Variational eigenerosion for rate‐dependent plasticity in concrete modeling at small strain

Abstract

Summary In the context of eigenfracture scheme, the work at hand introduces a variational eigenerosion approach for inelastic materials. The theory seizes situations where the material accumulates large amounts of plastic deformations. For these cases, the surface energy entering the energy balance equation is rescaled to favor fracture, thus energy minimization delivers automatically the crack‐tracking solution also for inelastic cases. The minimization approach is sound and preserves the mathematical properties necessary for the Γ‐limit proof, thus the existence of (local) minimizers is guaranteed by the Γ‐convergence theory. Although it is not possible to demonstrate that the obtained minimizers are global, satisfactory results are obtained with the local minimizers provided by the method. Furthermore, with the goal of addressing the constitutive behavior of concrete, a Drucker‐Prager viscoplastic consistency model is introduced in the microplane setting. The model delivers a rate‐dependent three‐surface smooth yield function that requires hardening and hardening‐rate parameters. The independent evolution of viscoplasticity in different microplanes induces anisotropy in the mechanical response. The sound performance of the model is illustrated via numerical examples for both rate‐independent and rate‐dependent plasticity.

Incorporation of gradient-enhanced microplane damage model into isogeometric analysis

“…Crack propagation results are reported in reference (Ožbolt et al (2013), in which the experiments equivalent to our numerical simulations are conducted at different loading rates. Numerous attempts have been made so far with various damage or crack models to predict the experimental observations, see for example Qinami et al (2015), Indriyantho et al (2019); Qinami et al (2019) to only name a few.…”

“…Also, for the highest loading rate of 4300 mm/s, the numerical simulations show two branches which are consistent with the experimental results, see Figure 16(f). Although the first branch has successfully been simulated in previous researches (Ožbolt et al (2013); Qinami et al (2015), Indriyantho et al (2019); Qinami et al (2019), the secondary branch has not been ever to the best of our knowledge. Thus, our result is the first successful example for this peculiar phenomenon.…”

Impaktsicherheit von Baukonstruktionen durch mineralisch gebundene Komposite: Bauteilebene

“…Die Modellierung von Rissausbreitung in Festkörpern durch einen rissbeschreibenden Parameter, dessen Evolution durch die Variation eines Energiefunktionals bestimmt wird, ist vielversprechend [19, 21]. Die verwendete Phasenfeld‐Methode beschreibt die diskrete Rissfläche Γ durch eine regularisierte Näherung Γ l und ermöglicht die Quantifizierung der für die Bildung der Rissfläche notwendigen Energie.…”

Modelling of High Velocity Impact on Concrete Structures Using a Rate-Dependent Plastic-Damage Microplane Approach at Finite Strains

“…To deliver rate dependency of concrete at dynamic cases, the proposed model is also supplemented by a viscoplastic function, a so-called consistency type formulation, adopted from [ 36 ] and applied in [ 37 , 38 ], which is expressed as where denotes the viscosity parameter with an arbitrary value. As a consequence, considering rate dependency, Equation ( 18 ) yields where the function is modified as and, now, the intersection point T increases controlled not only by the parameter as in Equation ( 25 ) but also by the viscoplastic function as All functions , , and as seen in Equation ( 40 ) are now a function of , which are rate-dependent functions.…”