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A Model for Kidney Tissue Damage under High Speed Loading
Author(s) -
Weinberg Kerstin,
Colonius Tim,
Ortiz Michael
Publication year - 2004
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200410098
Subject(s) - finite strain theory , finite element method , viscoplasticity , mechanics , discretization , shock wave , constitutive equation , deformation (meteorology) , materials science , physics , classical mechanics , mathematical analysis , mathematics , thermodynamics , composite material
In a medical procedure to comminute kidney stones the patient is subjected to hypersonic waves focused at the stone. Unfortunately such shock waves also damage the surrounding kidney tissue. We present here a model for the mechanical response of the soft tissue to such a high speed loading regime. The material model combines shear induced plasticity with irreversible volumetric expansion as induced, e.g., by cavitating bubbles. The theory is based on a multiplicative decomposition of the deformation gradient and on an internal variable formulation of continuum thermodynamics. By the use of logarithmic and exponential mappings the stress update algorithms are extended from small‐strain to the finite deformation range. In that way the time‐discretized version of the porous‐viscoplastic constitutive updates is described in a fully variational manner. By numerical experiments we study the shock‐wave propagation into the tissue and analyze the resulting stress states. A first finite element simulation shows localized damage in the human kidney. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)