26 research outputs found
A comparison of delamination models: Modeling, properties, and applications
This contribution presents recent results in the modeling and the analysis of delamination problems. It addresses adhesive contact, brittle, and cohesive zone models both in a quasistatic and a viscous, dynamic setting for the bulk part. Also different evolution laws for the delaminating surface are discussed
Mesh adaptivity for quasi-static phase-field fractures based on a residual-type a posteriori error estimator
In this work, we consider adaptive mesh refinement for a monolithic
phase-field description for fractures in brittle materials. Our approach is
based on an a posteriori error estimator for the phase-field variational
inequality realizing the fracture irreversibility constraint. The key goal is
the development of a reliable and efficient residual-type error estimator for
the phase-field fracture model in each time-step. Based on this error
estimator, error indicators for local mesh adaptivity are extracted. The
proposed estimator is based on a technique known for singularly perturbed
equations in combination with estimators for variational inequalities. These
theoretical developments are used to formulate an adaptive mesh refinement
algorithm. For the numerical solution, the fracture irreversibility is imposed
using a Lagrange multiplier. The resulting saddle-point system has three
unknowns: displacements, phase-field, and a Lagrange multiplier for the crack
irreversibility. Several numerical experiments demonstrate our theoretical
findings with the newly developed estimators and the corresponding refinement
strategy.Comment: This is the preprint version of an accepted article to be published
in the GAMM-Mitteilungen 2019.
https://onlinelibrary.wiley.com/journal/1522260
An iterative staggered scheme for phase field brittle fracture propagation with stabilizing parameters
This paper concerns the analysis and implementation of a novel iterative staggered scheme for quasi-static brittle fracture propagation models, where the fracture evolution is tracked by a phase field variable. The model we consider is a two-field variational inequality system, with the phase field function and the elastic displacements of the solid material as independent variables. Using a penalization strategy, this variational inequality system is transformed into a variational equality system, which is the formulation we take as the starting point for our algorithmic developments. The proposed scheme involves a partitioning of this model into two subproblems; phase field and mechanics, with added stabilization terms to both subproblems for improved efficiency and robustness. We analyze the convergence of the proposed scheme using a fixed point argument, and find that under a natural condition, the elastic mechanical energy remains bounded, and, if the diffusive zone around crack surfaces is sufficiently thick, monotonic convergence is achieved. Finally, the proposed scheme is validated numerically with several bench-mark problems.publishedVersio
-convergence for high order phase field fracture: continuum and isogeometric formulations
We consider second order phase field functionals, in the continuum setting,
and their discretization with isogeometric tensor product B-splines. We prove
that these functionals, continuum and discrete, -converge to a brittle
fracture energy, defined in the space . In particular, in the
isogeometric setting, since the projection operator is not Lagrangian (i.e.,
interpolatory) a special construction is needed in order to guarantee that
recovery sequences take values in ; convergence holds, as expected, if
, being the size of the physical mesh and
the internal length in the phase field energy
A posteriori estimator for the adaptive solution of a quasi-static fracture phase-field model with irreversibility constraints
Within this article, we develop a residual type a posteriori error estimator
for a time discrete quasi-static phase-field fracture model. Particular
emphasize is given to the robustness of the error estimator for the variational
inequality governing the phase-field evolution with respect to the phase-field
regularization parameter . The article concludes with numerical
examples highlighting the performance of the proposed a posteriori error
estimators on three standard test cases; the single edge notched tension and
shear test as well as the L-shaped panel test
Truncated Nonsmooth Newton Multigrid for phase-field brittle-fracture problems
We propose the Truncated Nonsmooth Newton Multigrid Method (TNNMG) as a
solver for the spatial problems of the small-strain brittle-fracture
phase-field equations. TNNMG is a nonsmooth multigrid method that can solve
biconvex, block-separably nonsmooth minimization problems in roughly the time
of solving one linear system of equations. It exploits the variational
structure inherent in the problem, and handles the pointwise irreversibility
constraint on the damage variable directly, without penalization or the
introduction of a local history field. Memory consumption is significantly
lower compared to approaches based on direct solvers. In the paper we introduce
the method and show how it can be applied to several established models of
phase-field brittle fracture. We then prove convergence of the solver to a
solution of the nonsmooth Euler-Lagrange equations of the spatial problem for
any load and initial iterate. Numerical comparisons to an operator-splitting
algorithm show a speed increase of more than one order of magnitude, without
loss of robustness
Phase field approximation of cohesive fracture models
We obtain a cohesive fracture model as a -limit of scalar damage
models in which the elastic coefficient is computed from the damage variable
through a function of the form , with diverging for close to the value describing undamaged
material. The resulting fracture energy can be determined by solving a
one-dimensional vectorial optimal profile problem. It is linear in the opening
at small values of and has a finite limit as . If the
function is allowed to depend on the index , for specific choices we
recover in the limit Dugdale's and Griffith's fracture models, and models with
surface energy density having a power-law growth at small openings