ABSTRACT
ABSTRACT: The effective macroscopic behavior of most materials depends significantly on the structure exhibited at the microscopic level. In the last decades, considerable effort has thus been directed towards the development of continuum theories accounting for the inherent microstructure of materials. A unified theory is to date however not available. Yet a reliable and efficient use of microstructured materials would benefit from the former which is also the foundation of any subsequent numerical analysis. Focusing on two kinds of microstructured materials (gradient continua, micromorphic continua), an attempt is thus made to identify their role and their potential with regard to numerical implementations in a generic theory. An analysis of both continua in the framework of various variational formulations based on the Dirichlet principle shows that they are closely related (which is intuitively not obvious): a gradient continuum can e.g. be modeled by applying a mixed variational principle to a micromorphic continuum. This has considerable consequences for the numerical implementation: the Euler-Lagrange equations describing the seemingly more intricate micromorphic continuum require only C0 continuous approximations when implemented into a FEM code, while, in contrast, the Euler-Lagrange equations deduced for the gradient continuum require C1 differentiability of the involved unknowns. Numerical tests have been performed for microstretch continua, which are a special subclass of micromorphic continua.
