Solution approaches for large strain mechanics

In summary, the conversation discusses different solution approaches for the governing equation of momentum in solid mechanics, specifically the total and updated Lagrangian methods. The updated Lagrangian approach allows for the use of small strain approximation, while the rate form allows for the use of objective rate but requires a hyperelastic relation for materials undergoing large elastic strains.
  • #1
bcl
16
1
I’m studying large strain and deformation solid mechanics and I have a (seemingly) basic question on solution approaches. Is my interpretation below correct?

The governing equation of momentum for solid mechanics can be solved using a total or updated Lagrangian approach. The updated Lagrangian form is sometimes expressed in rate form. The rate form (of the updated Lagrangian approach) permits use of the small strain approximation since only the increment of displacement is considered from the current time t to time t+dt. However, when using a rate form, the stress rate appears in the equation of virtual work, and therefore an objective rate must be used.
 
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  • #2
No, you can only use small strain "linear elasticity" if the material is undergoing small elastic strains. If it's a polymer or something that is undergoing large elastic strains, then you have to use a hyperelastic relation. In rate form, this would be called "hypo"-elasticity.
 

1. What is large strain mechanics?

Large strain mechanics is a branch of mechanics that studies the behavior of materials under large deformations. It is used to analyze the behavior of materials that experience significant changes in shape and volume, such as rubber, plastic, and biological tissues.

2. What are the different solution approaches for large strain mechanics?

There are two main solution approaches for large strain mechanics: the total Lagrangian approach and the updated Lagrangian approach. The total Lagrangian approach is based on the initial configuration of the material, while the updated Lagrangian approach is based on the current configuration.

3. What are the advantages of the total Lagrangian approach?

The total Lagrangian approach is advantageous because it is more accurate for large deformations and can handle complex material behavior. It also allows for easier implementation of boundary conditions and is better suited for nonlinear material models.

4. What are the advantages of the updated Lagrangian approach?

The updated Lagrangian approach is advantageous because it is more computationally efficient for problems with large deformations. It also avoids some numerical issues that can arise with the total Lagrangian approach, such as element distortion and mesh tangling.

5. How do these solution approaches differ from the small strain mechanics approach?

The small strain mechanics approach assumes that the deformations of a material are small and can be linearized, whereas the large strain mechanics approach allows for significant changes in shape and volume. This means that the equations used in each approach are different, and the large strain mechanics approach requires more complex solution methods.

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