期刊
ARCHIVE OF APPLIED MECHANICS
卷 80, 期 5, 页码 453-465出版社
SPRINGER
DOI: 10.1007/s00419-009-0383-1
关键词
Multiphase; Phase transition; Growth; Remodeling; Biomechanics; Tissue modeling
类别
A continuum triphase model (i.e., a solid filled with fluid containing nutrients) based on the theory of porous media (TPM) is proposed for the phenomenological description of growth and remodeling phenomena in isotropic and transversely isotropic biological tissues. In this study, particular attention is paid on the description of the mass exchange during the stress-strain- and/or nutrient-driven phase transition of the nutrient phase to the solid phase. In order to define thermodynamically consistent constitutive relations, the entropy inequality of the mixture is evaluated in analogy to Coleman and Noll (Arch Ration Mech Anal 13:167-178, 1963). Thereby, the choose of independent process variables is motivated by the fact that the resulting phenomenological description derives both a physical interpretability and a comprehensive description of the coupled processes. Based on the developed thermodynamical restrictions constitutive relations for stress, mass supply and permeability are proposed. The resulting system of equation is implemented into a mixed finite element scheme. Thus, we obtain a coupled calculation concept to determine the solid motion, inner pressure as well as the solid, fluid and nutrient volume fractions.
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