Homogenized estimates for soft fiber-composites and tissues with two families of fibers

The macroscopic response of hyperelastic fiber composites is characterized in terms of the behaviors of their constituting phases. To this end, we make use of a unique representation of the deformation gradient in terms of a set of transversely isotropic invariants. Respectively, these invariants correspond to extension along the fibers, transverse dilatation, out-of-plane shear along the fibers, in-plane shear in the transverse plane, and the coupling between the shear modes. With the aid of this representation, it is demonstrated that under a combination of out-of-plane shear and extension along the fibers there is a class of nonlinear materials for which the exact expression for the macroscopic behavior of a composite cylinder assemblage can be determined. The macroscopic response of the composite to shear in the transverse plane is approximated with the aid of an exact result for sequentially laminated composites. Assuming no coupling between the shear modes, these results allow to construct a closed-form homogenized model for the macroscopic response of a fiber composite with neo-Hookean phases. A new variational estimate allows to extend these results to more general classes of materials. The resulting explicit estimates for the macroscopic stresses developing in composites and connective tissues with one and two families of fibers are compared with corresponding finite element simulations of periodic composites and with experimental results. Estimates for the critical stretch ratios at which the composites loose stability at the macroscopic level are compared with the corresponding numerical results too. It is demonstrated that both the primary stress–strain curves and the critical stretch ratios are in fine agreement with the corresponding numerical results

Portability and Scalability of OpenMP Offloading on State-of-the-art Accelerators

Over the last decade, most of the increase in computing power has been gained by advances in accelerated many-core architectures, mainly in the form of GPGPUs. While accelerators achieve phenomenal performances in various computing tasks, their utilization requires code adaptations and transformations. Thus, OpenMP, the most common standard for multi-threading in scientific computing applications, introduced offloading capabilities between host (CPUs) and accelerators since v4.0, with increasing support in the successive v4.5, v5.0, v5.1, and the latest v5.2 versions. Recently, two state-of-the-art GPUs - the Intel Ponte Vecchio Max 1100 and the NVIDIA A100 GPUs - were released to the market, with the oneAPI and GNU LLVM-backed compilation for offloading, correspondingly. In this work, we present early performance results of OpenMP offloading capabilities to these devices while specifically analyzing the potability of advanced directives (using SOLLVE's OMPVV test suite) and the scalability of the hardware in representative scientific mini-app (the LULESH benchmark). Our results show that the vast majority of the offloading directives in v4.5 and 5.0 are supported in the latest oneAPI and GNU compilers; however, the support in v5.1 and v5.2 is still lacking. From the performance perspective, we found that PVC is up to 37% better than the A100 on the LULESH benchmark, presenting better performance in computing and data movements.Comment: 13 page