its shape. The area of each zone (kg x m) represent the necessary energy to deform the sample of (unknown) material under test.

ZONE 2: The law between stress and strain is no more linear.  Even stopping to apply the force, the original elasticity of the material is damaged and lost and it is impossible to bring back the material to its original dimension. Noticeable is the negative slope in this zone. The deformation continues with decreasing force up to a minimum and the slope changes sign again, due (presumably) to work hardening of the material.

ZONE 3: The minimum point reached can be considered the beginning of actual failure, characterized by large deformations with smaller forces, which again follow a law that is substantially linear here, but is not necessarily the case in all materials.

Observers rightly pointed out that there may be several reasons why the stress-strain curve of a concrete model in Abaqus may show a certain behavior. So that various elements to find an explanation should include: Material properties; Concrete model; Failure criteria; Loading conditions. 

In search of an explanation one might also think of an overlap in the proposed graph between load in action and reaction. But, as far as I can see (e.g. refer to the image below - Image source: https://caeassistant.com/blog/fiding-reaction-force-on-a-body / ) Abaqus distinguishes very well in the graphical results between action and reaction by presenting two separate graphs with different trends, especially in the case of dynamic loads.

In this case, however, the question was asked on a single graph without specifying whether it concerns active load (e.g. Zone 1) and reactive load (e.g. Zone 2 plus Zone 3) combined together, also excluding a part of reactive load until the start of the Zone 2 (All this trying to imagine a possible explanation). But it is not the case. So I am inclined to assume that the positive slope of Zone 3 is the result of work hardening, just as the specific literature mentions about it (search for: work hardening effect in unreinforced concrete). Anyhow, in case anyone has a different, specific explanation, I'd appreciate hearing about it.

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