A comparative assessment of different adaptive spatial refinement strategies in phase-field fracture models for brittle fracture - Rohracker, Maurice; Kumar, Paras; Mergheim, Julia (Forces in Mechanics, 2023)
For the smeared approximation of a discrete crack, phase-field fracture simulations of brittle materials require suitable finite element meshes in regions where crack propagation is expected to get an accurate resolution of the phase-field function. The straightforward option is to pre-refine the mesh in regions of the expected crack paths. However, this could lead to very computationally intensive simulations due to the high number of elements. Alternatively, adaptive spatial refinement of the finite element mesh is utilized based on appropriate error indicators to obtain the required accuracy in the areas of crack propagation. Different error indicators can be used: the most common one for phase-field fracture simulations is the threshold-based approach, in which elements are refined depending on the value of the phase-field function. Alternatively, the Kelly error indicator can be used as a criterion for spatial adaptivity. It considers the jumps in the gradients of the phase-field function between the elements. We additionally introduce here an error indicator based on configurational forces, that depend on the Eshelby stress tensor. For mode I loading in linear elastic fracture mechanics, the configurational forces have a close connection to the J-Integral and the critical fracture energy Gc, respectively. Therefore, a suitable norm of the configurational forces is introduced as an error indicator here. These three error indicators are introduced and compared to each other in terms of accuracy and efficiency by means of numerical examples for crack growth in the single edge notched shear test.
Keywords: Phase-Field Fracture Simulations; Spatial Adaptivity; Brittle Fracture; Single Edge Notched Shear Test

A graded interphase enhanced phase-field approach for modeling fracture in polymer composites - Kumar, Paras; Steinmann, Paul; Mergheim, Julia (Forces in Mechanics, 2022)
The superiority of nanosized filler particles in improving the elastic and fracture behavior of polymers, in comparison to microsized inclusions, has been substantiated by several experimental observations. Accurate modeling of crack propagation in such heterogeneous materials, however, involves resolution of complex crack topologies while taking into account the coalescence and branching of multiple cracks. Such complexity renders the traditional sharp crack modeling approaches, such as those based on the idea of partition of unity, to be of limited suitability, especially in 3D, since these involve explicit tracking of the evolving crack surfaces. Consequently, phase-field fracture approaches have come up as an attractive alternative to the traditional sharp crack models, especially when complex crack topologies need to be handled. Furthermore, standard two-phase continuum models, owing to their lack of the necessary length scale, are unable to capture the previously mentioned smaller is stronger size effect. In order to remedy this shortcoming, in context of finite strain hyperelasticity, a graded interphase based enhancement of the standard first-order continuum model was introduced in our previous work. The present contribution extends the idea of graded interphases to the phase-field fracture approach. Herein, an interphase region around filler particles, as observed experimentally, having continuously varying or graded material properties is considered. Fracture behavior of the composite material can be controlled by means of the degree of grading employed in determining the elastic and fracture properties within the interphase region. An optimal combination of the graded interphase parameters yields a tougher macroscopic response, as observed in case of tougher interphases, in comparison to the one obtained with a standard phase-field fracture model, The appropriateness of the introduced technique for modeling a wide spectrum of experimentally observed fracture behaviors, depending upon the degree of adhesion between the filler and the matrix phases, is depicted by means of extensive numerical experimentation.
CRIS-Team Scopus Importer:2022-12-09
Keywords: Graded interphases; Micro-scale modeling; Phase-field fracture; Polymer composites

Computational Fracture Modeling in Heterogeneous Materials - Recent Advances and Future Challenges - Kumar, Paras; Phansalkar, Dhananjay; Mergheim, Julia; Leyendecker, Sigrid; Steinmann, Paul (conference, WCCM-APCOM 15th World Congress on Computational Mechanics & 8th Asian Pacific Congress on Computational Mechanics, 2022)

Computational modeling of fracture in polymer nanocomposites undergoing large deformations via the graded-interphase-enhanced phase-field fracture approach - Kumar, Paras; Mergheim, Julia (Proceedings in Applied Mathematics and Mechanics, 2023)
“The phenomenon of fracture in polymer composites, polymer nano-composites in particular, entails a multitude of intricate mechanisms including branching and merging of several cracks along with particle debonding and subsequent plastic void growth. This work involves an extension of the standard phase-field fracture approach by means of the graded interphase concept in order to facilitate the modeling of a wide-spectrum of fracture responses, which can be observed in experimental studies concerning the fracture behavior of polymer nano-composites. Herein, motivated by the microstructure morphology of polymer nano-composites, a continuous grading of the elastic and fracture properties is considered within a finite thickness interphase region around the filler particles. Appropriate tuning of the graded-interphase model parameters enables to capture a variety of fracture responses, including cohesive failure between the filler particle and the matrix, as demonstrated via the presented numerical examples, which focus on polymer nano- composites undergoing large deformations prior to fracture.”

Energy Corrected Finite Elements for Elliptic PDEs and Linear Elasticity - Kumar, Paras (Friedrich-Alexander-Universität Erlangen-Nürnberg, 2018)

Enhanced computational homogenization techniques for modelling size effects in polymer composites - Kumar, Paras; Steinmann, Paul; Mergheim, Julia (Computational Mechanics, 2021)
Several experimental investigations corroborate nanosized inclusions as being much more efficient reinforcements for strengthening polymers as compared to their microsized counterparts. The inadequacy of the standard first-order computational homogenization scheme, by virtue of lack of the requisite length scale to model such size effects, necessitates enhancements to the standard scheme. In this work, a thorough assessment of one such extension based on the idea of interface energetics is conducted. Systematic numerical experimentation and analysis demonstrate the limitation of the aforementioned approach in modeling mechanical behavior of composite materials where the filler material is much stiffer than the matrix. An alternative approach based on the idea of continuously graded interphases is introduced. Comprehensive evaluation of this technique by means of representative numerical examples reveals it to be the appropriate one for modeling nano-composite materials with different filler-matrix stiffness combinations.
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Keywords: Computational Homogenization; Interface; Interphase; Nano-Composite; Size Effect

Size Effects in Computational Homogenization of Polymer Nano-Composites - Kumar, Paras; Mergheim, Julia (Proceedings in Applied Mathematics & Mechanics, 2021)