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Mathematics and Mechanics of Solids
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Material Identification of Nonlinear Solids Infused with a Fluid

J. Hron

Departments of Mechanical Engineering and Biomedical Engineering, Texas A&M University, College Station, TX 77843, USA

J. D. Humphrey

Departments of Mechanical Engineering and Biomedical Engineering, Texas A&M University, College Station, TX 77843, USA

K. R. Rajagopal

Departments of Mechanical Engineering and Biomedical Engineering, Texas A&M University, College Station, TX 77843, USA

It is common in the theory of mixtures to prescribe a constitutive relation for the homogenized mixture rather than for each of the individual constituents. Such a relation should describe well the behavior of the mixture, that is experimental data. In this paper, we offer a theoretical framework to guide the performance and interpretation of biaxial tests on solid-fluid mixtures and, in particular, to identify forms of the response functions directly from the data. Moreover, in contrast to prior work, we include the effects of the inertia of the fluid constituent. The potential importance of the latter is illustrated via solutions for an assumed form of the Helmholtz potential for the mixture.

Key Words: Mixture theory • constitutive relations • finite deformations • soft tissues • biaxial tests

Mathematics and Mechanics of Solids, Vol. 7, No. 6, 629-646 (2002)
DOI: 10.1177/108128602029661
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