An energy‐momentum scheme for extended continuum models with rotational degrees of freedom

In mechanical engineering, the finite element method is well-known in simulation of homogeneous materials without microstructures. But, particular, microstructures can improve with respect to their applicability engineering. Examples are 2D- and 3D-fiber-reinforced materials, which manufactured microscale or mesoscale, respectively. An efficient these provides an anisotropic continuum formulation. However, demand continua extended kinematics. The introduction such possible by mixed methods. this paper, we introduce internal rotational degrees freedom model also a stiffness fiber flexure twist. kinematic formulation be explained using covariant based on curvilinear convected coordinates. context, new objective deformation measures power-conjugate stress tensors derived. Therefore, corresponding energy-momentum scheme obtained simulates numerical examples stable accordance discrete balance laws. These demonstrate additional material curvature-twist strain energy functions Kauderer-type parameter studies different directions.