A Bayesian estimation method for variational phase-field fracture problems

Khodadadian, Amirreza; Noii, Nima; Parvizi, Maryam; Abbaszadeh, Mostafa; Wick, Thomas; Heitzinger, Clemens

doi:10.1007/s00466-020-01876-4

Cited by 72 publications

(57 citation statements)

References 39 publications

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“…At the end of this section, it should be underlined that some fracture models other than the MTS and MS criteria, which are both based on the Theory of Critical Distances (TCD), have been recently proposed in literature. One of them is the phase-field fracture model [41]. In this model, the fracture problem is described by a phase-field method and by using the Bayesian inversion, the problem can be solved on a rather coarse mesh and the corresponding parameters can be fitted.…”

Section: Resultsmentioning

confidence: 99%

Fracture Behavior of Two Biopolymers Containing Notches: Effects of Notch Tip Plasticity

et al. 2020

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This paper analyzes the notch effect on the fracture behavior of two biomaterials (a brittle bone cement and a ductile dental material) under mode I loading. U-notched Brazilian disk (UNBD) specimens of both materials were tested under remote compression, determining the corresponding fracture loads and load-displacement curves. Additionally, cracked rectangular and semicircular bend (SCB) specimens were tested under symmetric three-point bending in order to determine the fracture toughness of the two materials. Then, fracture loads were derived theoretically by applying the maximum tangential stress (MTS) and the mean stress (MS) criteria. Due to the brittle linear elastic behavior of the bone cement material, the MTS and MS criteria were directly applied to this material; however, given the significant nonlinear behavior of the dental material, the two fracture criteria were combined with the Equivalent Material Concept (EMC) for the fracture analyses of the dental material specimens. The results reveal a very good accuracy of both the MTS and the MS criteria for the fracture analysis of bone cement notched specimens. In the case of the dental material, very good results are also obtained when combining the MTS and the MS criteria with the EMC. The proposed approach can be useful for the fracture analysis of a wide range of biopolymers, from brittle to ductile behavior.

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Section: Resultsmentioning

confidence: 99%

Fracture Behavior of Two Biopolymers Containing Notches: Effects of Notch Tip Plasticity

et al. 2020

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“…In particular due to the over-complicated geometry and content of concrete at multi-scales, in Figure 8 an example for PF modeling of water-induced failure mechanics in concrete microstructure is presented. In recent years, several brittle [ 259 , 260 , 261 , 262 , 263 , 264 , 265 , 266 , 267 , 268 , 269 , 270 , 271 , 272 , 273 , 274 , 275 , 276 , 277 , 278 , 279 , 280 , 281 , 282 , 283 , 284 , 285 , 286 , 287 , 288 , 289 , 290 , 291 , 292 , 293 , 294 , 295 , 296 ] and ductile [ 149 , 297 , 298 , 299 , 300 , 301 , 302 , 303 , 304 , 305 , 306 , 307 , 308 ...…”

Section: Phase-field Modeling For Fracture Mechanismsmentioning

confidence: 99%

A Review on Cementitious Self-Healing and the Potential of Phase-Field Methods for Modeling Crack-Closing and Fracture Recovery

et al. 2020

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Improving the durability and sustainability of concrete structures has been driving the enormous number of research papers on self-healing mechanisms that have been published in the past decades. The vast developments of computer science significantly contributed to this and enhanced the various possibilities numerical simulations can offer to predict the entire service life, with emphasis on crack development and cementitious self-healing. The aim of this paper is to review the currently available literature on numerical methods for cementitious self-healing and fracture development using Phase-Field (PF) methods. The PF method is a computational method that has been frequently used for modeling and predicting the evolution of meso- and microstructural morphology of cementitious materials. It uses a set of conservative and non-conservative field variables to describe the phase evolutions. Unlike traditional sharp interface models, these field variables are continuous in the interfacial region, which is typical for PF methods. The present study first summarizes the various principles of self-healing mechanisms for cementitious materials, followed by the application of PF methods for simulating microscopic phase transformations. Then, a review on the various PF approaches for precipitation reaction and fracture mechanisms is reported, where the final section addresses potential key issues that may be considered in future developments of self-healing models. This also includes unified, combined and coupled multi-field models, which allow a comprehensive simulation of self-healing processes in cementitious materials.

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“…After analyzing the results, we created a Finite Element Model (FEM) in a commercial software (ABAQUS) in order to simulate the transient effects of applying and removing strain. Finite element is a common solver of problems related to the mechanical behavior of materials and, recently, it has been widely used [ 23 , 24 , 25 ]. The adequate results of simulating these responses show that both relaxation and recovery can be modeled with accuracy and hence are possible to be described by the viscoelastic theory, as commercial software, such as ABAQUS, uses time domain constitutive equations of viscoelasticity [ 26 ].…”

Section: Introductionmentioning

confidence: 99%

Transient Effects of Applying and Removing Strain on the Mechanical Behavior of Rubber

2020

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For viscoelastic materials, the relationship between stress and strain depends on time, where the applied strain (or stress) can be expressed as a step function of time. In the present work, we investigated two temporary effects in the response of viscoelastic materials when a given strain is applied and then removed. The application of strain causes a stress response over time, also known as relaxation. By contrast, recovery is the response that occurs following the removal of an applied stress or strain. Both stress and relaxation constitute transient stages of a viscoelastic material exposed to a permanent force. In the current work, we performed several experimental tests to record the recovery in response to the total or partial removal of the strain. By observing and analyzing the mechanical response of the material to strain, we deduced that recovery is a procedure not only related to creep but also to relaxation. Hence, we created a model that simulates the behavior of viscoelastic materials, contributing to the prediction of relevant results concerning different conditions.

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A Bayesian estimation method for variational phase-field fracture problems

Cited by 72 publications

References 39 publications

Fracture Behavior of Two Biopolymers Containing Notches: Effects of Notch Tip Plasticity

Fracture Behavior of Two Biopolymers Containing Notches: Effects of Notch Tip Plasticity

A Review on Cementitious Self-Healing and the Potential of Phase-Field Methods for Modeling Crack-Closing and Fracture Recovery

Transient Effects of Applying and Removing Strain on the Mechanical Behavior of Rubber

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