Polytopal composite finite elements for modeling concrete fracture based on nonlocal damage models

TL;DR

This paper introduces Polytopal Composite Finite Elements (PCFEM) with an assumed strain formulation on polygonal meshes, improving the accuracy of nonlocal damage models in capturing localized concrete fracture behaviors.

Contribution

It develops a novel assumed strain technique based on the Hu-Washizu principle for polygonal meshes, enhancing damage modeling accuracy and reducing mesh sensitivity.

Findings

Accurately captures highly localized damage in concrete fracture.

Reduces mesh sensitivity in nonlocal damage simulations.

Validates method through comparison with experimental and numerical data.

Abstract

The paper presents an assumed strain formulation over polygonal meshes to accurately evaluate the strain fields in nonlocal damage models. An assume strained technique based on the Hu-Washizu variational principle is employed to generate a new strain approximation instead of direct derivation from the basis functions and the displacement fields. The underlying idea embedded in arbitrary finite polygons is named as Polytopal composite finite elements (PCFEM). The PCFEM is accordingly applied within the framework of the nonlocal model of continuum damage mechanics to enhance the description of damage behaviours in which highly localized deformations must be captured accurately. This application is helpful to reduce the mesh-sensitivity and elaborate the process-zone of damage models. Several numerical examples are designed for various cases of fracture to discuss and validate the computational capability of the present method through comparison with published numerical results and experimental data from the literature.