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A number of investigators have shown that the nonlinear stress–strain data for articular cartilage can be described by a two-parameter (A,B) exponential stress–strain (σ-ε) relationship: σ = A[exp(Bε) − 1]. It can be shown from this representation that the derivative or tangent modulus is directly related to the stress: dσ/dε = Bε + C. Table 1 provides the coefficients A, B, and C and the tensile Young’s modulus (E) determined from the linear portion of the tensile σ–ε curve for bovine cartilage after cutting several slices from the uppermost surface, both parallel and perpendicular to split-lines. Using this data, calculate the tangent modulus for each slice for parallel specimens and perpendicular samples at 5 %, 10 %, and 15 % tensile strains. (i) Compare this result with the Young’s modulus (E). (ii) Explain the differences and similarities found relative to E. Table 1 parameters A, B, and C (= AB) and Young’s modulus, E, of bovine articular cartilage ( the second picture is part of standard answer)

 
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