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

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

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: An energy‐momentum scheme for extended continuum models with rotational degrees of freedom ; volume:21 ; number:1 ; year:2021 ; extent:2 ; Proceedings in applied mathematics and mechanics ; 21, Heft 1 (2021) (gesamt 2)

Contributors, Places and Time

• Creator: Groß, Michael ; Dietzsch, Julian ; Kalaimani, Iniyan

Further information

• DOI: 10.1002/pamm.202100004
• URN: urn:nbn:de:101:1-2021121514145774895424
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 15.08.2025, 7:24 AM CEST