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Fractional-order nonlinear hereditariness of tendons and ligaments of the human knee

Luca-Deseri's picture


Luca-Deseri's picture

In this paper, the authors pointed out the main features of a wide experimental campaign devoted to investigate the mechanical behaviour of knee tendons subjected to long-standing loads. The results of the experimental campaign show that creep and relaxation behaviour of the tendons may be well captured by power laws in the ranges of strain (1–5%) and stress (0–16 Mpa) considered.

The order of the power law proved to be different between creep and relaxation proving that some form of nonlinearity is involved in the micromechanics of the tissue so that no linear theory of fractional hereditariness may be used to capture the mechanics of tendons. Moreover, it has been observed that the material parameters are significative dependent on the applied stress in creep tests as well as on the applied strain during relaxation.

These features, already observed in other mechanical tests in the last 20 years, have never been conducted in combination on human tendons, yielding one to conclude that the finding relaxation runs faster than creep is valid also on human knee patellar and hamstring tendons.

Based on this observation, the paper was devoted to the introduction of an analytical model to describe creep and relaxation showing that some closed-form expression relating creep and relaxation parameters could be established.

Direct comparison among results of such expressions and the measured values showed excellent matches with slight coefficient of variations and, in order to show that such relations hold whatever kind of test is considered, a numerical validation has been introduced with other than constant value of the applied strain (stress), namely linear and harmonically varying strain (stress).

The obtained results showed excellent match among the initial and the recovered values of the applied stress (strain) leading one to conclude that the proposed relations may be a benchmark to provide clinical support to the surgeons that apply pre-stress to the tendons before surgical replacement to reconstruct anterior cruciate ligaments functionality.

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