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<p>A fast and accurate intrusive Reduced Order Model (ROM) for Drucker-Prager plasticity problems, in which material properties and cyclic load path are parametric inputs, is described. Efficiency is achieved via multiple reduction methods: Proper Orthogonal Decomposition-Galerkin (POD-Galerkin) to reduce the total number of degrees of freedom (DoFs), Discrete Empirical Interpolation Method (DEIM) to accelerate the computation of nonlinear terms, and clustering to enable the use of multiple Local DEIM (LDEIM) subspaces. Full Order Model (FOM) consists of a two-dimensional FEA of a deformable solid with Drucker-Prager plasticity. Offline, the temporal and parameterized training data generated from FOM runs is classified using <i>k</i>-means clustering algorithm, whereby LDEIM basis vectors are computed. Online, nearest neighbor classifier identifies the appropriate LDEIM. ROM has three hyper-parameters (the size of ROM, the number of clusters, and the number of DEIM measurement points per cluster), influencing both accuracy and speed-up. In a micromechanics porous media problem, parameterized by Young’s modulus and hardening modulus, it is demonstrated the ROM performance for inputs within and outside of the training domain; error and speed up vary with inputs—accuracy is highest for inputs within the training domain (Error: <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(1.0-3.5\)</EquationSource> </InlineEquation>% vs <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(1.0-9.2\)</EquationSource> </InlineEquation>% ), while speed-up varies from 106 to 134 times. In a cyclic plasticity problem, parameterized for load path, ROMs built with LDEIM achieve stable and accurate online performance with a substantial speed-up for test load paths. Under FOMs with <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\sim 10^3\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\sim 5\cdot 10^4\)</EquationSource> </InlineEquation> DoFs, speed-ups are <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\sim 11\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\sim 770\)</EquationSource> </InlineEquation> times, respectively. Larger speed-ups seem likely for larger FOMs.</p>

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An efficient parameterized local reduced order model for Drucker-Prager plasticity

  • 期刊论文

  • 发表日期：

    2025年7月31日

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  • Saeed Hatefi Ardakani,
  • Giovanni Zingaro,
  • Robert Gracie

摘要

A fast and accurate intrusive Reduced Order Model (ROM) for Drucker-Prager plasticity problems, in which material properties and cyclic load path are parametric inputs, is described. Efficiency is achieved via multiple reduction methods: Proper Orthogonal Decomposition-Galerkin (POD-Galerkin) to reduce the total number of degrees of freedom (DoFs), Discrete Empirical Interpolation Method (DEIM) to accelerate the computation of nonlinear terms, and clustering to enable the use of multiple Local DEIM (LDEIM) subspaces. Full Order Model (FOM) consists of a two-dimensional FEA of a deformable solid with Drucker-Prager plasticity. Offline, the temporal and parameterized training data generated from FOM runs is classified using k-means clustering algorithm, whereby LDEIM basis vectors are computed. Online, nearest neighbor classifier identifies the appropriate LDEIM. ROM has three hyper-parameters (the size of ROM, the number of clusters, and the number of DEIM measurement points per cluster), influencing both accuracy and speed-up. In a micromechanics porous media problem, parameterized by Young’s modulus and hardening modulus, it is demonstrated the ROM performance for inputs within and outside of the training domain; error and speed up vary with inputs—accuracy is highest for inputs within the training domain (Error: \(1.0-3.5\) % vs \(1.0-9.2\) % ), while speed-up varies from 106 to 134 times. In a cyclic plasticity problem, parameterized for load path, ROMs built with LDEIM achieve stable and accurate online performance with a substantial speed-up for test load paths. Under FOMs with \(\sim 10^3\) and \(\sim 5\cdot 10^4\) DoFs, speed-ups are \(\sim 11\) and \(\sim 770\) times, respectively. Larger speed-ups seem likely for larger FOMs.