scholarly journals Matrix-free multigrid solvers for phase-field fracture problems

2020 ◽  
Vol 372 ◽  
pp. 113431 ◽  
Author(s):  
D. Jodlbauer ◽  
U. Langer ◽  
T. Wick
Keyword(s):  
Phase Field ◽  
Multigrid Solvers ◽  
Matrix Free

scholarly journals Parallel Matrix-Free Higher-Order Finite Element Solvers for Phase-Field Fracture Problems

2020 ◽  
Vol 25 (3) ◽  
pp. 40
Author(s):  
Daniel Jodlbauer ◽  
Ulrich Langer ◽  
Thomas Wick
Keyword(s):  
Finite Elements ◽  
Phase Field ◽  
Variational Problems ◽  
Discrete Version ◽  
Active Set ◽  
Newton Step ◽  
Variational Equality ◽  
Primal Dual ◽  
Fracture Models ◽  
Matrix Free

Phase-field fracture models lead to variational problems that can be written as a coupled variational equality and inequality system. Numerically, such problems can be treated with Galerkin finite elements and primal-dual active set methods. Specifically, low-order and high-order finite elements may be employed, where, for the latter, only few studies exist to date. The most time-consuming part in the discrete version of the primal-dual active set (semi-smooth Newton) algorithm consists in the solutions of changing linear systems arising at each semi-smooth Newton step. We propose a new parallel matrix-free monolithic multigrid preconditioner for these systems. We provide two numerical tests, and discuss the performance of the parallel solver proposed in the paper. Furthermore, we compare our new preconditioner with a block-AMG preconditioner available in the literature.

scholarly journals PRISMS-PF: A general framework for phase-field modeling with a matrix-free finite element method

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Stephen DeWitt ◽  
Shiva Rudraraju ◽  
David Montiel ◽  
W. Beck Andrews ◽  
Katsuyo Thornton
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Phase Field ◽  
General Framework ◽  
Phase Field Modeling ◽  
Field Modeling ◽  
Matrix Free ◽  
Element Method

A TEM study of the influence of microstructure on the superplastic behavior of a U-5.8 wt.% Nb alloy

1986 ◽  
Vol 44 ◽  
pp. 568-569
Author(s):  
G. Mackiewicz Ludtka
Keyword(s):  
Grain Size ◽  
Heating Rate ◽  
Phase Field ◽  
Single Phase ◽  
Superplastic Behavior ◽  
Two Phase ◽  
Single Phase Field

Historically, metals exhibit superplasticity only while forming in a two-phase field because a two-phase microstructure helps ensure a fine, stable grain size. In the U-5.8 Nb alloy, superplastici ty exists for up to 2 h in the single phase field (γ1) at 670°C. This is above the equilibrium monotectoid temperature of 647°C. Utilizing dilatometry, the superplastic (SP) U-5.8 Nb alloy requires superheating to 658°C to initiate the α+γ2 → γ1 transformation at a heating rate of 1.5°C/s. Hence, the U-5.8 Nb alloy exhibits an anomolous superplastic behavior.

Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness

2020 ◽  
Vol 71 (7) ◽  
pp. 853-867
Author(s):  
Phuc Pham Minh
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Phase Field ◽  
Deformation Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Rectangular Plates ◽  
Equilibrium Equations ◽  
Third Order ◽  
Free Vibration Frequency

The paper researches the free vibration of a rectangular plate with one or more cracks. The plate thickness varies along the x-axis with linear rules. Using Shi's third-order shear deformation theory and phase field theory to set up the equilibrium equations, which are solved by finite element methods. The frequency of free vibration plates is calculated and compared with the published articles, the agreement between the results is good. Then, the paper will examine the free vibration frequency of plate depending on the change of the plate thickness ratio, the length of cracks, the number of cracks, the location of cracks and different boundary conditions

Sign in / Sign up

Export Citation Format

Share Document