ArXiv (open access)
Key ideas
- Cosserat materials form an extension of linearized elasticity by relaxing the symmetry condition on the stress tensor.
- With the additional rotation and couple stress variables, the Cosserat equations form a saddle point problem in four variables.
- The Cosserat equations correspond to a well-posed Hodge-Laplace problem on the Cosserat complex.
Main findings
- Two families of mixed finite element discretizations are proposed:
- The strongly coupled spaces form a subcomplex of the Cosserat complex.
- The weakly coupled spaces can be used if the equations degenerate to linearized elasticity. They utilize tuples of $\mathbb{RT}_0$ for the stress tensors.
- Optimal convergence is shown theoretically and numerically for both families.
