Hyperelastic bulk active term. Stress S_{ij} = A J C_{ij}^{-1}, where A is the activation in [0, F_{\rm max}].
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\int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v})
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dw_tl_bulk_active | (material, virtual, state) |
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Hyperelastic bulk penalty term. Stress S_{ij} = K(J-1)\; J C_{ij}^{-1}.
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\int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v})
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dw_tl_bulk_penalty | (material, virtual, state) |
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Hyperelastic bulk pressure term. Stress S_{ij} = -p J C_{ij}^{-1}.
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\int_{\Omega} S_{ij}(p) \delta E_{ij}(\ul{u};\ul{v})
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dw_tl_bulk_pressure | (virtual, state, state_p) |
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Diffusion term in the total Lagrangian formulation with linearized deformation-dependent permeability \ull{K}(\ul{u}) = J \ull{F}^{-1} \ull{k} f(J) \ull{F}^{-T}, where \ul{u} relates to the previous time step (n-1) and f(J) = \max\left(0, \left(1 + \frac{(J - 1)}{N_f}\right)\right)^2 expresses the dependence on volume compression/expansion.
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\int_{\Omega} \ull{K}(\ul{u}^{(n-1)}) : \pdiff{q}{\ul{X}} \pdiff{p}{\ul{X}}
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dw_tl_diffusion | (material_1, material_2, virtual, state, parameter) |
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Base class for all hyperelastic surface terms in TL formulation family.
Base class for all hyperelastic terms in TL formulation family.
The subclasses should have the following static method attributes: - stress_function() (the stress) - tan_mod_function() (the tangent modulus)
The common (family) data are cached in the evaluate cache of state variable.
Hyperelastic Mooney-Rivlin term. Effective stress S_{ij} = \kappa J^{-\frac{4}{3}} (C_{kk} \delta_{ij} - C_{ij} - \frac{2}{3 } I_2 C_{ij}^{-1}).
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\int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v})
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dw_tl_he_mooney_rivlin | (material, virtual, state) |
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Hyperelastic neo-Hookean term. Effective stress S_{ij} = \mu J^{-\frac{2}{3}}(\delta_{ij} - \frac{1}{3}C_{kk}C_{ij}^{-1}).
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\int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v})
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dw_tl_he_neohook | (material, virtual, state) |
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Surface flux term in the total Lagrangian formulation, consistent with DiffusionTLTerm.
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\int_{\Gamma} \ul{\nu} \cdot \ull{K}(\ul{u}^{(n-1)}) \pdiff{p}{\ul{X}}
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d_tl_surface_flux | (material_1, material_2, parameter_1, parameter_2) |
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Surface traction term in the total Lagrangian formulation, expressed using \ul{\nu}, the outward unit normal vector w.r.t. the undeformed surface, \ull{F}(\ul{u}), the deformation gradient, J = \det(\ull{F}), and \ull{\sigma} a given traction, often equal to a given pressure, i.e. \ull{\sigma} = \pi \ull{I}.
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\int_{\Gamma} \ul{\nu} \cdot \ull{F}^{-1} \cdot \ull{\sigma} \cdot \ul{v} J
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dw_tl_surface_traction | (opt_material, virtual, state) |
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Volume of a D-dimensional domain, using a surface integral in the total Lagrangian formulation, expressed using \ul{\nu}, the outward unit normal vector w.r.t. the undeformed surface, \ull{F}(\ul{u}), the deformation gradient, and J = \det(\ull{F}). Uses the approximation of \ul{u} for the deformed surface coordinates \ul{x}.
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1 / D \int_{\Gamma} \ul{\nu} \cdot \ull{F}^{-1} \cdot \ul{x} J
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d_tl_volume_surface | (parameter) |
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Volume term (weak form) in the total Lagrangian formulation.
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\begin{array}{l} \int_{\Omega} q J(\ul{u}) \\ \mbox{volume mode: vector for } K \from \Ical_h: \int_{T_K} J(\ul{u}) \\ \mbox{rel\_volume mode: vector for } K \from \Ical_h: \int_{T_K} J(\ul{u}) / \int_{T_K} 1 \end{array}
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dw_tl_volume | (virtual, state) |
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