QUIZ #12

In lesson 2.5 of this chapter, we introduced a nonlinear 1D elastic model in which the tangent stiffness follows a linear relation with strain.  

If c = 20 and E₀ = 230 GPa, what’s the maximum compressive stress that can be achieved by this constitutive model?

I have a truss-type finite element 5 mm long with the following material properties:

• Elastic modulus: 185 GPa
• Tensile strength: 340 MPa
• Fracture energy: 8 kJ/m²

Select the correct statements:

Based on the data from the previous question.

What is the element size that we have to use such that the strain at damage initiation () is equal to the ultimate strain ()?

Let’s say that we are applying the user material developed in section 3 of this chapter (linear elastic with damage in 1D) on an element that is initially subjected to a tensile load until the damage variable reaches a value of 0.6.

Afterwards, the element is subjected to a compressive stress state. What is the elastic modulus of the material under this compressive load?

(Data: The initial elastic modulus of the material is 100 GPa)

Let’s say that we modify the UMAT of lesson 3.11 and we delete the element when the damage variable reaches 0.9 by including these lines at the end of the subroutine:

      IF (STATEV(1) .GT. 0.9) THEN
        STATEV(2) = 0.0
      ENDIF

What happens with the energy dissipated by the element? (Tip: modify the subroutine, run the simulation and read the energy dissipated after deleting the element).

In lesson 4.4, we applied a uniaxial loading state onto the solid element with the linear elastic isotropic user material.

Keeping constant the material properties (E = 210000 MPa, ν = 0.3), modify the boundary conditions as follows:

• LEFT, XSYMM
• BOTTOM, YSYMM
• BACK and FRONT, ZSYMM
• RIGHT. Apply displacement U1 = 0.01

Select the right statements:

Based on the previous question. We apply a YSYMM boundary condition on the TOP set of the element applying the same load (U1 = 0.01 @ RIGHT).

Select the statements that are correct: