Mesoscopic Modeling for Continua with Pores: Application in Biological Soft Tissue

A model for the simulation of Kirkendall voiding in metallic materials is presented based on vacancy diffusion, elastic-plastic and rate-dependent deformation of the material. Starting with a phenomenological explanation of the Kirkendall effect we briefly discuss the consequences on the reliability of microelectronic components. Then, a constitutive model for void nucleation and growth is introduced, which can be used to predict the temporal development of voids in solder joints during thermal cycling. We present numerical studies and discuss the potential of the results for the failure analysis of joining connections.

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“…The surface energy of one void with radius is written as (17) where is the surface energy per unit undeformed area [N/m].…”

Section: B Surface Energymentioning

confidence: 99%

“…To derive an evolution equation for the void distribution we make use of a mesoscopic concept described in detail, e.g., in [13], [17], and [18]. In this paper, we do not account for a dependence of the void distribution on the spatial position , and set .…”

Section: Evolution Of a Void Ensemblementioning

confidence: 99%

Condensation and Growth of Kirkendall Voids in Intermetallic Compounds

Weinberg

Böhme

2009

IEEE Trans. Comp. Packag. Technol.

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“…A detailed model of cavitation induced damage is outlined in Weinberg and Böhme (2008), here we will shortly summarize the basic ideas. From the mechanical point of view the (ESWL-treated) human kidney is a conglomerate of liquid-containing cells in which the hypersonic excitation activates the nucleation and oscillation of bubbles.…”

Section: Materials Modelmentioning

confidence: 99%

“…we obtain an ordinary differential equation for every pore radius a(t), see Weinberg and Böhme (2008) for more details. Solving this equation for different initial conditions yields a constitutive relation for bubble growth.…”

Section: Materials Modelmentioning

confidence: 99%

Kidney damage in extracorporeal shock wave lithotripsy: a numerical approach for different shock profiles

Weinberg

Ortiz

2008

Biomech Model Mechanobiol

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In shock-wave lithotripsy--a medical procedure to fragment kidney stones--the patient is subjected to hypersonic waves focused at the kidney stone. Although this procedure is widely applied, the physics behind this medical treatment, in particular the question of how the injuries to the surrounding kidney tissue arise, is still under investigation. To contribute to the solution of this problem, two- and three-dimensional numerical simulations of a human kidney under shock-wave loading are presented. For this purpose a constitutive model of the bio-mechanical system kidney is introduced, which is able to map large visco-elastic deformations and, in particular, material damage. The specific phenomena of cavitation induced oscillating bubbles is modeled here as an evolution of spherical pores within the soft kidney tissue. By means of large scale finite element simulations, we study the shock-wave propagation into the kidney tissue, adapt unknown material parameters and analyze the resulting stress states. The simulations predict localized damage in the human kidney in the same regions as observed in animal experiments. Furthermore, the numerical results suggest that in first instance the pressure amplitude of the shock wave impulse (and not so much its exact time-pressure profile) is responsible for damaging the kidney tissue.

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“…Evidently, the void radius r is positive and so we consider only positive distributions

f (r)

here. Moreover, there are many examples, where the probability of large pores, cavities or inclusions is significantly smaller than the probability of small ones, see [] and discussions therein. This corresponds to right‐skewed distributions.…”

Section: Pore Distribution Functionsmentioning

confidence: 99%

Stereological transformation of pore size distributions with application to soft polymer and FDM‐printed specimens

2019

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The presence of voids or cavities inside a material plays an important role in several applications. Recently, their investigation has gained attention to understand the effect of such inhomogeneities on 3D‐printed structures. Such structures could be already weakened due to the procedure of additive manufacturing. Voids can be visualized by computed tomography but practically a micrograph obtained by a planar cut through the material is simpler and cheaper. This requires, however, the reconstruction of the three‐dimensional distribution from statistical micrograph analyses. Here the reliability of such reconstruction is studied. To this end, spherical voids are considered whose size distribution can be characterized by one scalar number, e.g. the void radius. The corresponding distributions are typically positive right‐tailed, indicating more small than large voids. Following the work of S. D. Wicksell, the distributions of the observed planar cut are linked to the distribution of the spherical void size in space. The calculation of the stereological transformations is outlined in detail and several examples are provided to point on misleading conclusions. The presented analysis is applied to three typical soft‐polymer materials.

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Mesoscopic Modeling for Continua with Pores: Application in Biological Soft Tissue

Cited by 7 publications

References 9 publications

Condensation and Growth of Kirkendall Voids in Intermetallic Compounds

Condensation and Growth of Kirkendall Voids in Intermetallic Compounds

Kidney damage in extracorporeal shock wave lithotripsy: a numerical approach for different shock profiles

Stereological transformation of pore size distributions with application to soft polymer and FDM‐printed specimens

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