Aggregate modulus

In relation to biomechanics, the aggregate modulus (Ha) is a measurement of the stiffness of a material at equilibrium when fluid has ceased flowing through it.^[1] The aggregate modulus can be calculated from Young's modulus (E) and the Poisson ratio (v).^[1][2]

${\displaystyle Ha={\frac {E(1-v)}{(1+v)(1-2v)}}}$

The aggregate modulus of a similar specimen is determined from a unidirectional deformational testing configuration, i.e., the only non-zero strain component is E₁₁.^[3] This configuration is opposed to the Young's modulus, which is determined from a unidirectional loading testing configuration, i.e., the only non-zero stress component is, say, in the e₁ direction.^[3] In this test, the only non-zero component of the stress tensor is T₁₁.^[3]

References

1. Mansour, J. M. (2003). Biomechanics of cartilage. Kinesiology: the mechanics and pathomechanics of human movement, 2, 66-79.
2. Boschetti, Federica; Pennati, Giancarlo; Gervaso, Francesca; Peretti, Giuseppe M.; Dubini, Gabriele (2004). "Biomechanical properties of human articular cartilage under compressive loads". Biorheology. 41 (3–4): 159–166. ISSN 0006-355X. PMID 15299249.
3. Loret, Benjamin; Simões, Fernando M. F. (2017-05-08), "Biomechanical topics in soft tissues", Biomechanical Aspects of Soft Tissues, Boca Raton, FL: CRC Press, pp. 1–10, ISBN 978-1-315-11078-3, retrieved 2022-03-15