The effect of local inertia around the crack-tip in dynamic fracture of soft materials
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ORIGINAL PAPER
The effect of local inertia around the crack-tip in dynamic fracture of soft materials Anshul Faye1
· Yoav Lev2 · K. Y. Volokh2
Received: 3 January 2019 / Accepted: 25 January 2019 © Springer Nature Switzerland AG 2019
Abstract Phase-field or gradient-damage approaches offer elegant ways to model cracks. Material stiffness decreases in the cracked region with the evolution of the phase-field or damage variable. This variable and, consequently, the decreased stiffness are spatially diffused, which essentially means the loss of the internal links and the bearing capacity of the material in a finite region. Considering the loss of material stiffness without the loss of inertial mass seems to be an incomplete idea when dynamic fracture is considered. Loss of the inertial mass in the damaged material region may have significant effect on the dynamic failure processes. In the present work, dynamic fracture is analyzed using a theory, which takes into account the local loss of both material stiffness and inertia. Numerical formulation for brittle fracture at large deformations is based on the Cosserat point method, which allows suppressing the hourglass type deformation modes in simulations. Based on the developed algorithms, the effect of the material inertia around a crack tip is studied. Two different problems with single and multiple cracks are considered. Results suggest that in dynamic fracture the localized loss of mass plays an important role at the crack tip. It is found, particularly, that the loss of inertia leads to lower stresses at the crack tip and, because of that, to narrower cracks as compared to the case in which no inertia loss is considered. It is also found that the regularized problem formulation provides global convergence in energy under the mesh refinement. At the same time, the local crack pattern might still depend on the geometry of the unstructured mesh. Keywords Fracture · Material sink · Dynamic · Phase-field · Coupled · Inertia
1 Introduction Understanding and modeling of the crack propagation is arguably the central problem in solid mechanics. Two major classes of approaches for analysis of crack propagation are surface and bulk material failure models, also known as Cohesive Surface Model (CSM) and Continuum Damage Model (CDM), respectively. CSM defines interaction between the separating surfaces using traction-separation laws [2, 7, 9, 11, 14, 25, 27, 35, 43, 50]. They are most effective when possible crack paths are already known. If the path is not known, then defining the criteria for nucleation and growth of cracks still remains a challenge [26]. On the other hand, CDM describes the failure via damage constitutive laws [5, 12, 15, 18, 20, 22, 23, 38, 44, 45, 49]. When using CDM, important features such as damage nucleation, propagation, and branching naturally derive from Anshul Faye
[email protected] Yoav Lev [email protected] K. Y. Volokh [email protected] 1
Department of Mechanical Engineering, Indian Institute of Technology Bhilai, Rai
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