A single Gauss point continuum finite element formulation for gradient-extended damage at large deformations

Barfusz, Oliver; Brepols, Tim; Velden, Tim van der; Frischkorn, Jan; Reese, Stefanie

doi:10.1016/j.cma.2020.113440

Cited by 26 publications

(23 citation statements)

References 76 publications

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“…Investigating the influence of reduced integration finite elements seems to be of high benefit. Especially the element formulations Q1SP (see Reese 2005) or Q1STx (see Schwarze and Reese 2011;Barfusz et al 2021) could improve the computation in terms of computational accuracy as well as computational speed. With this at hand, it is easy to show that the main invariants J with ∈ 1, 2, 3 are identical for both, the Mandel and the Kirchhoff stress tensor, i.e.…”

Section: Discussionmentioning

confidence: 99%

A macroscopic approach for stress-driven anisotropic growth in bioengineered soft tissues

Lamm

Jockenhövel

Brepols

et al. 2022

Biomech Model Mechanobiol

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The simulation of growth processes within soft biological tissues is of utmost importance for many applications in the medical sector. Within this contribution, we propose a new macroscopic approach for modelling stress-driven volumetric growth occurring in soft tissues. Instead of using the standard approach of a-priori defining the structure of the growth tensor, we postulate the existence of a general growth potential. Such a potential describes all eligible homeostatic stress states that can ultimately be reached as a result of the growth process. Making use of well-established methods from visco-plasticity, the evolution of the growth-related right Cauchy–Green tensor is subsequently defined as a time-dependent associative evolution law with respect to the introduced potential. This approach naturally leads to a formulation that is able to cover both, isotropic and anisotropic growth-related changes in geometry. It furthermore allows the model to flexibly adapt to changing boundary and loading conditions. Besides the theoretical development, we also describe the algorithmic implementation and furthermore compare the newly derived model with a standard formulation of isotropic growth.

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Section: Discussionmentioning

confidence: 99%

A macroscopic approach for stress-driven anisotropic growth in bioengineered soft tissues

Lamm

Jockenhövel

Brepols

et al. 2022

Biomech Model Mechanobiol

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“…is considered, where η f and η p are material parameters that characterize the viscous response of the fracture and plasticity evolutions, respectively. Then, minimization of ( 17) with respect to u, the plasticity variables (ε p , α) subject to the hardening law (6), and the crack phase-field ḋ subject to the irreversibility condition ḋ ≥ 0 provide the governing equations for the elasticity problem, the plasticity problem, and the fracture problem, respectively. Such a variational structure results in a convenient numerical implementation based on incremental energy minimization, for which an algorithmic representation of the energy functional ( 15) is defined as…”

Section: Energy Quantities and Variational Principlesmentioning

confidence: 99%

“…Recently, in the setting of continuum mechanics, a new perspective was proposed for embedding microscopic mechanisms into the macromechanical continuum formulation based on a multi-field incremental variational framework for gradient-extended standard dissipative solids [1,2]. Typical examples are theories of gradient-enhanced damage [3][4][5][6], phase-field models [7][8][9], and strain gradient plasticity [10][11][12]. Such models incorporate non-local effects based on length scales, which reflect properties of the material microstructure size with respect to the macro-structure size.…”

Section: Introductionmentioning

confidence: 99%

Bayesian inversion for unified ductile phase-field fracture

et al. 2021

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The prediction of crack initiation and propagation in ductile failure processes are challenging tasks for the design and fabrication of metallic materials and structures on a large scale. Numerical aspects of ductile failure dictate a sub-optimal calibration of plasticity- and fracture-related parameters for a large number of material properties. These parameters enter the system of partial differential equations as a forward model. Thus, an accurate estimation of the material parameters enables the precise determination of the material response in different stages, particularly for the post-yielding regime, where crack initiation and propagation take place. In this work, we develop a Bayesian inversion framework for ductile fracture to provide accurate knowledge regarding the effective mechanical parameters. To this end, synthetic and experimental observations are used to estimate the posterior density of the unknowns. To model the ductile failure behavior of solid materials, we rely on the phase-field approach to fracture, for which we present a unified formulation that allows recovering different models on a variational basis. In the variational framework, incremental minimization principles for a class of gradient-type dissipative materials are used to derive the governing equations. The overall formulation is revisited and extended to the case of anisotropic ductile fracture. Three different models are subsequently recovered by certain choices of parameters and constitutive functions, which are later assessed through Bayesian inversion techniques. A step-wise Bayesian inversion method is proposed to determine the posterior density of the material unknowns for a ductile phase-field fracture process. To estimate the posterior density function of ductile material parameters, three common Markov chain Monte Carlo (MCMC) techniques are employed: (i) the Metropolis–Hastings algorithm, (ii) delayed-rejection adaptive Metropolis, and (iii) ensemble Kalman filter combined with MCMC. To examine the computational efficiency of the MCMC methods, we employ the $$\hat{R}{-}convergence$$ R ^ - c o n v e r g e n c e tool. The resulting framework is algorithmically described in detail and substantiated with numerical examples.

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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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A single Gauss point continuum finite element formulation for gradient-extended damage at large deformations

Cited by 26 publications

References 76 publications

A macroscopic approach for stress-driven anisotropic growth in bioengineered soft tissues

A macroscopic approach for stress-driven anisotropic growth in bioengineered soft tissues

Bayesian inversion for unified ductile phase-field fracture

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

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