SpECTRE
v2024.03.19
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The linear elasticity equation formulated as a set of coupled first-order PDEs. More...
#include <FirstOrderSystem.hpp>
Public Types | |
using | primal_fields = tmpl::list< Tags::Displacement< Dim > > |
using | primal_fluxes = tmpl::list< Tags::MinusStress< Dim > > |
using | background_fields = tmpl::list<> |
using | inv_metric_tag = void |
using | fluxes_computer = Fluxes< Dim > |
using | sources_computer = void |
using | boundary_conditions_base = elliptic::BoundaryConditions::BoundaryCondition< Dim > |
Static Public Attributes | |
static constexpr size_t | volume_dim = Dim |
The linear elasticity equation formulated as a set of coupled first-order PDEs.
This system formulates the elasticity equation (see Elasticity
):
\begin{align*} \nabla_i T^{ij} = f_\mathrm{ext}^j \\ T^{ij} = -Y^{ijkl} \nabla_{(k} \xi_{l)} \end{align*}
The system can be formulated in terms of these fluxes and sources (see elliptic::protocols::FirstOrderSystem
):
\begin{align*} F^{ij} &= -T^{ij} = Y^{ijkl} \nabla_{(k} \xi_{l)} \\ S^j &= 0 \\ f^j &= f_\mathrm{ext}^j \text{.} \end{align*}