Crack Propagation Behavior Under Static and Dynamic Loading using the VIB Model

CRACK PROPAGATION BEHAVIOR UNDER STATIC AND DYNAMIC LOADING USING THE VIRTUAL INTERNAL BOND MODEL

K. Jimmy Hsia (CSM Senior Academic Lead, ARL), TAM and NCSA/UIUC
Ganesh Thiagarajan, NCSA/UIUC
Yonggang Huang, MIE/UIUC

Research Objectives:

Numerical simulations of crack initiation, propagation and branching using the finite element framework.
Implementation of the Virtual Internal Bond (VIB) method (Gao and Kliein, Journal of Mechanics of Physics and Solids,Vol. 46, No. 2, pp. 187-218) as a user defined material model in ABAQUS (a commercial finite element package).
Numerically simulate the responses of structures, made of homogeneous materials or with bi-material interfaces, under static and dynamic loading.
Study the numerical stability, convergence and performance of the model.

Methodology:

The VIB model has been implemented in both the implicit and explicit integration schemes using the user defined material model routines (UMAT and VUMAT) and various case studies have been performed.

Results:

The following case studies were performed and the results are presented in the figures indicated below. The explicit scheme had proved to be the most effective scheme, both for convergence and its ability to predict crack behavior in a robust manner.

Plate with a central hole problem subjected to uniaxial deformation along the y-direction (Figures 1 and 2)
Impact of a deformable disk against a rigid wall (Figures 3 to 8)
To view a movie (Quicktime format) of the
Impact Simulation click here.
Buckling driven delamination (Figure 9)

Significance:

One of the biggest advantages of the VIB model is that it is capable of simulating fracture by using a hyperelastic constitutive model, based physically on the internal bond behavior between the material points. Neither a separate fracture criterion nor a computationally intensive cohesive boundary element formulation is needed.

Figure 1. Crack Pattern for Plate with Hole Problem (Uniaxial loading (y-direction))

Figure 2. Crack Branching Behavior for Plate with Hole Problem

Figure 3. Stage 1: Before Impact

Figure 4. Stage 2: At Impact

Figure 5. Stage 3: During Impact

Figure 6. Stage 4: Before Separation

Figure 7. Stage 5: After Separation

Figure 8. Stage 6: End Deformation

Figure 9. Buckling Driven Delamination