Journal
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
Volume 99, Issue -, Pages 394-408Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jmps.2016.09.010
Keywords
Micromorphic theory; Homogenization; Gradient theory; Generalized continua
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The micromorphic theory of Eringen and Mindlin, including special cases like strain gradient theory or Cosserat theory, is widely used to model size effects and localization phenomena. The heuristic construction of such theories based on thermodynamic considerations is well established. However, the identification of corresponding constitutive laws and of the large number of respective constitutive parameters limits the practical application of such theories. In the present contribution, a closed procedure for the homogenization of a Cauchy continuum at the microscale towards a fully micromorphic continuum is derived including explicit definitions of all involved generalized macroscopic stress and deformation measures. The boundary value problem to be solved on the microscale is formulated either for using static or kinematic boundary conditions. The procedure is demonstrated with an example.
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