On a phase-field approach to model fracture of small intestine walls

Nagaraja, Sindhu; Leichsenring, Kay; Ambati, Marreddy; Lorenzis, Laura De; Böl, Markus

doi:10.1016/j.actbio.2021.06.002

Cited by 18 publications

(11 citation statements)

References 101 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For plane stress conditions the incompressibility can be introduced by substitution [36], avoiding the complexities of mixed formulations. Models for brittle phase-field fracture of soft materials at the limit of incompressibility have been developed following penalty formulations for rubbers [37] and biological tissues [38,39]. Penalty formulations in the context of phase field modeling, as they attempt to enforce near incompressibility, inadvertently impact crack initiation and propagation as they limit the ability of cracks (represented in a diffuse manner) to open.…”

Section: Introductionmentioning

confidence: 99%

“…Models for brittle phase-field fracture of soft materials at the limit of incompressibility have been developed following penalty formulations for rubbers 37 and biological tissues. 38,39 Penalty formulations in the context of phase field modeling, as they attempt to enforce near incompressibility, inadvertently impact crack initiation and propagation as they limit the ability of cracks (represented in a diffuse manner) to open. Crack opening requires elimination of near incompressibility to accommodate for the additional free volume in the crack which is now represented in a diffuse way.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stabilized formulation for phase‐field fracture in nearly incompressible hyperelasticity

Ang

Bouklas

2022

Numerical Meth Engineering

View full text Add to dashboard Cite

This work presents a stabilized formulation for phase-field fracture of hyperelastic materials near the limit of incompressibility. At this limit, traditional mixed displacement and pressure formulations must satisfy the inf-sup condition for solution stability. The mixed formulation coupled with the damage field can lead to an inhibition of crack opening as volumetric changes are severely penalized effectively creating a pressure-bubble. To overcome this bottleneck, we utilize a mixed formulation with a perturbed Lagrangian formulation which enforces the incompressibility constraint in the undamaged material and reduces the pressure effect in the damaged material. A mesh-dependent stabilization technique based on the residuals of the Euler-Lagrange equations multiplied with a differential operator acting on the weight space is used, allowing for linear interpolation of all field variables of the elastic sub-problem. This formulation was validated with three examples at finite deformations: a plane-stress pure-shear test, a two-dimensional geometry in plane-stress, and a threedimensional notched sample. In the last example, we incorporate a hybrid formulation with an additive strain energy decomposition to account for different behaviors in tension and compression. The results show close agreement with analytical solutions for crack tip opening displacements and performs well at the limit of incompressibility.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stabilized formulation for phase‐field fracture in nearly incompressible hyperelasticity

Ang

Bouklas

2022

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…To the best knowledge of the authors, this paper is the first to investigate mechanically-induced damage to the large intestine. Although a phase-field approach to model the fracture in the small intestine wall has been recently presented by Nagaraja et al [ 36 ], the study is limited to uniaxial tension experiments, non-hysteresis mechanics, and overall damage parameters rather than a layer-or-fiber specific fracture analysis. The continuum damage evolution proposed by Comellas et al [ 20 ] has been adapted in this paper to constitutively describe the true stress–strain response of the porcine large intestine during biaxial tensile loading until complete failure.…”

Section: Introductionmentioning

confidence: 99%

Layer-Specific Damage Modeling of Porcine Large Intestine under Biaxial Tension

et al. 2022

View full text Add to dashboard Cite

The mechanical behavior of the large intestine beyond the ultimate stress has never been investigated. Stretching beyond the ultimate stress may drastically impair the tissue microstructure, which consequently weakens its healthy state functions of absorption, temporary storage, and transportation for defecation. Due to closely similar microstructure and function with humans, biaxial tensile experiments on the porcine large intestine have been performed in this study. In this paper, we report hyperelastic characterization of the large intestine based on experiments in 102 specimens. We also report the theoretical analysis of the experimental results, including an exponential damage evolution function. The fracture energies and the threshold stresses are set as damage material parameters for the longitudinal muscular, the circumferential muscular and the submucosal collagenous layers. A biaxial tensile simulation of a linear brick element has been performed to validate the applicability of the estimated material parameters. The model successfully simulates the biomechanical response of the large intestine under physiological and non-physiological loads.

show abstract

“…Due to its diffuse modeling approach which has the advantage that no remeshing at discontinuities is necessary, the phase-field approach to fracture has been applied to a broad range of problems such as fracture including inelastic deformations, 14,15 viscoelastic materials, 16,17 interface failure, 18,19 heterogeneous materials, 20,21 dynamic loading, 22,23 fatigue failure, [24][25][26] or fracture with anisotropy. 27,28 The phase-field approach to fracture has been applied to plates and shells in many different ways, focusing on various aspects. The first approach to couple a shell with the phase-field model for fracture was presented by Ulmer et al 29 in 2012, where a shell is considered as combination of a Kirchhoff plate and a standard membrane.…”

Section: Introductionmentioning

confidence: 99%

“…A comprehensive overview of the existing phase‐field fracture formulations considering monotonic loads is presented in Reference 13, see also the references therein. Due to its diffuse modeling approach which has the advantage that no remeshing at discontinuities is necessary, the phase‐field approach to fracture has been applied to a broad range of problems such as fracture including inelastic deformations, 14,15 viscoelastic materials, 16,17 interface failure, 18,19 heterogeneous materials, 20,21 dynamic loading, 22,23 fatigue failure, 24‐26 or fracture with anisotropy 27,28 …”

Section: Introductionmentioning

confidence: 99%

Phase‐field modeling of brittle fracture along the thickness direction of plates and shells

Ambati

Heinzmann

Seiler

et al. 2022

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

The prediction of fracture in thin-walled structures is decisive for a wide range of applications. Modeling methods such as the phase-field method usually consider cracks to be constant over the thickness which, especially in load cases involving bending, is an imperfect approximation. In this contribution, fracture phenomena along the thickness direction of structural elements (plates or shells) are addressed with a phase-field modeling approach. For this purpose, a new, so called "mixed-dimensional" model is introduced, which combines structural elements representing the displacement field in the two-dimensional shell midsurface with continuum elements describing a crack phase-field in the three-dimensional solid space. The proposed model uses two separate finite element discretizations, where the transfer of variables between the coupled twoand three-dimensional fields is performed at the integration points which in turn need to have corresponding geometric locations. The governing equations of the proposed mixed-dimensional model are deduced in a consistent manner from a total energy functional with them also being compared to existing standard models. The resulting model has the advantage of a reduced computational effort due to the structural elements while still being able to accurately model arbitrary through-thickness crack evolutions as well as partly along the thickness broken shells due to the continuum elements. Amongst others, the higher accuracy as well as the numerical efficiency of the proposed model are tested and validated by comparing simulation results of the new model to those obtained by standard models using numerous representative examples.

show abstract

On a phase-field approach to model fracture of small intestine walls

Cited by 18 publications

References 101 publications

Stabilized formulation for phase‐field fracture in nearly incompressible hyperelasticity

Stabilized formulation for phase‐field fracture in nearly incompressible hyperelasticity

Layer-Specific Damage Modeling of Porcine Large Intestine under Biaxial Tension

Phase‐field modeling of brittle fracture along the thickness direction of plates and shells

Contact Info

Product

Resources

About