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 -