Rate-dependent phase-field damage modeling of rubber and its experimental parameter identification

Abstract

Phase-field models have the advantage in that no geometric descriptions of cracks are required, which means that crack coalescence and branching can be treated without additional effort. Miehe et al. [1] introduced a rate-independent phase-field damage model for finite strains in which a viscous damage regularization was proposed. We extend the model to depend on the loading rate and time by incorporating rubber's strain-rate dependency in the constitutive description of the bulk, as well as in the damage driving force. The parameters of the model are identified using experiments at different strain rates. Local strain fields near the crack tip, obtained with digital image correlation (DIC), are used to help identify the length scale parameter. Three different degradation functions are assessed for their accuracy to model the rubber's rate-dependent fracture. An adaptive time-stepping approach with a corrector scheme is furthermore employed to increase the computational efficiency with a factor of six, whereas an active set method guarantees the irreversibility of damage. Results detailing the energy storage and dissipation of the different model constituents are included, as well as validation results that show promising capabilities of rate-dependent phase-field modeling.

Fatigue phase-field damage modeling of rubber using viscous dissipation: Crack nucleation and propagation

“…• Applying a cyclic load to the rate-dependent phase-field damage model of [16], we show that this model describes fatigue damage but yields poor accuracy.…”

“…Consequently, they are able to handle crack propagation, branching and coalescence. The extension to finite strains and rubber was first published in [22], while [16] presented a rate-dependent phase-field damage model for rubbers.…”

“…the stress required to nucleate a crack [30]. [16] has shown that incorrect length scale parameters are identified if the identification is only based on the global mechanical response. To overcome this issue, local strain measurements should be included in the identification process.…”

“…• Therefore, we propose an extension of our previous constitutive model [16] so that fatigue damage under cyclic loading can accurately be described.…”

Fusing the Seth–Hill strain tensors to fit compressible elastic material responses in the nonlinear regime

“…The increase of man-made materials that can undergo large elastic compressible deformations (Wismans et al, 2010;Schraedler et al, 2011;Kucheyev et al, 2012;Pokorný et al, 2017), as well as the increased interest in biological tissues that can undergo large elastic compressible deformations (Cotin et al, 1999;Baaijens et al, 2005;Hrapko et al, 2006;Carniel & Fancello, 2017), is partially responsible for this. In contrast to hypoelasticity (Truesdell, 1955;Khan et al, 2010;Beex & Peerlings, 2012), hyperelasticity also allows the formulation of error estimators in terms of stored and dissipated energies (Lovadina & Stenberg, 2006;Bui et al, 2018), which are invariant scalars, and it avoids erroneous energy dissipation of dissipative material models (Håkanson et al, 2005;Harrysson & Ristinmaa, 2008;Loew et al, 2019). Hyperelasticity is thus not only important for incompressible materials, but also for compressible materials.…”