A computational approach to identify the material parameters of the relaxed micromorphic model
arXiv:2401.15648 · doi:10.1016/j.cma.2024.116944
Abstract
We determine the material parameters in the relaxed micromorphic generalized continuum model for a given periodic microstructure in this work. This is achieved through a least squares fitting of the total energy of the relaxed micromorphic homogeneous continuum to the total energy of the fully-resolved heterogeneous microstructure, governed by classical linear elasticity. The relaxed micromorphic model is a generalized continuum that utilizes the $\Curl$ of a micro-distortion field instead of its full gradient as in the classical micromorphic theory, leading to several advantages and differences. The most crucial advantage is that it operates between two well-defined scales. These scales are determined by linear elasticity with microscopic and macroscopic elasticity tensors, which respectively bound the stiffness of the relaxed micromorphic continuum from above and below. While the macroscopic elasticity tensor is established a priori through standard periodic first-order homogenization, the microscopic elasticity tensor remains to be determined. Additionally, the characteristic length parameter, associated with curvature measurement, controls the transition between the micro- and macro-scales. Both the microscopic elasticity tensor and the characteristic length parameter are here determined using a computational approach based on the least squares fitting of energies. This process involves the consideration of an adequate number of quadratic deformation modes and different specimen sizes. We conduct a comparative analysis between the least square fitting results of the relaxed micromorphic model, the fitting of a skew-symmetric micro-distortion field (Cosserat-micropolar model), and the fitting of the classical micromorphic model with two different formulations for the curvature...
References in corpus (18)
- A unifying perspective: the relaxed linear micromorphic continuum
- Determination of Metamaterial Parameters by Means of a Homogenization Approach Based on Asymptotic Analysis
- Additive manufacturing introduced substructure and computational determination of metamaterials parameters by means of the asymptotic homogenization
- Verification of asymptotic homogenization method developed for periodic architected materials in strain gradient continuum
- Reflection and transmission of elastic waves at interfaces embedded in non-local band-gap metamaterials: a comprehensive study via the relaxed micromorphic model
- Micromorphic Computational Homogenization for Mechanical Metamaterials with Patterning Fluctuation Fields
- Size-effects of metamaterial beams subjected to pure bending: on boundary conditions and parameter identification in the relaxed micromorphic model
- Unfolding engineering metamaterials design: relaxed micromorphic modeling of large-scale acoustic meta-structures
- Korn inequalities for incompatible tensor fields in three space dimensions with conformally invariant dislocation energy
- Analytical solutions of the cylindrical bending problem for the relaxed micromorphic continuum and other generalized continua (including full derivations)
- Primal and mixed finite element formulations for the relaxed micromorphic model
- Lagrange and based Finite Element formulations for the relaxed micromorphic model
- Extended Micromorphic Computational Homogenization for Mechanical Metamaterials Exhibiting Multiple Geometric Pattern Transformations
- Computational homogenization of higher-order continua
- Optimal incompatible Korn-Maxwell-Sobolev inequalities in all dimensions
- Reduced integration schemes in micromorphic computational homogenization of elastomeric mechanical metamaterials
- Green's functions for the isotropic planar relaxed micromorphic model -- concentrated force and concentrated couple
- Korn-Maxwell-Sobolev inequalities for general incompatibilities