Module elastic_viscoplastic 

Elastic-viscoplastic solid constitutive models.

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Elastic-viscoplastic solid constitutive models are defined by an elastic stress tensor function of the elastic deformation gradient, a plastic dissipation potential, and the Kröner-Lee decomposition of the deformation gradient.

\mathbf{P}:\dot{\mathbf{F}} - \mathbf{P}_\mathrm{e}:\dot{\mathbf{F}}_\mathrm{e} \geq 0

The second law of thermodynamics is satisfied by ensuring that the dissipation potential is minimized and vanishes at zero rate,

\frac{\partial\phi}{\partial\mathbf{D}_\mathrm{p}}:\mathbf{D}_\mathrm{p} - \phi \geq 0 \quad\text{and}\quad \phi(\mathbf{0}) = 0

by requiring the inequality to hold for arbitrary deformation gradient rates, which yields the stress and an asymmetric tangent,

\mathbf{P} = \mathbf{P}_\mathrm{e}\cdot\mathbf{F}_\mathrm{p}^{-T} \quad\Longrightarrow\quad \mathcal{C}_{iJkL} \neq \mathcal{C}_{kLiJ}

and by minimizing the dissipation potential less the plastic power with respect to the plastic stretching rate, yielding the flow rule.

\mathbf{M}_\mathrm{e}' = \frac{\partial\phi}{\partial\mathbf{D}_\mathrm{p}} \quad\Longleftrightarrow\quad \mathbf{D}_\mathrm{p} = \frac{\partial\phi^*}{\partial\mathbf{M}_\mathrm{e}'}

The dissipation potential and its dual sum to the plastic power at the conjugate pair, which therefore must be non-negative.

\phi(\mathbf{D}_\mathrm{p}) + \phi^*(\mathbf{M}_\mathrm{e}') = \mathbf{M}_\mathrm{e}':\mathbf{D}_\mathrm{p} \geq 0

Re-exports

pub use crate::constitutive::solid::elastic_plastic::AppliedLoad;

pub use crate::constitutive::solid::elastic_plastic::ElasticPlasticOrViscoplastic;

pub use crate::constitutive::solid::elastic_plastic::PlasticTangents;

Traits

ElasticViscoplastic

Required methods for elastic-viscoplastic solid constitutive models.

FirstOrderRoot

First-order root-finding methods for elastic-viscoplastic solid constitutive models.

RootRkmkDae

RKMK-DAE stage-equilibrium methods for elastic-viscoplastic solid constitutive models. The sibling of FirstOrderRoot that keeps F_p on its manifold instead of marching it additively, by resolving F from equilibrium at every stage abscissa rather than freezing it across the window — so the coupling is the tableau’s own order, not first order. Blanket over any ElasticViscoplastic model, same as FirstOrderRoot itself.

ZerothOrderRoot

Zeroth-order root-finding methods for elastic-viscoplastic solid constitutive models.