Publications

This paper presents efforts to improve the hierarchical parallelism of a two scale simulation code. Two methods to improve the GPU parallel performance were developed and compared. The first used the NVIDIA Multi-Process Serviceand the second moved the entire sub-problem loop into a single kernel using Kokkos hierarchical parallelism and a PackedView data structure. Both approaches improved parallel performance with the second method providing the greatest improvements.

This article presents MuMFiM, an open source application for multiscale modeling of fibrous materials on massively parallel computers. MuMFiM uses two scales to represent fibrous materials such as biological network materials (extracellular matrix, connective tissue, etc.). It is designed to make use of multiple levels of parallelism, including distributed parallelism of the macro and microscales as well as GPU accelerated data-parallelism of the microscale. Scaling results of the GPU accelerated microscale show that solving microscale problems concurrently on the GPU can lead to a 1000x speedup over the solution of a single RVE on the GPU. In addition, we show nearly optimal strong and weak scaling results of MuMFiM on up to 128 nodes of AiMOS (Rensselaer Polytechnic Institute) which is composed of IBM AC922 nodes with 6 Volta V100 GPU and 2 20 core Power 9 CPUs each. We also show how MuMFiM can be used to solve problems of interest to the broader engineering community, in particular providing an example of the facet capsule ligament (FCL) of the human spine undergoing uniaxial extension.

Indentation is often used to measure the stiffness of soft materials whose main structural component is a network of filaments, such as the cellular cytoskeleton, connective tissue, gels, and the extracellular matrix. For elastic materials, the typical procedure requires fitting the experimental force-displacement curve with the Hertz model, which predicts that $f=k \delta ^{1.5}$ and $k$ is proportional to the reduced modulus of the indented material, $E/(1-\nu^2)$ . Here we show using explicit models of fiber networks that the Hertz model applies to indentation in network materials provided the indenter radius is larger than approximately $12 l_c$, where $l_c$ is the mean segment length of the network. Using smaller indenters leads to a relation between force and indentation displacement of the form $f=\delta^q$, where $q$ is observed to increase with decreasing indenter radius. Using the Hertz model to interpret results of indentations in network materials using small indenters leads to an inferred modulus smaller than the real modulus of the material. The origin of this departure from the classical Hertz model is investigated. A compacted, stiff network region develops under the indenter, effectively increasing the indenter size and modifying its shape. This modification is marginal when large indenters are used. However, when the indenter radius is small, the effect of the compacted layer is pronounced as it changes the indenter profile from spherical towards conical. This entails an increase of exponent $q$ above the value of 1.5 corresponding to spherical indenters.

This article presents the displacement field produced by a point force acting on an athermal random fiber network (the Green function for the network). The problem is defined within the limits of linear elasticity, and the field is obtained numerically for nonaffine networks characterized by various parameter sets. The classical Green function solution applies at distances from the point force larger than a threshold which is independent of the network parameters in the range studied. At smaller distances, the nonlocal nature of fiber interactions modifies the solution.

model-traits is a C++ library for setting up scientific models and computational analysis. It provides a minimal API for applying boundary conditions (or other attributes) to the geometry of a model. model-traits can either be used directly as a library, or can be used to generate input files for an existing analysis code. The library design is optimized to make adding new input and output file formats easy and maintainable without patching the core library.

Materials with a stochastic fiber network as the main structural constituent are broadly encountered in engineering and in biology. These materials are characterized by multiscale heterogeneity and hence their properties evaluated numerically or experimentally are generally dependent on the size of the sample considered. In this work we evaluate the size effect on the linear and non-linear mechanical response of three-dimensional stochastic fiber networks and determine its dependence on material parameters and on the degree of affinity of network deformation. The size effect is more pronounced in non-affine networks than in affine networks and decreases slowly when the model size increases. In order to eliminate this effect, models lager than can be effectively solved with current computers have to be considered. To address this issue, we propose a method that allows using relatively small models, while accurately predicting the small and large strain behaviors of the network. The method is based on the generalized boundary conditions introduced in (Glüge 2013, Computational Materials Science 79, 408–416), which are being adapted here to the requirements imposed by fibrous materials.

A 60-mm diameter disk of 2024 aluminum was indented by opposing steel indenters over a central 10 mm region. Residual stress measurements made using neutron diffraction and the contour method matched each other, but not a finite element (FE) model with a calibrated model for plastic anisotropy of the aluminum. Since residual stresses are only the endpoint of the process, in situ data was needed to determine which portion of the load/unload process was causing model deficiencies. The indentation process was repeated on a new specimen with three-dimensional Digital Image Correlation (3D-DIC) to map full-field strain information and with resistance strain gauges to obtain high fidelity strain information at discrete locations. The DIC data was too noisy to extract strains, so displacements were analyzed after rigid body motion was removed. The deformation field revealed geometric imperfections of the indenters that were within tolerance, but had significant effect on the stress state. An updated FE model including geometric imperfections in the indenters gave better agreement with the DIC data. It did not however allow the material model to become the dominant effect and thus model calibration was unsuccessful.

Regular composite materials are made from a small number of constituent phases, usually two, which are arranged spatially such to maximize the stiffness and strength of the material. In this article, we review results related to defining a new class of stochastic composite materials with large microstructural variability both in terms of the composition and spatial distribution of constituents. Further, new data on Green functions in stochastic continua is presented.