1. STRENGHT, LAMINA FAILURE CRITERIA
Zdeněk Padovec

2. Symbols F (failure) isotropic material composite material
indexes L (Longitudinal), T (Transversal), c (compression), t (tension)
isotropic material
tensile strength (compressive strength) Ft, (Fc), may or may not be equal (cast iron, concrete Fc Ft)
shear strength S, 𝑆= 𝐹 von Mises, 𝑆= 𝐹 2 Tresca
composite material
FTt and FLT crucial
tensile strength in longitudinal direction
compressive strength in longitudinal direction
tensile strength in transverse direction
compressive strength in transverse direction
in-plane shear strength

3. Strength criterions
non-interactive criterions – no coupling between normal and shear stresses
maximum stress criterion
maximum strain criterion
interactive criterions - coupling between normal and shear stresses
Hill criterion
Tsai – Hill criterion
Hoffmann criterion
Tsai – Wu criterion
Puck criterion
LaRC criterion …

4. Non-interactive criterions
maximum stress criterion σmax
failure occurs when at least one of the stresses in material coordinates exceeds the corresponding experimental value of strength

5. Non-interactive criterions
maximum strain criterion εmax
conditions
Hooke´s Law
limit values of strain components

6. Non-interactive criterions
maximum strain criterion εmax
with the use of Hooke´s Law
for
for
for
for

7. Interactive criterions
Hill criterion
stress components in main directions L, T, T´
parameters A – F are related to the strength of material
assumption – SAME STRENGTH IN TENSION AND COMPRESSION – Fit= Fic
based on von Mises criterion for isotropic materials
Hill extends this criterion for orthotropic materials
this can be rewritten

8. Interactive criterions
Tsai - Hill criterion
simplification FT= FT´
Hoffmann criterion
generalized Hill´s criterion, DIFFERENT TENSILE AND COMPRESSIVE STRENGHT Fit≠ Fic

9. Interactive criterions
Tsai - Wu criterion
general theory of failure
based on polynomial function
can be written as
plane stress case or

10. Interactive criterions
Tsai - Wu criterion
where
based on biaxial test

11. Graphics solution of some criterions
Maximum stress
Maximum strain