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Öğrenci Grubu

Herkese Açık·73 üye
Elijah Hill
Elijah Hill

VERIFIED Full Simulation Mechanical 2007 Crack



This paper presents an experimental study to understand the localized soft-tissue deformation phase immediately preceding crack growth as observed during the cutting of soft tissue. Such understanding serves as a building block to enable realistic haptic display in simulation of soft tissue cutting for surgical training. Experiments were conducted for soft tissue cutting with a scalpel blade while monitoring the cutting forces and blade displacement for various cutting speeds and cutting angles. The measured force-displacement curves in all the experiments of scalpel cutting of pig liver sample having a natural bulge in thickness exhibited a characteristic pattern: repeating units formed by a segment of linear loading (deformation) followed by a segment of sudden unloading (localized crack extension in the tissue). During the deformation phase immediately preceding crack extension in the tissue, the deformation resistance of the soft tissue was characterized with the local effective modulus (LEM). By iteratively solving an inverse problem formulated with the experimental data and finite element models, this measure of effective deformation resistance was determined. Then computational experiments of model order reduction were conducted to seek the most computationally efficient model that still retained fidelity. Starting with a 3-D finite element model of the liver specimen, three levels of model order reduction were carried out with computational effort in the ratio of 1.000:0.103:0.038. We also conducted parametric studies to understand the effect of cutting speed and cutting angle on LEM. Results showed that for a given cutting speed, the deformation resistance decreased as the cutting angle was varied from 90 degrees to 45 degrees. For a given cutting angle, the deformation resistance decreased with increase in cutting speed.




FULL Simulation Mechanical 2007 crack


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These models provided new insight into key parameters and driving forces, however, the micro-mechanical processes involved during dynamical crack propagation are still essentially unknown. While their direct observation is so far not feasible, the discrete element method (DEM) has previously been successfully used to study the influence of snow microstructure on the mechanical behavior of snow18,19,20,21 and crack propagation in weak layers15,22. Therefore, DEM is an appealing method to study the effect of the complex and highly porous snow microstructure on the dynamics of crack propagation, which does not require the assumption of a complex macroscopic constitutive model. DEM allows the generation of highly porous samples crucial to model snow failure and was, for instance, used to perform 2-D simulations of a PST yielding good agreement with field experiments. However, the oversimplified shape (triangular structure) and the 2-D character of the weak layer employed by Gaume et al.15 prevented a detailed analysis of the internal stresses during crack propagation.


Our aim is therefore to numerically simulate an exemplary experimental PST with a 3-D DEM model to better understand the micromechanics involved during dynamical snow fracture. We first present a method to evaluate the location of the crack tip, which is particularly challenging due to the closure of crack faces during propagation. Our model reproduced the experimentally observed displacement field, accelerations and crack propagation speed well. Furthermore, the model provides detailed insight into the micro-mechanical processes and stresses within the weak layer and allows us to identify the main drivers of crack propagation.


During the simulation, we tracked micro-mechanical quantities: the position of bond-breaking events, normal displacement and acceleration as well as shear and normal stresses at the top of the basal layer. The temporal evolution of these quantities revealed six distinct sections during the fracture process (Fig. 4, labeled at the top from 1 to 5). In the following, we describe five of the six sections for the situation shown in Fig. 4, i.e. when the crack tip is at about at 2.3 m, corresponding to a simulation time of 0.344 s.


Mechanical parameters during crack propagation: snapshot at 0.344 s (after the start of the simulation). (a) Average normal slab displacement in blue and average normal slab acceleration in green. (b) Top view of the weak layer showing the bond states: in grey broken bonds, in red bonds that are breaking at current time step. The blue line shows the breaking bond distribution along the length of the beam. (c) Normal stress \(\sigma _zz\) and (d) shear stress \(\tau _zx\) along the length of the beam. The light red box highlights the fracture process zone (FPZ). The light yellow box highlights the part of the beam where the stresses are redistributed. The orange vertical dashed lines indicate the start and end of the different sections (1, 2, 3, 4, and 5).


