Soft tissue mechanics are essential for organ function, yet experimental measurement is hindered by small size, large deformation, active contraction, dissection damage, and the lack of a natural state, with most data derived from one‑dimensional tests that do not capture two‑dimensional behavior. The study summarizes laboratory rheology of soft tissues and introduces a mathematical stress–strain model to serve as a foundation for organ function analysis. The authors propose an orthotropic constitutive relation σij = Cijkl′ekl + Cijkleklexp{…} + pδi, incorporating strain invariants J2, loading/unloading constants, and applicable to skin, mesentery, and muscle under constant‑rate loading, with index ranges 1–3 (or 1–2 for plane stress). They report newly acquired two‑dimensional data from skin elongation tests and mesentery torsion experiments.
To understand the physiological function of vital organs we must know the mechanical properties of the tissues. Experimental determination of the mechanical properties of living tissues has many difficulties, such as the small size, large deformation, active contraction, damage due to dissection, i naccessibility or non-existence of a "natural" state, and the necessity of keeping the specimens alive. In this paper, major features of the rheology of soft tissues obtained in our laboratory are summarized, and a mathematical description is offered to serve as a starting point for the analysis of the function of the organs. Almost all published rheological data on soft tissues were obtained in one-dimensional condition—simple elongation of a slender cylindrical body, strip-biaxial or homogeneous—biaxial tension of a membrane. Recently we have collected data on two-dimensional testing of the skin, and torsion of the mesentery. From these we propose the following stress (σij)-strain (eij) relation for such tissues as the skin, the mesentery, and the muscle in the passive state, when subjected to loading and unloading at a constant rate σij=Cijkl′ekl+Cijkleklexp{amn(emn−emn(0))+b(J2−J2(0))δij}+pδi where J2=16[(e11−e22)2+(e22−e33)2+(e33−e11)2]+e122+e232+e312 is the second strain invarient; x1, x2, x3 are axes of orthotropic symmetry, Cijkl, Cijkl′ are orthotropic tensors of rank 4 familiar in the classical theory of elasticity, amn and b are constants which differ in loading from unloading (defined by whether ∂(amnemn+bJ2)/∂t is positive or negative), but are only slightly dependent on the strain rate. This equation does not apply to highly structured tissues such as blood vessels or the lung. amn emn(0) and J2(0) are the largest values of these strain invariants for which the formulas are expected to be applicable. The indexes range over 1, 2, 3. For membranes in plane stress the indexes range over 1, 2 and the p term should be deleted. The summation convention over a repeated index is used.