Node-to-segment and node-to-surface interface finite elements for fracture mechanics

TL;DR

This paper introduces a novel interface finite element for fracture mechanics that allows non-matching discretizations, simplifies modeling of non-propagating cracks, and ensures internal equilibrium, demonstrated through detailed nonlinear fracture examples.

Contribution

A new node-to-segment and node-to-surface interface element for fracture mechanics that improves flexibility and modeling capabilities over classical methods.

Findings

Allows non-matching discretizations of crack faces.

Facilitates modeling of non-propagating cracks.

Ensures internal rotational equilibrium of the interface element.

Abstract

The topologies of existing interface elements used to discretize cohesive cracks are such that they can be used to compute the relative displacements (displacement discontinuities) of two opposing segments (in 2D) or of two opposing facets (in 3D) belonging to the opposite crack faces and enforce the cohesive traction-separation relation. In the present work we propose a novel type of interface element for fracture mechanics sharing some analogies with the node-to-segment (in 2D) and with the node-to-surface (in 3D) contact elements. The displacement gap of a node belonging to the finite element discretization of one crack face with respect to its projected point on the opposite face is used to determine the cohesive tractions, the residual vector and its consistent linearization for an implicit solution scheme. The following advantages with respect to classical interface finite elements are demonstrated: (i) non-matching finite element discretizations of the opposite crack faces is possible; (ii) easy modelling of cohesive cracks with non-propagating crack tips; (iii) the internal rotational equilibrium of the interface element is assured. Detailed examples are provided to show the usefulness of the proposed approach in nonlinear fracture mechanics problems.