Drucker stability postulate
E554925
The Drucker stability postulate is a fundamental criterion in plasticity theory that asserts materials must not exhibit negative incremental work, ensuring stable and physically realistic material behavior under loading.
Statements (41)
| Predicate | Object |
|---|---|
| instanceOf |
material stability criterion
ⓘ
stability postulate in plasticity theory ⓘ |
| appliesIn |
rate-independent plasticity
ⓘ
small-strain plasticity formulations ⓘ |
| appliesTo |
incremental loading processes
ⓘ
inelastic materials ⓘ plastic materials ⓘ |
| assumes | incremental work is defined as stress increment times plastic strain increment ⓘ |
| category |
constitutive modeling assumption
ⓘ
material stability postulate NERFINISHED ⓘ |
| contrastsWith |
materials exhibiting strain softening
ⓘ
non-associated plastic flow that may violate stability ⓘ |
| coreIdea |
incremental plastic work must be nonnegative
ⓘ
materials must not exhibit negative incremental work ⓘ |
| ensures |
incremental work conjugacy between stress and strain
ⓘ
physically realistic material behavior ⓘ stable material response under loading ⓘ |
| field |
continuum mechanics
ⓘ
plasticity theory ⓘ solid mechanics ⓘ |
| goal |
ensure uniqueness and stability of boundary value problem solutions
ⓘ
prevent non-physical predictions in plasticity models ⓘ |
| historicalContext | introduced in mid-20th century plasticity literature ⓘ |
| implies |
monotonicity of the stress–strain relation in plastic range
ⓘ
no material instability under small perturbations ⓘ no spontaneous energy generation by the material ⓘ |
| influences |
criteria for numerical convergence in nonlinear analysis
ⓘ
design of elastoplastic constitutive laws ⓘ |
| mathematicalFormulation | Δσ_ij Δε_ij^p ≥ 0 for all admissible increments ⓘ |
| namedAfter | Daniel C. Drucker NERFINISHED ⓘ |
| relatedTo |
convexity of the yield surface
ⓘ
maximum plastic dissipation principle ⓘ normality flow rule ⓘ second law of thermodynamics ⓘ |
| requires |
no negative plastic dissipation under admissible loading paths
ⓘ
positive or zero plastic dissipation ⓘ |
| usedBy |
engineers analyzing metal plasticity
ⓘ
researchers developing plasticity theories ⓘ |
| usedFor |
assessing stability of constitutive models
ⓘ
deriving conditions on yield functions and flow rules ⓘ validating plasticity models in finite element analysis ⓘ |
Referenced by (1)
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