We developed a 3-D discrete element model to investigate the micro-mechanical processes at play during crack propagation in snow fracture experiments. Microscopic model properties were calibrated based on macroscopic snowpack quantities using the method developed by Bobillier et al.18. The field data of a PST fracture experiment was recorded during winter 2019 and analyzed with image correlation techniques11. The experiment provides bulk snow properties and the displacement field during crack propagation and allows studying mixed-mode failure of a porous weak snow layer. Our DEM model of the PST accurately reproduced the observed dynamics of crack propagation including the structural collapse of the weak layer. Moreover, our PST model provides insight into the micro-mechanics of the failure processes before and during self-sustained crack propagation.


The DEM model of the PST experiment allows insight into the micro-mechanical behavior of weak layer failure. We suggest six sections to describe the crack dynamics during a PST experiment; (1) sawing, (2) weak layer collapse, (3) fracture process zone, (4) elastic redistribution, (5) undisturbed (initial) stress state, and slab-substratum contact (6). We looked into three of these sections in more detail: (2) The structural weak layer collapse (crushing) where the stresses remain low and only a few bonds are breaking. (3) The fracture process zone where the material softens and most of the bonds are breaking and where the stress is maximal. (4) The elastic redistribution zone where the stresses are converging to the initial undistributed stress state and no bonds are breaking. During steady state propagation, we observed that these three sections travel along the beam keeping their behavior, which is defined by the geometrical and mechanical properties (Fig. 5; Supplementary Movie 2). Frame by frame, the stresses were analyzed and the results indicated a mixed-mode bond failure with a main normal stress component (Supplementary Movie 2). We also noted (not shown) that the PST width does not influence the crack tip morphology. Before reaching a steady state speed regime, we defined a transitional regime where we observed a decrease in the normal stress and an increase of the shear stress component.


Gaume et al.15 introduced a 2-D DEM model of a PST experiment to study crack propagation. Their model consisted of a single particle base layer, a triangular shape for the weak layer structure and a square particle matrix for the slab layer. Their simple model was used to study the influence of mechanical parameters on crack propagation. However, the simplistic layer representation precluded a detailed micro-mechanical analysis. The model presented here overcomes this limitation and allows insight into the micro-mechanics, yet at the expense of high computational cost. Still, to keep the computational cost reasonable (hours to day), the particle radius chosen does not represent single snow grains, but represents a mesoscale model of snow18. To permit this analysis, we discretized the column length and the mesh size was driven by the particle size, which remains the main model limitation. Observing the final slab state suggested the existence of plastic deformation and slab fracture. By modifying slab tensile strength, we were able to reproduce the observed slab fracture (Appendix 1). However, the contact law we use does not allow for non-recoverable slab deformation.


As our DEM approach allows insight into bond-breaking events and stresses, we suggest six sections to describe the crack dynamics during a PST experiment. In particular, three distinct sections travel along the beam while keeping their behavior during the steady state stress regime: weak layer structural collapse, fracture process zone, and elastic redistribution. The detailed micro-mechanical analysis of stresses for weak layer failure suggests that the main drivers of crack propagation is the mixed mode stress concentration at the crack tip (compression and shear).


In future, we will perform a parameter study to describe the drivers of crack speed at the slope scale leading to avalanche release. The effects of slope angle and mechanical parameters on crack propagation will be studied to eventually improve the prediction of avalanche size.


Defect formation is a common problem in selective laser melting (SLM). This paper provides a review of defect formation mechanisms in SLM. It summarizes the recent research outcomes on defect findings and classification, analyzes formation mechanisms of the common defects, such as porosities, incomplete fusion holes, and cracks. The paper discusses the effect of the process parameters on defect formation and the impact of defect formation on the mechanical properties of a fabricated part. Based on the discussion, the paper proposes strategies for defect suppression and control in SLM.


Defects in an SLM process cause stress concentration in the fabricated part, which may lead to the part failure. When stress exceeds the material limit, a crack may form and gradually propagate in the part. The following Sections 4.1-4.2 are dedicated to discussing the influence of defects on the mechanical properties in the SLM parts.


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