A variational minimization formulation for hydraulically induced fracturing in elastic-plastic solids

TL;DR

This paper introduces a variational modeling framework for hydraulic fracturing in elastic-plastic solids, combining phase-field fracture modeling with plasticity criteria, and employing advanced finite element methods for robust simulations.

Contribution

It presents a novel variational formulation that integrates fracture propagation and plasticity effects in hydraulic fracturing simulations.

Findings

Framework successfully models fracture propagation in elastic-plastic media.

Finite element implementation overcomes locking issues in plastic deformation.

Numerical examples demonstrate robustness and accuracy of the approach.

Abstract

A variational modeling framework for hydraulically induced fracturing of elastic-plastic solids is developed in the present work. The developed variational structure provides a global minimization problem. While fracture propagation is modeled by means of a phase-field approach to fracture, plastic effects are taken into account by using a Drucker-Prager-type yield-criterion function. This yield-criterion function governs the plastic evolution of the fluid-solid mixture. Fluid storage and transport are described by a Darcy-Biot-type formulation. Thereby the fluid storage is decomposed into a contribution due to the elastic deformations and one due to the plastic deformations. A local return mapping scheme is used for the update of the plastic quantities. The global minimization structure demands a $H($div$)$-conforming finite-element formulation. Furthermore this is combined with an enhanced-assumed-strain formulation in order to overcome locking phenomena arising from the plastic deformations. The robustness and capabilities of the presented framework will be shown in a sequence of numerical examples.