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The ability to selectively remove the structurally most relevant components of arterial wall tissues such as collagen and elastin enables ex vivo biomechanical testing of the remaining tissues, with the aim of assessing their individual mechanical contributions. Resulting passive material parameters can be utilized in mathematical models of the cardiovascular system. Using eighteen wall specimens fromnon-atherosclerotic human abdominal aortas (55±11 years; 9 female, 9 male), we tested enzymatic approaches for the selective digestion of collagen and elastin, focusing on their application to human abdominal aortic wall tissues from different patients with varying sample morphologies. The study resulted in an improved protocol for elastin removal, showing how the enzymatic process is affected by inadequate addition of trypsin inhibitor. We applied the resulting protocol to circumferential and axial specimens from the media and the adventitia, and performed cyclic uniaxial extension tests in the physiological and supra-physiological loading domain. The collagenase-treated samples showed a (linear) response without distinct softening behavior, while the elastase-treated samples exhibited a nonlinear, anisotropic response with pronounced remanent deformations (continuous softening), presumably caused by some sliding of collagen fibers within the damaged regions of the collagen network. In addition, our data showed that the stiffness in the initial linear stress-stretch regime at low loads is lower in elastin-free tissue compared to control samples (i.e. collagen uncrimping requires less force than the stretching of elastin), experimentally confirming that elastin is responsible for the initial stiffness in elastic arteries. Utilizing a continuum mechanical description to mathematically capture the experimental results we concluded that the inclusion of a damage model for the non-collagenous matrix material is, in general, not necessary. To model the softening behavior, continuous damage was included in the fibers by adding a damage variable which led to remanent strains through the consideration of damage. © 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.