We develop a three-dimensional, hierarchically parallel, finite strain multiscale solver capable of computing nonlinear multiscale solutions with over 1 billion finite elements and over 574 million nonlinear equations on 1552 computing cores. In the vein of FE 2 , we use the nested iterative procedure and devote the solver to multiscale cohesive modeling of heterogeneous hyperelastic layers. The hierarchically parallel multiscale solver takes advantage of a client-server non-blocking communication matrix that limits latency, starvation, and overhead by overlaying computations at different scales. We perform simulations of real-scale engineering devices and bridge O.10 6 / in length-scales, spanning from O.10 1 / mm to O.10 1 / nm in spatial resolution. Verification of the hierarchically parallel solver is provided together with a mesh convergence study. Moreover, we report on the scaling performance.

Multi-scale simulations at extreme scales in terms of both physical length scales and computational resources are presented. In this letter, we introduce a hierarchically parallel computational homogenization solver that employs hundreds of thousands of computing cores and resolves O(10 5) in material length scales (from O(cm) to O(100 nm)). Simulations of this kind are essential in understanding the multi-scale essence of many natural and synthetically made materials. Thus, we present a simulation consisting of 53.8 Billion finite elements with 28.1 Billion nonlinear equations that is solved on 393,216 computing cores (786,432 threads). The excellent parallel performance of the computational homogenization solver is demonstrated by a strong scaling test from 4,096 to 262,114 cores. A fully coupled multi-scale damage simulation shows a complex crack profile at the micro-scale and the macroscopic crack tunneling phenomenon. Such large and predictive simulations are an important step towards Virtual Materials Testing and can aid in development of new material formulations with extreme properties. Furthermore, the high computational efficiency of our computational homogenization solver holds great promise for utilizing the next generation of exascale parallel computing platforms that are expected to accelerate computations through orders of magnitude increase in parallelism rather than speed of each processor.

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 imagebased 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.

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