Hierarchical NURBS and a higher-order phase-field approach to fracture for finite-deformation contact problems

Abstract

Highlights• We present a hierarchical refinement scheme for isogeometric analysis.• A frictional Mortar contact algorithm for hierarchical refined NURBS is introduced.• A higher-order phase-field approach to brittle fracture is applied to the concept of HNURBS and combined with frictional contact problems. AbstractIn this paper we investigate variationally consistent Mortar contact algorithms applied to a phase-field approach to brittle fracture. Phase-field approaches allow for an efficient simulation of complex fracture problems, as they arise in contact and impact situations. To improve accuracy and convergence, a fourth-order phase-field model is considered, requiring C 1 continuity throughout the domain. An isogeometrical framework is used for the spatial discretisation subject to hierarchical refinements to resolve local features. This reduces the computational effort tremendously, as will be shown in a series of representative examples.

Phase‐field approach to fracture for finite‐deformation contact problems

“…Furthermore we use a hierarchical refinement scheme for the NURBS (HNURBS), see [4]. For the contact boundaries we obtain the following discrete virtual work contribution…”

“…e denotes the elastic part of a strain energy density (for more informations see [4]). For the contact description we need to enforce the well-known Karush-Kuhn-Tucker conditions given by equations (1) 5 , comprised of the impenetrability condition, the condition which only permits compressive tractions and the complementarity condition, respectively.…”

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The present contribution deals with a variationally consistent Mortar contact algorithm applied to a phase-field fracture approach for finite deformations, see [4]. A phase-field approach to fracture allows for the numerical simulation of complex fracture patterns for three dimensional problems, extended recently to finite deformations (see [2] for more details).

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“…Equations (1) 8 are the initial conditions for both, the displacement as well as the phase-field. The IBVP is supplemented by the constitutive relations for the second Piola-Kirchhoff stress tensor and the driving force for the phase-fieldwheree denotes the elastic part of a strain energy density (for more informations see [4]). For the contact description we need to enforce the well-known Karush-Kuhn-Tucker conditions given by equations (1) 5 , comprised of the impenetrability condition, the condition which only permits compressive tractions and the complementarity condition, respectively.…”

A Higher Order Phase-Field Approach to Fracture for Finite-Deformation Contact Problems

“…The present contribution provides a comprehensive computational framework for large deformational contact and phase-fracture analysis and is based on the recently appeared publication [16]. A phase-field approach to fracture allows for the efficient numerical treatment of complex fracture patterns for three dimensional problems.…”