[ f = \sigma'_1 - \sigma'_3 - ( \sigma'_1 + \sigma'_3 ) \sin\phi - 2c \cos\phi ]
, the direction of plastic flow is independent of the yield surface shape. This is a crucial requirement for realistic soil modeling to prevent unrealistic volumetric expansion during shear. C. The Hardening/Softening Rule
Calculating ultimate bearing capacity without over-simplifying soil failure geometry. fundamentals of plasticity in geomechanics pdf
To simulate these behaviors accurately, engineers must transition from elastic models to elastoplastic frameworks. 2. The Three Pillars of Elastoplasticity Theory
Limitation: The Mohr-Coulomb surface forms an irregular hexamid in principal stress space, which introduces mathematical singularities (sharp corners) that complicate numerical simulations. Drucker-Prager Yield Criterion [ f = \sigma'_1 - \sigma'_3 - (
): The plastic strain vector is orthogonal to the yield surface. While mathematically elegant, this overpredicts the volume expansion (dilatancy) of sands. Non-Associated Flow Rule (
For those looking to delve deeper, several textbooks have become definitive resources. While free PDFs of copyrighted materials are often unauthorized, legitimate access may be available through university library systems or digital catalogs. The Three Pillars of Elastoplasticity Theory Limitation: The
Because plasticity is path-dependent, the governing differential equations must be integrated over discrete time or load steps. Two main algorithms are used:
For in-depth, mathematical, and practical understanding, the following resources are considered foundational: by H.S. Yu.
Standard metal plasticity models like Von Mises or Tresca fail in geomechanics because they ignore pressure-dependence. Soil and rock require shear strength models that scale with confining pressure.
dϵijp=dλ𝜕g𝜕σijd epsilon sub i j end-sub to the p-th power equals d lambda the fraction with numerator partial g and denominator partial sigma sub i j end-sub end-fraction is a non-negative scalar called the plastic multiplier.