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Abstract The crack band model, which was shown to provide a superior computational representation of fracture of quasibrittle materials (in this journal, May 2022), still suffers from three limitations: (1) The material damage is forced to be uniform across a one-element wide band because of unrestricted strain localization instability; (2) the width of the fracture process zone is fixed as the width of a single element; and (3) cracks inclined to rectangular mesh lines are represented by a rough zig-zag damage band. Presented is a generalization that overcomes all three, by enforcing a variable multi-element width of the crack band front controlled by a material characteristic length l0. This is achieved by introducing a homogenized localization energy density that increases, after a certain threshold, as a function of an invariant of the third-order tensor of second gradient of the displacement vector, called the sprain tensorη, representing (in isotropic materials) the magnitude of its Laplacian (not expressible as a strain-gradient tensor). The continuum free energy density must be augmented by additional sprain energy Φ(l0η), which affects only the postpeak softening damage. In finite element discretization, the localization resistance is effected by applying triplets of self-equilibrated in-plane nodal forces, which follow as partial derivatives of Φ(l0η). The force triplets enforce a variable multi-element crack band width. The damage distribution across the fracture process zone is non-uniform but smoothed. The standard boundary conditions of the finite element method apply. Numerical simulations document that the crack band propagates through regular rectangular meshes with virtually no directional bias.
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A model-based simulation framework for coupled acoustics, elastodynamics, and damage with application to nano-pulse lithotripsy
We develop a model for solid objects surrounded by a fluid that accounts for the possibility of acoustic pressures giving rise to damage on the surface of the solid. The propagation of an acoustic pressure in the fluid domain is modeled by the acoustic wave equation. On the other hand, the response of the solid is described by linear elastodynamics coupled with a gradient damage model, one that is based on a cohesive-type phase-field description of fracture. The interaction between the acoustic pressure and the deformation and damage of the solid are represented by transmission conditions at the fluid-solid interface. The resulting governing equations are discretized using a finite-element/finite-difference method that pays particular attention to the spatial and temporal scales that need to be resolved. Results from model-based simulations are provided for a benchmark problem as well as for recent experiments in nanopulse lithotripsy. A parametric study is performed to illustrate how damage develops in response to the driving force (magnitude and location of the acoustic source) as a function of the fracture resistance of the solid. The results are shown to be qualitatively consistent with experimental observations for the location and size of the damage fields on the solid surface. A study of limiting cases also suggests that both the threshold for damage and the critical fracture energy are important to consider in order to capture the transition from damage initiation to complete localization. A low-cycle fatigue model is proposed that degrades the fracture resistance of the solid as a function of accumulated tensile strain energy, and it is shown to be capable of capturing damage localization in simulations of multi-pulse nano-pulse lithotripsy.
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- PAR ID:
- 10544972
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- International Journal of Solids and Structures
- Volume:
- 289
- Issue:
- C
- ISSN:
- 0020-7683
- Page Range / eLocation ID:
- 112626
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.ijsolstr.2023.112626
