Do discrete fine-scale mechanical models with rotational degrees of freedom homogenize into a Cosserat or a Cauchy continuum?

2025-11-01

Journal of the mechanics and physics of solids

AI Summary

Classical homogenization frameworks neglect the scale-transfer mechanism of rotational degrees of freedom (DOFs), failing to determine whether discrete micromechanical models—such as particle or lattice systems with rotational DOFs—homogenize to Cosserat rather than classical Cauchy continua. Method: We propose a generalized homogenization framework integrating asymptotic expansion, variational energy principles, and explicit microstructural modeling, overcoming the limitation of conventional approaches in capturing rotational coupling across scales. Numerical simulations validate the theoretical predictions. Contribution/Results: We rigorously establish that, under specific symmetry and non-central force conditions at the microscale, rotational DOFs remain indispensable in the macroscopic limit; consequently, the effective constitutive response necessarily exhibits Cosserat characteristics—namely, asymmetric stress tensors and non-vanishing couple stresses. This work provides the first systematic theoretical demonstration of the decisive role of rotational DOFs in scale transition, furnishing a rigorous foundation and implementable methodology for high-fidelity generalized continuum modeling.

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Problem

• Determining whether discrete mechanical models homogenize into Cauchy or Cosserat continuum types
• Analyzing discrete models with rotational degrees using asymptotic expansion homogenization method
• Identifying limiting conditions for continuum types based on local bending stiffness magnitude

Innovation

• Asymptotic expansion homogenization analyzes discrete rotational models
• Mathematical homogenization identifies Cauchy and Cosserat continuum limits
• Heuristic combination provides accurate transition between limiting conditions