Failure criterion

Isotropic

For isotropic materials, the following five failure criteria are available, followed by the strength constants needed:

1. Max principal stress. Strength constants (2):

   • 1 tensile strength (\(X\))

   • 1 compressive strength (\(X'\)).

2. Max principal strain. Strength constants (2):

   • 1 tensile strength (\(X_{\varepsilon}\))

   • 1 compressive strength (\(X'_{\varepsilon}\)).

3. Max shear stress or Tresca. Strength constant (1):

   • 1 shear strength (\(S\)).

4. Max shear strain. Strength constant (1):

   • 1 shear strength (\(S_{\varepsilon}\))

5. Mises. Strength constant (1):

   • 1 strength (\(X\)).

Different failure criterion will use different strength properties. This is summarized in the table below.

Failure criterion	x/xt/t1	y/yt/t2	z/zt/t3	xc/c1	yc/c2	zc/c3	s/s12	t/s13	r/s23
Max principal stress	\(X\)			\(X'\)
Max principal strain	\(X_{\varepsilon}\)			\(X'_{\varepsilon}\)
Max shear stress							\(S\)
Max shear strain							\(S_{\varepsilon}\)
Mises	\(X\)

More details can be found in the VABS users manual.

Specification

• <failure_criterion> - Name or ID of the failure criterion used.

  • 1 or max principal stress

  • 2 or max principal strain

  • 3 or max shear stress or tresca

  • 4 or max shear strain

  • 5 or mises

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Not isotropic

For other type materials (transversely isotropic, orthotropic / engineering, anisotropic), the following five failure criteria are available:

1. Max stress. Strength constants (9):

   • 3 tensile strengths in three directions (\(X, Y, Z\))

   • 3 compressive strengths in three directions (\(X', Y', Z'\))

   • 3 shear strengths in three principal planes (\(S, T, R\))

2. Max strain. Strength constants (9):

   • 3 tensile strengths in three directions (\(X_{\varepsilon}, Y_{\varepsilon}, Z_{\varepsilon}\))

   • 3 compressive strengths in three directions (\(X'_{\varepsilon}, Y'_{\varepsilon}, Z'_{\varepsilon}\))

   • 3 shear strengths in three principal planes (\(S_{\varepsilon}, T_{\varepsilon}, R_{\varepsilon}\))

3. Tsai-Hill. Strength constants (6):

   • 3 normal strengths in three directions (\(X, Y, Z\))

   • 3 shear shear strengths in three principal planes (\(S, T, R\)).

4. Tsai-Wu. Strength constants (9):

   • 3 tensile strengths in three directions (\(X, Y, Z\))

   • 3 compressive strengths in three directions (\(X', Y', Z'\))

   • 3 shear strengths in three principal planes (\(S, T, R\))

5. Hashin. Strength constants (6):

   • 2 tensile strengths in two directions (\(X, Y\))

   • 2 compressive strengths in two directions (\(X', Y'\))

   • 2 shear strengths in two principal planes (\(S, R\))

Different failure criterion will use different strength properties. This is summarized in the table below.

Failure criterion	x/xt/t1	y/yt/t2	z/zt/t3	xc/c1	yc/c2	zc/c3	s/s12	t/s13	r/s23
Max stress	\(X\)	\(Y\)	\(Z\)	\(X'\)	\(Y'\)	\(Z'\)	\(S\)	\(T\)	\(R\)
Max strain	\(X_{\varepsilon}\)	\(Y_{\varepsilon}\)	\(Z_{\varepsilon}\)	\(X'_{\varepsilon}\)	\(Y'_{\varepsilon}\)	\(Z'_{\varepsilon}\)	\(S_{\varepsilon}\)	\(T_{\varepsilon}\)	\(R_{\varepsilon}\)
Tsai-Hill	\(X\)	\(Y\)	\(Z\)				\(S\)	\(T\)	\(R\)
Tsai-Wu	\(X\)	\(Y\)	\(Z\)	\(X'\)	\(Y'\)	\(Z'\)	\(S\)	\(T\)	\(R\)
Hashin	\(X\)	\(Y\)		\(X'\)	\(Y'\)		\(S\)		\(R\)

More details can be found in the VABS users manual.

Specification

• <failure_criterion> - Name or ID of the failure criterion used.

  • 1 or max stress

  • 2 or max strain

  • 3 or tsai-hill

  • 4 or tsai-wu

  • 5 or hashin