A variationally consistent augmented Lagrangian contact framework for peridynamic impact and brittle fracture in plates

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Galadima, Yakubu Kasimu and Oterkus, Selda and Oterkus, Erkan (2026) A variationally consistent augmented Lagrangian contact framework for peridynamic impact and brittle fracture in plates. Engineering Fracture Mechanics, 344. 112400. ISSN 0013-7944 (https://doi.org/10.1016/j.engfracmech.2026.112400)

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Abstract

A variationally consistent framework is presented that couples a Peridynamic (PD) solid with a rigid-body impactor through an augmented Lagrangian (AL) contact formulation for dynamic impact and brittle fracture. Contact tractions computed in the AL stage are transferred to the PD domain as conservative volumetric body forces using a partition-of-unity operator, providing a mesh-objective loading representation while preserving global momentum. Supported edges are enforced as unilateral (Signorini-type) constraints within an explicit velocity–Verlet integrator. The approach is verified and validated on three benchmarks: (i) normal drop-ball impact to assess normal contact kinematics and rebound dynamics, (ii) oblique impact to evaluate coupled normal–tangential response with frictional stick–slip transitions, and (iii) contact-induced brittle failure of a soda-lime-glass plate. Across the first two benchmarks, predicted normal/tangential force histories and impactor velocity evolution closely match reference solutions. In the glass-plate benchmark, the simulations reproduce a three-mechanism fracture response comprising Hertzian conical cracks, plate-scale flexural/radial cracking, and bending-induced secondary circumferential cracks that cut across radially released sectors. Crack-front kinematics are quantified directly from the PD bond-break damage field. The resulting crack-tip speeds are sub-Rayleigh, consistent with reported ranges for dynamic fracture in glass. The proposed AL–PD coupling and boundary treatment provide a robust and extensible foundation for predictive simulation of frictional contact, impact dynamics, and fragmentation in engineering materials.

ORCID iDs

Galadima, Yakubu Kasimu ORCID logoORCID: https://orcid.org/0000-0001-7208-1864, Oterkus, Selda ORCID logoORCID: https://orcid.org/0000-0003-0474-0279 and Oterkus, Erkan ORCID logoORCID: https://orcid.org/0000-0002-4614-7214;
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