TY - JOUR

T1 - Formulating and heuristic solving of contact problems in hybrid data-driven computational mechanics

AU - Gebhardt, Cristian G.

AU - Lange, Senta

AU - Steinbach, Marc C.

N1 - Funding Information: Cristian G. Gebhardt gratefully acknowledges the financial support from the European Research Council through the ERC Consolidator Grant \u201CDATA-DRIVEN OFFSHORE\u201D (Project ID 101083157). Marc C. Steinbach gratefully acknowledges the financial support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) \u2013 SFB1463 \u2013 434502799.

PY - 2024/7

Y1 - 2024/7

N2 - In this work we consider the hybrid Data-Driven Computational Mechanics (DDCM) approach, in which a smooth constitutive manifold is reconstructed to obtain a well-behaved nonlinear optimization problem (NLP) rather than the much harder discrete-continuous NLP (DCNLP) of the direct DDCM approach. The key focus is on the addition of geometric inequality constraints to the hybrid DDCM formulation. Therein, the required constraint force leads to a contact problem in the form of a mathematical program with complementarity constraints (MPCC), a problem class that is still less complex than the DCNLP. For this MPCC we propose a heuristic quick-shot solution approach, which can produce verifiable solutions by solving up to four NLPs. We perform various numerical experiments on three different contact problems of increasing difficulty to demonstrate the potential and limitations of this approach.

AB - In this work we consider the hybrid Data-Driven Computational Mechanics (DDCM) approach, in which a smooth constitutive manifold is reconstructed to obtain a well-behaved nonlinear optimization problem (NLP) rather than the much harder discrete-continuous NLP (DCNLP) of the direct DDCM approach. The key focus is on the addition of geometric inequality constraints to the hybrid DDCM formulation. Therein, the required constraint force leads to a contact problem in the form of a mathematical program with complementarity constraints (MPCC), a problem class that is still less complex than the DCNLP. For this MPCC we propose a heuristic quick-shot solution approach, which can produce verifiable solutions by solving up to four NLPs. We perform various numerical experiments on three different contact problems of increasing difficulty to demonstrate the potential and limitations of this approach.

KW - Contact problem

KW - Data-driven computational mechanics

KW - Heuristic solving

KW - Hybrid formulation

KW - Mathematical program with complementarity constraints

UR - http://www.scopus.com/inward/record.url?scp=85191157460&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2311.04083

DO - 10.48550/arXiv.2311.04083

M3 - Article

AN - SCOPUS:85191157460

VL - 134

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

SN - 1007-5704

M1 - 108031

ER -