Constitutive laws in structural mechanics - Identification and application

The use of calculation tools has become quite common in the field of civil engineering when it comes to dimensioning a new structure, whatever its intended function. This can be explained by the fact that many different constraints have been imposed on the engineer.

Examples include :

• ecological constraints aimed at making new structures more energy-efficient;

• or robustness in the event of accidental loading, such as earthquakes.

These various constraints have led to changes in conventional engineering practices, such as the use of new, more insulating materials or the introduction of a redundant structural system. The complexity induced by these constraints has contributed to an increase in the use of conventional structural calculation tools in the design office environment.

However, when it comes to design or dimensioning, these tools are based on the assumption that the behavior of the various materials making up the structure is linear. In the case of existing structures, on the other hand, the problem is generally to assess their level of compliance with the requirements imposed by the public authorities.

In the event of non-compliance, and depending on the function of the structure, it must be brought up to standard. This is particularly true when it comes to the structural resistance of a structure to earthquakes. Safety margins must therefore be assessed in relation to one or more limit states: this is known as "structural assessment".

To achieve this, it is necessary to study the behavior of structures in an operating domain where the assumption of material linearity is no longer verified. In this case, the engineer must use so-called "non-linear" calculation methods. This brings with it a number of problems to which it is essential to be aware.

First of all, the technical and scientific literature can easily attest to the vast amount of work carried out with the aim of representing the fracture behavior of civil engineering materials as faithfully as possible. Today, the laws describing the behavior of steel are recognized as relatively reliable and robust. However, such maturity has not yet been reached when it comes to describing the behavior of concrete under complex loading.

One of the first questions that engineers need to answer is how to select reliable behavior laws whose scope of application they have mastered. Then, because every material is different, it is necessary to particularize the behavior laws selected. This step generally involves determining a number of parameters: this is known as "identification".

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