2D Elastic Isotropic Cosserat Coupled Stress Computation

template<typename T, typename PointJacobianMatrixType, typename PointStressIntegrandViewType, typename PointPropertiesType, typename PointAccelerationType>
void impl_compute_cosserat_couple_stress(const std::true_type, const std::integral_constant<specfem::dimension::type, specfem::dimension::type::dim2>, const std::integral_constant<specfem::element::medium_tag, specfem::element::medium_tag::elastic_psv_t>, const std::integral_constant<specfem::element::property_tag, specfem::element::property_tag::isotropic_cosserat>, const PointJacobianMatrixType &point_jacobian_matrix, const PointPropertiesType &point_properties, const T factor, const PointStressIntegrandViewType &F, PointAccelerationType &acceleration)

Compute couple stress contribution for 2D elastic isotropic Cosserat media.

Implements moment equilibrium equation for micropolar continuum with rotational degrees of freedom. Computes angular acceleration from stress tensor asymmetry due to couple stress effects.

Moment equilibrium equation: \( j\ddot{\phi}_y = (\sigma_{xz} - \sigma_{zx}) \)

Coordinate transformation: \( \mathbf{J}^{-1} = \frac{1}{\det(\mathbf{J})} \begin{bmatrix} \gamma_z & -\xi_z \\ -\gamma_x & \xi_x \end{bmatrix} \)

where:

  • \( j \): rotational inertia

  • \( \phi_y \): rotation about y-axis

  • \( \sigma_{xz} \neq \sigma_{zx} \): asymmetric stress tensor

  • \( \mathbf{J} \): Jacobian transformation matrix

Parameters:

  • point_jacobian_matrix – Coordinate transformation matrix

  • point_properties – Cosserat material properties

  • factor – Integration scaling factor

  • F – Stress integrand components in reference coordinates

  • acceleration[in, out] – Acceleration field (rotational component modified)