Multiscale modeling of structures via a localized hyperreduced-order method

  • Giuliodori, Agustina (CIMNE)
  • Soudah, Eduardo (CIMNE)

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In this research, a novel approach is presented to model structures in the small strain regime using reduced-order modeling (ROM) and domain decomposition techniques. The approach involves dividing the structure into subdomains with ``fictitious'' interfaces and parameterizing the subdomain and interface fields with reduced-order bases computed using Singular Value Decomposition (SVD) on solution snapshots. The amplitude of the interfaces acts as coarse-scale displacement unknowns, allowing for a solution strategy that avoids the nested local/global problem of traditional methods. The coarse-grid cells serve as special types of finite elements with kinematics extracted from the computational experiments. The relation between coarse-scale and fine-scale displacements is established through inter-scale operators that can be precomputed in an offline stage. Additionally, a hyperreduced scheme based on the Empirical Cubature Method (ECM) is considered for evaluating internal forces by sampling stresses at strains at a reduced set of integration points, enabling the consideration of material nonlinearities . The proposed method has been tested on structures typically modeled by either solid or beam finite elements. In the latter case, it is shown that this methodology enables easy incorporation of this type of empirically derived finite elements into existing 3D FE codes for solid elements, in the sense that the user need not worry about deriving generalized constitutive equations as in standard FE beam implementations (because generalized forces are directly related to Cauchy stresses at the ECM integration points, and in turn, Cauchy stresses to infinitesimal strains through standard 3D constitutive equations).