## Mechanical Engineering ETDs

#### Title

A Mesh Objective Algorithm for Modeling Mode-I Cracks Using a Standard Finite Element Formulation

#### Publication Date

9-1-2015

#### Abstract

A computationally efficient mesh objective algorithm for modeling mode-I cracks is developed and implemented within a standard finite element formulation. The algorithm applies the crack opening displacements across the standard nodal degrees of freedom that is consistent with formalism of the conventional smeared crack approach. Various versions of the conventional smeared crack approach have been proposed since the introduction of the finite element method. The approach has not been successful for the following reasons: (i) accumulation of spurious shear resulting in stress locking, (ii) misalignment of the stress field around the cracked element, and (iii) incorrect prediction of the crack propagation direction. Four new and distinct techniques are developed to preclude both spurious shear accumulation and misalignment of the stress field around the crack tip to provide mesh objective results. First, to preclude shear locking, a modified failure constitutive model is developed, which derives an alternative for the stress increment rather than using the full strain field of the cracked element. The crack orientation is held fixed after crack initiation to provide an accurate representation of the crack orientation and resulting crack path. A tangent crack stiffness is derived to provide an explicit update for the stress components without the need for an iterative solver for both linear and nonlinear softening. Next, a computationally efficient crack tracking algorithm is implemented to preclude the misalignment of the stress field. The tracking algorithm uses the crack orientation predicted from the failure model and a series of crack segments to define the crack path. An hourglass control method is developed for an element undergoing softening. The tangent crack stiffness is used to derive hourglass forces that help obtain mesh objectivity when one-point quadrature is applied. Finally, a cross-over scaling method is used to provide the correct characteristic crack length to obtain complete mesh objectivity. The developed methods work collectively to provide a fully explicit and efficient algorithm for modeling mode-I failure in brittle materials without mesh bias. It is demonstrated that the algorithm predicts load deflection curves and crack paths that are independent of both mesh size and orientation when modeling failure at an angle through a finite element mesh. The methods developed are expected to be applicable to higher dimensions and for mode-II failure.

#### Keywords

smeared crack approach, failure model, mode-I failure, decohesion model, cohesive zone, concrete fracture, computational fracture mechanics, hourglass control, cross-over scaling, finite element method, material failure, mesh objective, double edge notch, softening, fracture energy

#### Degree Name

Mechanical Engineering

#### Level of Degree

Doctoral

#### Department Name

Mechanical Engineering

#### First Advisor

Schreyer, Howard

#### First Committee Member (Chair)

Khraishi, Tariq

#### Second Committee Member

Shen, Yu-Lin

#### Third Committee Member

Sulsky, Deborah

#### Fourth Committee Member

Taylor, Paul

#### Sponsors

Sandia National Laboratories

#### Document Type

Dissertation

#### Language

English

#### Recommended Citation

Burnett, Damon. "A Mesh Objective Algorithm for Modeling Mode-I Cracks Using a Standard Finite Element Formulation." (2015). http://digitalrepository.unm.edu/me_etds/26