Crack Propagation in a Brittle Elastic Material With Defects

1999 ◽  
Vol 66 (1) ◽  
pp. 79-86 ◽  
Author(s):  
M. Valentini ◽  
S. K. Serkov ◽  
D. Bigoni ◽  
A. B. Movchan
Keyword(s):  
Asymptotic Solution ◽  
Asymptotic Analysis ◽  
Isotropic Medium ◽  
Numerical Solutions ◽  
Porous Ceramics ◽  
Qualitative Description ◽  
Mode I ◽  
Pure Mode ◽  
Two Dimensional

A two-dimensional asymptotic solution is presented for determination of the trajectory of a crack propagating in a brittle-elastic, isotropic medium containing small defects. Brittleness of the material is characterized by the assumption of the pure Mode I propagation criterion. The defects are described by Po´lya-Szego¨ matrices, and examples for small elliptical cavities and circular inclusions are given. The results of the asymptotic analysis, which agree well with existing numerical solutions, give qualitative description of crack trajectories observed in brittle materials with defects, such as porous ceramics.

Two-dimensional viscous gravity currents flowing over a deep porous medium

2001 ◽  
Vol 440 ◽  
pp. 359-380 ◽  
Author(s):  
JAMES M. ACTON ◽  
HERBERT E. HUPPERT ◽  
M. GRAE WORSTER
Keyword(s):  
Porous Medium ◽  
Numerical Solutions ◽  
Gravity Current ◽  
Constant Volume ◽  
Two Dimensional ◽  
Theoretical Predictions ◽  
Self Similar ◽  
Coefficient Of Viscosity ◽  
Good Agreement

The spreading of a two-dimensional, viscous gravity current propagating over and draining into a deep porous substrate is considered both theoretically and experimentally. We first determine analytically the rate of drainage of a one-dimensional layer of fluid into a porous bed and find that the theoretical predictions for the downward rate of migration of the fluid front are in excellent agreement with our laboratory experiments. The experiments suggest a rapid and simple technique for the determination of the permeability of a porous medium. We then combine the relationships for the drainage of liquid from the current through the underlying medium with a formalism for its forward motion driven by the pressure gradient arising from the slope of its free surface. For the situation in which the volume of fluid V fed to the current increases at a rate proportional to t3, where t is the time since its initiation, the shape of the current takes a self-similar form for all time and its length is proportional to t2. When the volume increases less rapidly, in particular for a constant volume, the front of the gravity current comes to rest in finite time as the effects of fluid drainage into the underlying porous medium become dominant. In this case, the runout length is independent of the coefficient of viscosity of the current, which sets the time scale of the motion. We present numerical solutions of the governing partial differential equations for the constant-volume case and find good agreement with our experimental data obtained from the flow of glycerine over a deep layer of spherical beads in air.

Asymptotic Solution Near Focus of a Two-dimensional Shock and Instability Near Axis of a Cylindrical Shock with CCW Approach

1984 ◽  
Vol 39 (11) ◽  
pp. 1011-1022
Author(s):  
Shanbing Yu
Keyword(s):  
Asymptotic Solution ◽  
Small Perturbation ◽  
Perturbation Analysis ◽  
Numerical Solutions ◽  
Asymptotic Solutions ◽  
Polar Coordinates ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Whitham Equations

The Chester-Chisnell-Whitham equations in Cartesian and polar coordinates are written out for the two-dimensional case. The solution expanded near a point is obtained. The asymptotic solutions of order 2 near focus are presented. Linear small perturbation analysis for a converging cylindrical shock is given. To study the development of perturbations numerical solutions are carried out.

Fracture characterization and modeling of Gyroid filled 3D printed PLA structures

2021 ◽  
Vol 63 (5) ◽  
pp. 397-401
Author(s):  
Ahmet Refah Torun ◽  
Ali Sinan Dike ◽  
Ege Can Yıldız ◽  
İsmail Sağlam ◽  
Naghdali Choupani
Keyword(s):  
Fracture Toughness ◽  
Shear Fracture ◽  
Industrial Applications ◽  
Shear Mode ◽  
Mode I ◽  
Mode Ii ◽  
Mixed Mode Fracture ◽  
Pure Mode ◽  
Two Dimensional ◽  
3D Printed

Abstract Polylactic acid (PLA) is a commonly used biodegradable material in medical and increasingly in industrial applications. These materials are often exposed to various flaws and faults due to working and production conditions, and increasing the demand for PLA for various applications requires a full understanding of its fracture behavior. In addition to ABS, PLA is a widely used polymeric material in 3D printing. The gyroid type of filling is advantageous for overcoming the relatively higher brittleness of PLA in comparison with conventional thermoplastic polymers. In this study, the effects of various filling ratios on the fracture toughness of 3D printed PLA samples with gyroid pattern were investigated numerically and experimentally for pure mode I, combined mode I/II, and pure mode II. Two-dimensional finite element modeling was created, and the two-dimensional functions of stress intensity coefficients were extracted in loading mode I, mode I/II, and mode II at varied filling ratios of the gyroid PLA samples. Mixed-mode fracture tests for 3D printed PLA samples with a gyroid pattern at various filling ratios were performed by using a specially developed fracture testing fixture. The results showed that the amount of fracture toughness of the samples under study in tensile mode was much higher than those values in shear mode. Also, as the percentages of the filling ratios in the samples increased, both tensile and shear fracture toughness improved.

scholarly journals On the Numerical Determination of Shrinkage Stresses

1970 ◽  
Vol 37 (1) ◽  
pp. 123-127 ◽  
Author(s):  
F. Bauer ◽  
E. L. Reiss
Keyword(s):  
Iterative Method ◽  
Numerical Solutions ◽  
Mixed Boundary ◽  
Thin Strip ◽  
Heated Plate ◽  
Two Dimensional ◽  
Numerical Determination ◽  
Mixed Boundary Value Problem ◽  
Elastic Plates

An iterative method is employed to obtain numerical solutions of a two-dimensional mixed boundary-value problem for rectangular elastic plates. The theory of plane stress is used. This problem is encountered when the edge of a uniformly heated plate is bonded to a rigid body and then allowed to cool. The numerical results are compared with two formal asymptotic expansions of the solution. They correspond to the limiting cases of a thin strip and a long strip. The development of boundary layers near the edges of the plate is observed. The numerically determined stresses achieve their largest values at the corner of the bonded edge.

Sign in / Sign up

Export Citation Format

Share Document