SPH
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Equation of motion for solid body and constitutive equation for the stress tensor (Hooke's law) More...
#include <EquationTerm.h>
Public Member Functions | |
SolidStressForce (const RunSettings &settings) | |
virtual void | setDerivatives (DerivativeHolder &derivatives, const RunSettings &settings) override |
Sets derivatives required by this term. More... | |
virtual void | initialize (IScheduler &scheduler, Storage &storage, const Float t) override |
Initialize all the derivatives and/or quantity values before derivatives are computed. More... | |
virtual void | finalize (IScheduler &scheduler, Storage &storage, const Float t) override |
Computes all the derivatives and/or quantity values based on accumulated derivatives. More... | |
virtual void | create (Storage &storage, IMaterial &material) const override |
Creates all quantities needed by the term using given material. More... | |
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virtual | ~Polymorphic () |
Equation of motion for solid body and constitutive equation for the stress tensor (Hooke's law)
The equation computes acceleration from the divergence of the deviatoric stress \(S\). The equation of motion in the used SPH discretization reads:
\[ \frac{{\rm d} \vec v_i}{{\rm d} t} = \sum_j m_j \left(\frac{S_i + S_j}{\rho_i \rho_j}\right) \cdot \nabla W_{ij}\,, \]
Corresponding term of energy equation (viscous heating) is also added to the energy derivative:
\[ \frac{{\rm d} u_i}{{\rm d} t} = \frac{1}{\rho_i} S_i : \nabla \vec v_i \,, \]
where \(\nabla \vec v_i\) is the symmetrized velocity gradient.
The stress is evolved as a first-order quantity, using Hooke's law as constitutive equation:
\[ \frac{{\rm d} S_i}{{\rm d} t} = 2\mu \left( \nabla \vec v - {\bf 1} \, \frac{\nabla \cdot \vec v}{3} \right)\,, \]
where \(\mu\) is the shear modulus and \(\bf 1\) is the identity tensor.
This equation represents solid bodies, for fluids use NavierStokesForce.
Definition at line 149 of file EquationTerm.h.
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explicit |
Definition at line 142 of file EquationTerm.cpp.
Creates all quantities needed by the term using given material.
Called once for every body in the simulation.
Implements IEquationTerm.
Definition at line 204 of file EquationTerm.cpp.
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overridevirtual |
Computes all the derivatives and/or quantity values based on accumulated derivatives.
Called every time step after derivatives are evaluated and saved to storage.
Implements IEquationTerm.
Definition at line 177 of file EquationTerm.cpp.
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overridevirtual |
Initialize all the derivatives and/or quantity values before derivatives are computed.
Called at the beginning of every time step. Note that derivatives need not be zeroed out manually, this is already done by timestepping (for derivatives of quantities) and solver (for accumulated values).
Implements IEquationTerm.
Definition at line 173 of file EquationTerm.cpp.
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overridevirtual |
Sets derivatives required by this term.
The derivatives are then automatically evaluated by the solver, the equation term can access the result in finalize function. This function is called once for each thread at the beginning of the run.
Implements IEquationTerm.
Definition at line 151 of file EquationTerm.cpp.