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Inference of Substructured Reduced-Order Models for Dynamic Contact from Contact-free Simulations

Diana Manvelyan-Stroot, Yevgeniya Filanova, Igor Pontes Duff, Peter Benner, Utz Wever

TL;DR

The paper tackles dynamic contact in linear elasticity by developing a non-intrusive, data-driven ROM that preserves the contact interface. It combines force-informed operator inference with a Craig-Bampton–style substructure to recover reduced primal matrices and a coupling between boundary and interior DOFs, then switches to the adjoint dual system to solve a linear complementarity problem using Lemke's method; symmetry and positive definiteness are enforced via LMIs to guarantee LCP solvability. The approach yields a reduced model that accurately predicts displacements and, with careful coupling, contact pressures, even when data come from contact-free simulations. This has practical impact for real-time digital twins and online maintenance forecasting, enabling efficient yet physically consistent simulations of dynamic contact in large-scale structural systems.

Abstract

In this paper, we propose an operator-inference-based reduction approach for contact problems, leveraging snapshots from simulations without active contact. Contact problems are solved using adjoint methods, by switching to the dual system, where the corresponding Lagrange multipliers represent the contact pressure. The Craig-Bampton-like substructuring method is incorporated into the inference process to provide the reduced system matrices and the coupling of the contact and interior nodes. The maximum possible set of contact nodes must be known a priori. Characteristic properties of the inferred matrices, such as symmetry and positive definiteness, are enforced by appending additional constraints to the underlying least-squares problem. The resulting dual system, which forms a linear complementarity problem, is well-defined and can be effectively solved using methods such as Lemke's algorithm. The performance of the proposed method is validated on three-dimensional finite element models.

Inference of Substructured Reduced-Order Models for Dynamic Contact from Contact-free Simulations

TL;DR

The paper tackles dynamic contact in linear elasticity by developing a non-intrusive, data-driven ROM that preserves the contact interface. It combines force-informed operator inference with a Craig-Bampton–style substructure to recover reduced primal matrices and a coupling between boundary and interior DOFs, then switches to the adjoint dual system to solve a linear complementarity problem using Lemke's method; symmetry and positive definiteness are enforced via LMIs to guarantee LCP solvability. The approach yields a reduced model that accurately predicts displacements and, with careful coupling, contact pressures, even when data come from contact-free simulations. This has practical impact for real-time digital twins and online maintenance forecasting, enabling efficient yet physically consistent simulations of dynamic contact in large-scale structural systems.

Abstract

In this paper, we propose an operator-inference-based reduction approach for contact problems, leveraging snapshots from simulations without active contact. Contact problems are solved using adjoint methods, by switching to the dual system, where the corresponding Lagrange multipliers represent the contact pressure. The Craig-Bampton-like substructuring method is incorporated into the inference process to provide the reduced system matrices and the coupling of the contact and interior nodes. The maximum possible set of contact nodes must be known a priori. Characteristic properties of the inferred matrices, such as symmetry and positive definiteness, are enforced by appending additional constraints to the underlying least-squares problem. The resulting dual system, which forms a linear complementarity problem, is well-defined and can be effectively solved using methods such as Lemke's algorithm. The performance of the proposed method is validated on three-dimensional finite element models.

Paper Structure

This paper contains 20 sections, 47 equations, 11 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Dynamic contact
  3. Dynamic Contact Model
  4. Obstacle Problem
  5. Weak Formulation
  6. Contact Algorithm using Adjoint Methods
  7. Applied Reduction Methods
  8. Intrusive Hurty-Craig-Bampton Reduction
  9. Force-informed operator inference
  10. Non-intrusive substructuring-based reduction for dynamic contact
  11. Basic assumptions
  12. Inferring the primal system matrices
  13. Reduction basis for the interior subsystem
  14. Approximation of the coupling matrix
  15. Optimization problem for system matrices
  16. ...and 5 more sections

Figures (11)

  • Figure 1: Static mode.
  • Figure 2: FEM model of a console beam with a rigid plane obstacle.
  • Figure 3: Training snapshots for the console beam example.
  • Figure 4: Console beam example: SVD decay of the snapshot set that corresponds to the interior part of the full-order system simulation, and the interior subsystem snapshot set of the full-order system simulation with fixed boundary nodes.
  • Figure 5: Console beam model: Comparison of the contact simulation results ${\boldsymbol{q}}_B$ of the FOM and substructured OpInf ROMs with different coupling term approximations.
  • ...and 6 more figures