Computational Physics GroupKarel Matous |
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On mechanics and material length scales of failure in heterogeneous interfaces using a finite strain high performance solver
Department of Aerospace and Mechanical Engineering University of Notre Dame Notre Dame, IN, 46556, USA. Abstract Three-dimensional
simulations capable of resolving the large range of
spatial scales, from the failure-zone thickness up to
the size of the representative unit cell, in damage
mechanics problems of particle reinforced adhesives are
presented. We show that resolving this wide range of
scales in complex three-dimensional heterogeneous
morphologies is essential in order to apprehend fracture
characteristics, such as strength, fracture toughness
and shape of the softening profile. Moreover, we show
that computations that resolve essential physical length
scales capture the particle size-effect in fracture
toughness, for example. In the vein of image-based
computational materials science, we construct
statistically optimal unit cells containing hundreds to
thousands of particles. We show that these statistically
representative unit cells are capable of capturing the
first- and second-order probability functions of a given
data-source with better accuracy than traditional
inclusion packing techniques. In order to accomplish
these large computations, we use a parallel multiscale
cohesive formulation and extend it to finite strains
including damage mechanics. The high-performance
parallel computational framework is executed on up to
1024 processing cores. A mesh convergence and a
representative unit cell study are performed.
Quantifying the complex damage patterns in simulations
consisting of tens of millions of computational cells
and millions of highly nonlinear equations requires
data-mining the parallel simulations, and we propose two
damage metrics to quantify the damage patterns. A
detailed study of volume fraction and filler size on the
macroscopic traction-separation response of
heterogeneous adhesives is presented.
ConclusionsA 3D high-performance finite strain multiscale cohesive framework is used to study failure processes occurring at the microscale in heterogeneous adhesives, and their effect on the macroscopic homogenized cohesive response. An emphasis is placed on data-driven (image-based) modeling that resolves the wide range of spatial scales (lμ → lRUC). This wide range of spatial scales, consisting of tens of millions of computational cells and millions of highly nonlinear equations, necessitates an efficient solution strategy. We employ parallel computing and execute our framework on up to 1024 computing cores. The large amount of data generated during these simulations requires data-mining and analysis tools to understand the damage patterns and their evolution. Therefore, we propose two damage metrics (i.e., volume fraction of damage and effective crack thickness) that allow us to quantify the damage extent and its evolution. The proposed damage metrics can also serve to catalog materials since they relate the microstructure to overall failure characteristics, such as adhesive versus cohesive failure, strength, and fracture toughness. In addition, we construct statistically Representative Unit Cells of heterogeneous layers, and their representativeness is studied in terms of hyperelastic response, strength (limit traction), fracture toughness, and softening response (shape of the cohesive relation). The unit cell reconstruction procedure takes advantage of in-plane isotropic first- and second-order probability functions that are obtained from an image-based source. We show that statistically optimal unit cells yield statistically improved material representation in the L2 sense than material-blind packing algorithms such as random sequential addition. This leads to smaller standard deviations for physical quantities as compared to previous studies. Finally, we perform detailed computational studies to understand the effect of volume fraction and particle diameter on micro- and macro-failure characteristics. Our results are statistical in nature, and we present both the means and standard deviations over each set of five material realizations. We capture traditional trends that are observed in experiments, such as the stiffening effect due to the higher particle volume fraction. Additionally, we capture an elusive non-monotonic size-effect in fracture toughness as a function of particle diameter. Well resolved and verified microscale simulations presented in this work, can be the first step towards virtual materials testing. However, for simulations of this kind to reach their true predictive potential, careful model calibration at the micro-scale, and detailed model validation both at the micro- and macro-scale must be performed. Moreover, more complex constitutive models (i.e., anisotropic damage) and added physics (e.g., particle-matrix decohesion) are required. Thus, research in co-designed simulations and experiments is the natural next step. Acknowledgments
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