Towards the incorporation of damage into solid‐shells based on reduced integration

Abstract

AbstractSome years ago, a family of continuum finite elements based on reduced integration [1], [2], [3] was investigated. Many structural components with different kinds of elastic and inelastic material behaviour were considered and these elements showed accurate results while beeing more efficient than similar three‐dimensional formulations based on full integration. The objective of the present contribution is to extend the analysis to damage and fracture. To this end, we present the incorporation of a modified version of a gradient‐extended damage model [4] based on the micromorphic approach [5] into solids with only a single integration point. Due to the analogy to fully‐coupled thermomechanical problems, we adapt the derivation of a consistent hourglass stabilization from an earlier contribution for multi‐field problems [6]. A numerical benchmark problem of quasi‐brittle fracture reveals the accuracy and efficiency of the proposed approach. Besides the ability to deliver mesh‐independent results, the framework is especially suitable for highly constrained situations in which conventional low‐order finite elements suffer from well known locking phenomena.