Failure Criteria

This section gives you detailed formulas of failure criteria you can visualize as post-processing results.

The following topics are discussed:

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Failure Criteria for Composite Properties

In a composite context with an orthotropic material (orthotropic 2D, orthotropic 3D, or fiber), you can compute failure criteria and visualize them as post-processing results. The failure criteria are Tsai-Hill, Tsai-Wu, Maximum Failure and Hoffman.

The characteristics of orthotropic materials are defined in the ELFINI Linear Elastic Domain dialog box. See Modifying ELFINI Linear Elastic Material Properties.

  • Tensile stress limit X corresponds to the ultimate stress in tension along the X direction (S1T).
  • Compressive stress limit X corresponds to the ultimate stress in compression along the X direction (S1C).
  • Tensile stress limit Y corresponds to the ultimate stress in tension along the Y direction (S2T).
  • Compressive stress limit Y corresponds to the ultimate stress in compression along the Y direction (S2C).
  • Shear stress limit XY corresponds to the ultimate shear stress in the XY-plane (S12).
  • Shear stress limit XZ corresponds to the ultimate shear stress in the XZ-plane (S13).
  • Shear stress limit YZ corresponds to the ultimate shear stress in the YZ-plane (S23).

To learn more about the characteristics of orthotropic materials, see .

Tsai-Hill

ELFINI Linear Elastic Material Properties

For each lamina, the Tsai-Hill failure criterion requires that:

where:

  • S1 = S1C if
  • S1 = S1T if
  • S2 = S2C if
  • S2 = S2T if
  • For the term: if , S1 = S1T; otherwise S1 = S1C

Tsai-Wu

For each lamina, the Tsai-Wu failure criterion requires that:

Maximum Failure

The maximum failure criterion is defined as follows:

Hoffman

The Hoffman criterion requires that:

Special Cases

If one of the shear stress values (Shear stress limit XY, Shear stress limit YZ, or Shear stress limit XZ) is not defined in the ELFINI Linear Elastic Domain dialog box, the associated term is neglected in the formula (S12, S23 and S13 cannot be null in the formula).

For example, if you enter 0 as Shear stress limit XY value (S12=0) in the ELFINI Linear Elastic Domain dialog box, the Tsai-Hill failure criteria requires that:

This means that the shear stresses in the XY-plane are neglected.

The formulas are different depending on:

  • Material type:
    • Fiber materials: the shear stress values in the YZ-plane and in the XZ-plane are equal (S23 = S13).
    • Orthotropic 2D materials: terms associated to the Z-plane are neglected in the Tsai-Hill and Tsai-Wu formulas.
    • Orthotropic 3D materials: all terms can be considered in the formulas.
  • Finite element physical type:
    • Shell: all terms can be considered in the formulas.
    • Membrane: terms associated to the Z-plane are considered as null in the formulas.
    • Shear Panel: only shear effects in the XY-plane are taken into account in the formulas.

Failure Criteria for Isotropic Materials

If you work with an isotropic material, you can compute failure criteria and visualize them as post-processing results. Those criteria are Tresca, Tresca Stress and Von Mises.

Tresca Stress

The Tresca stress criterion is defined as follows:

where are the principal stresses.

Tresca

The Tresca criterion requires that:

where Re is the linear elastic limit.

Von Mises

The Von Mises criterion requires that:

where Re is the linear elastic limit.