Low Reynolds number airflow in the pulmonary acinus and aerosol particle kinetics therein are significantly conditioned by the nature of the tidal motion of alveolar duct geometry. At least two components of the ductal structure are known to exhibit stress-strain hysteresis: smooth muscle within the alveolar entrance rings, and surfactant at the air-tissue interface. We hypothesize that the geometric hysteresis of alveolar duct is largely determined by the interaction of the amount of smooth muscle & connective tissue in ductal rings, septal tissue properties, and surface tension-surface area characteristics of surfactant. To test this hypothesis, we have extended the well-known structural model of the alveolar duct by Wilson and Bachofen (J. Appl. Physiol. 52(4): 1064–1070, 1982) by adding realistic elastic and hysteretic properties of 1) the alveolar entrance ring, 2) septal tissue, and 3) surfactant. With realistic values for tissue and surface properties, we conclude that: 1) there is a significant, and underappreciated, amount of geometric hysteresis in alveolar ductal architecture; and 2) the contribution of smooth muscle and surfactant to geometric hysteresis are of opposite senses, tending toward cancellation. Quantitatively, the geometric hysteresis found experimentally by Miki et al. (J. Appl. Physiol. 75(4): 1630–1636, 1993) is consistent with little or no smooth muscle tone in anesthetized rabbits in control conditions, and with substantial smooth muscle activation following methacholine challenge. The observed local hysteretic boundary motion of the acinar duct would result in irreversible acinar flow fields, which might be important mechanistic contributors to aerosol mixing and deposition deep in the lung.

SUMMARYStress calculation for a biaxial isotropic material model of a biological membrane and for hysteretic models of muscle fibres and surfactant is presented in the paper. The non-linear elastic membrane model is defined by uniaxial and biaxial stress-stretch relations, while the hysteretic models of tissue fibres and surfactant are described by the stress-stretch and surface tension-surfactant area ratio constitutive relationships, respectively. The conditions when tissue is or is not covered by surfactant are considered. It is assumed that the material is subjected to cyclic loading. Quasi-static and steady conditions are considered.The models are implemented in large strain finite element incremented-iterative analysis of shell deformations. Numerical examples demonstrate characteristics of the computational procedures and structural response of biological membranes when subjected to cyclic loading.Hysteretic response of biological membranes subjected to cyclic loading is caused by hysteresis of fibres and hysteresis of surfactant. The hysteretic effects may play an important role in the physiology of human body.

SUMMARYThe Gurson material model has broad applications in fracture mechanics, large strain deformations and failure of metals. Void growth and void nucleation are included in the model considered in this paper. An implicit stress integration procedure with calculation of the consistent tangent moduli is developed for the Gurson model. The general 3D deformations and the plane stress conditions are considered. The procedure is robust, simple and computationally e cient, suitable for use within the ÿnite element method (FEM). It represents an application of the governing parameter method (GPM) for stress integration in case of inelastic material deformation. A large strain formulation, based on the multiplicative decomposition of the deformation gradient for material with plastic change of volume and logarithmic strains, is used in the paper. The developed numerical procedure for stress integration is applicable to small and large strains conditions. Solved examples illustrate the main features of the developed numerical algorithm.

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