v0.10.0
Classes | Namespaces | Functions | Variables
PlasticOps.hpp File Reference

Go to the source code of this file.

Classes

struct  PlasticOps::CommonData
 [Common data] More...
 
struct  PlasticOps::OpCalculatePlasticSurface
 [Operators definitions] More...
 
struct  PlasticOps::OpPlasticStress
 
struct  PlasticOps::OpCalculatePlasticFlowRhs
 
struct  PlasticOps::OpCalculateContrainsRhs
 
struct  PlasticOps::OpCalculatePlasticInternalForceLhs_dEP
 
struct  PlasticOps::OpCalculatePlasticFlowLhs_dU
 
struct  PlasticOps::OpCalculatePlasticFlowLhs_dEP
 
struct  PlasticOps::OpCalculatePlasticFlowLhs_dTAU
 
struct  PlasticOps::OpCalculateContrainsLhs_dU
 
struct  PlasticOps::OpCalculateContrainsLhs_dEP
 
struct  PlasticOps::OpCalculateContrainsLhs_dTAU
 
struct  PlasticOps::OpPostProcPlastic
 
struct  PlasticOps::Monitor
 

Namespaces

 PlasticOps
 

Functions

auto PlasticOps::diff_tensor ()
 [Operators definitions] More...
 
auto PlasticOps::diff_symmetrize ()
 
template<typename T >
double PlasticOps::trace (FTensor::Tensor2_symmetric< T, 2 > &t_stress)
 
template<typename T >
auto PlasticOps::deviator (FTensor::Tensor2_symmetric< T, 2 > &t_stress, double trace)
 
auto PlasticOps::diff_deviator (FTensor::Ddg< double, 2, 2 > &&t_diff_stress)
 
auto PlasticOps::hardening (double tau)
 
auto PlasticOps::hardening_dtau ()
 
double PlasticOps::platsic_surface (FTensor::Tensor2_symmetric< double, 3 > &&t_stress_deviator)
 
auto PlasticOps::plastic_flow (double f, FTensor::Tensor2_symmetric< double, 3 > &&t_dev_stress, FTensor::Ddg< double, 3, 2 > &&t_diff_deviator)
 
template<typename T >
auto PlasticOps::diff_plastic_flow_dstress (double f, FTensor::Tensor2_symmetric< T, 2 > &t_flow, FTensor::Ddg< double, 3, 2 > &&t_diff_deviator)
 
template<typename T >
auto PlasticOps::diff_plastic_flow_dstrain (FTensor::Ddg< T, 2, 2 > &t_D, FTensor::Ddg< double, 2, 2 > &&t_diff_plastic_flow_dstress)
 
double PlasticOps::contrains (double tau, double f)
 
double PlasticOps::sign (double x)
 
double PlasticOps::diff_constrain_dtau (double tau, double f)
 
auto PlasticOps::diff_constrain_df (double tau, double f)
 
template<typename T >
auto PlasticOps::diff_constrain_dstress (double &&diff_constrain_df, FTensor::Tensor2_symmetric< T, 2 > &t_plastic_flow)
 
template<typename T1 , typename T2 >
auto PlasticOps::diff_constrain_dstrain (T1 &t_D, T2 &&t_diff_constrain_dstress)
 

Variables

FTensor::Index< 'j', SPACE_DIMPlasticOps::j
 [Common data] More...
 
FTensor::Index< 'k', SPACE_DIMPlasticOps::k
 
FTensor::Index< 'l', SPACE_DIMPlasticOps::l
 
FTensor::Index< 'm', SPACE_DIMPlasticOps::m
 
FTensor::Index< 'i', SPACE_DIMPlasticOps::i
 
FTensor::Index< 'n', SPACE_DIMPlasticOps::n
 
FTensor::Index< 'I', 3 > PlasticOps::I
 
FTensor::Index< 'J', 3 > PlasticOps::J
 
FTensor::Index< 'M', 3 > PlasticOps::M
 
FTensor::Index< 'N', 3 > PlasticOps::N
 

Detailed Description

\[ \left\{ \begin{array}{ll} \frac{\partial \sigma_{ij}}{\partial x_j} - b_i = 0 & \forall x \in \Omega \\ \varepsilon_{ij} = \frac{1}{2}\left( \frac{\partial u_i}{\partial x_j} + \frac{\partial u_j}{\partial x_i} \right)\\ \sigma_{ij} = D_{ijkl}\left(\varepsilon_{kl}-\varepsilon^p_{kl}\right) \\ \dot{\varepsilon}^p_{kl} - \dot{\tau} \left( \left. \frac{\partial f}{\partial \sigma_{kl}} \right|_{(\sigma,\tau) } \right) = 0 \\ f(\sigma, \tau) \leq 0,\; \dot{\tau} \geq 0,\;\dot{\tau}f(\sigma, \tau)=0\\ u_i = \overline{u}_i & \forall x \in \partial\Omega_u \\ \sigma_{ij}n_j = \overline{t}_i & \forall x \in \partial\Omega_\sigma \\ \Omega_u \cup \Omega_\sigma = \Omega \\ \Omega_u \cap \Omega_\sigma = \emptyset \end{array} \right. \]

\[ \left\{ \begin{array}{ll} \left(\frac{\partial \delta u_i}{\partial x_j},\sigma_{ij}\right)_\Omega-(\delta u_i,b_i)_\Omega -(\delta u_i,\overline{t}_i)_{\partial\Omega_\sigma}=0 & \forall \delta u_i \in H^1(\Omega)\\ \left(\delta\varepsilon^p_{kl} ,D_{ijkl}\left( \dot{\varepsilon}^p_{kl} - \dot{\tau} A_{kl} \right)\right) = 0 & \forall \delta\varepsilon^p_{ij} \in L^2(\Omega) \cap \mathcal{S} \\ \left(\delta\tau,c_n\dot{\tau} - \frac{1}{2}\left\{c_n \dot{\tau} + (f(\pmb\sigma,\tau) - \sigma_y) + \| c_n \dot{\tau} + (f(\pmb\sigma,\tau) - \sigma_y) \|\right\}\right) = 0 & \forall \delta\tau \in L^2(\Omega) \end{array} \right. \]

Definition in file PlasticOps.hpp.