Computational Physics Group

Karel Matous










On mechanics and material length scales of failure in heterogeneous interfaces using a finite strain high performance solver

M. Mosby and K. Matous

Department of Aerospace and Mechanical Engineering
University of Notre Dame
Notre Dame, IN, 46556, USA.


    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.


    A 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.


     This work was supported by the National Science Foundation under grant number CMMI-1153435.

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2015 Notre Dame and Dr. Karel Matous