Natural strain has advantages for biotissue models and can be quickly and accurately approximated
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2003 Elsevier Science Ltd. All rights reserved. Except for lung, the instantaneous bulk modulus of soft biotissues is much greater than the shear moduH. Because a net flow of water into or out of the tissue is needed to change the volume appreciably, the dilatation is greatly dependent on loading frequency. In contrast, the response to distortion (i.e. shear) in cyclic loading is insensitive to frequency. Since the dilatational and the distortional response of soft tissues are drastically different, a strain tensor that intrinsically separates dilatation from distortion is potentially advantageous. Toward this end, natural strain InV is useful because dilatation and distortion additively decouple into the spherical and deviatoric parts of InV, respectively. Also, with a novel method of approximating it, InV can be quickly and accurately calculated for biotissues. For this approximation, the error diminishes as the strain decreases. The percent error is less than 0.25% for the entire range of deformation of soft tissues. For pure shear, the approximation is exact. Regardless of the distortion, the dilatational or spherical part of this approximation for InV is always exact.
