Numerical methods for variational phase-field fracture problems

Lecturer: Prof. Thomas Wick

ECTS: 1.50, hours: 1.0

course no.: 327.018

Time and place: blocked lecture between 8 March and 15 March 2018 (details see below)

Abstract:

This course is devoted to numerical modeling of fracture processes modeled in terms of a variational phase-field method. Using this approach, roughly-speaking, lower-dimensional fractures in a given displacement field are represented with the help of a smoothed indicator function, the so-called phase-field variable. In part I, we briefly recapitulate mathematical modeling, including  advantages and shortcomings of the phase-field fracture approach, followed by properties on the continuous level. Afterwards in part II, we concentrate on numerical aspects. First, we introduce Ambrosio-Tortorelli elliptic functionals to approximate the lower-dimensional crack path in the same dimension as the displacement field. Second, we focus on the treatment of crack irreversibility. Third, discretizations in time and space are considered. Forth, we address the numerical solution of the nonlinear and linear subproblems. In part III of this course, we introduce local mesh adaptivity to enhance the accuracy of certain quantities of interest and/or the crack path, while keeping the computational cost reasonable. All concepts are substantiated with algorithms and numerical tests.

Lecture notes can be found here.

Schedule:

Thu, 8 March 2018 13:45 - 15:15

Fri, 9 March 2018, 08:30 -10:00

Mon, 12 March 2018, 13:45 - 15:15

Tue, 13 March 2018, 13:45 - 15:15

Tue, 13 March 2018, 15:30 - 17:00

Wed, 14 March 2018, 15:30 - 17:00

Thu, 15 March 2018, 13:45 - 15:15

Lecture Room: S2 416-1