Publications

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In classical statistical thermodynamics, calculating the configuration integral is both vital and elusive. Analytic relations for configuration integrals are desirable for modeling purposes, but it is typically impossible to obtain them. Certain systems become analytically tractable after replacing steep potential energies with harmonic potentials or athermal rigid constraints, but these approximations are often inadequate, especially when modeling the stretching of molecules. It is therefore necessary to develop a systematic approach to improve upon the approximations provided by these reference systems. Here, a general asymptotic approach is introduced, where the configuration integral for the full system is obtained in terms of that of the reference system and several corrections. This asymptotic approach is first demonstrated using the simple example of a classical three-dimensional oscillator. Next, the approach is applied to modeling the stretching of single polymer chains and to modeling thermally assisted crack growth, where results are verified with respect to numerical calculations. Overall, this asymptotic approach is a valid and effective tool for statistical thermodynamics in general.

The DevOps movement, which aims to accelerate the continuous delivery of high-quality software, has taken a leading role in reshaping the software industry. Likewise, there is growing interest in applying DevOps tools and practices in the domains of computational science and engineering (CSE) to meet the ever-growing demand for scalable simulation and analysis. Translating insights from industry to research computing, however, remains an ongoing challenge; DevOps for science and engineering demands adaptation and innovation in those tools and practices. There is a need to better understand the challenges faced by DevOps practitioners in CSE contexts in bridging this divide. To that end, we conducted a participatory action research study to collect and analyze the experiences of DevOps practitioners at a major US national laboratory through the use of storytelling techniques. We share lessons learned and present opportunities for future investigation into DevOps practice in the CSE domain.

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The damage mechanisms that lead to failure in engineering alloys have been studied extensively, but converting this knowledge into constitutive models that are suitable for engineering-scale analysis remains a challenge. Evolution laws for continuum damage have been developed in the past and have proven effective but suffer from many non-physical assumptions that inhibit the overall accuracy of the model. Further, the assumptions inherent in these existing models prevent them from being applicable to a broad class of materials. At the same time, computational models of fine-scale damage mechanisms continue to advance making it tractable to generate large training data sets through computer simulation. Data-driven machine learning approaches can leverage these data sets to avoid making limiting assumptions, and instead produce models directly from the results of microstructural simulations and/or experiments. Many of these machine learning approaches are rapid and accurate, but they offer little to no insight into the underlying relationships among state variables being discovered. Conversely, genetic programming symbolic regression (GPSR) is a machine learning method that produces analytic expressions relating the state variables, allowing maximal insight and interpretability. To that end, we propose using GPSR as a data-driven method of obtaining microstructurally informed continuum damage models. Data is generated using microstructural simulations of damage evolution, parameterized over microstructural statistics (i.e., pore shape) and nominally applied deformations. Analytic expressions for damage evolution are obtained from the data using GPSR, and these expressions are then utilized within a continuum constitutive model. Overall, this approach is a promising method of automatically obtaining analytic relations describing constitutive phenomena in a material.

Presented in this document is a small portion of the tests that exist in the Sierra/SolidMechanics (Sierra/SM) verification test suite. Most of these tests are run nightly with the Sierra/SM code suite, and the results of the test are checked versus the correct analytical result. For each of the tests presented in this document, the test setup, a description of the analytic solution, and comparison of the Sierra/SM code results to the analytic solution is provided. Mesh convergence is also checked on a nightly basis for several of these tests. This document can be used to confirm that a given code capability is verified or referenced as a compilation of example problems. Additional example problems are provided in the Sierra/SM Example Problems Manual. Note, many other verification tests exist in the Sierra/SM test suite, but have not yet been included in this manual.

Presented in this document are tests that exist in the Sierra / SolidMechanics example problem suite, which is a subset of the Sierra / SM regression and performance test suite. These examples showcase common and advanced code capabilities. A wide variety of other regression and verification tests exist in the Sierra / SM test suite that are not included in this manual.

This user’s guide documents capabilities in Sierra/SolidMechanics which remain “in-development” and thus are not tested and hardened to the standards of capabilities listed in Sierra/SM 5.10 User’s Guide. Capabilities documented herein are available in Sierra/SM for experimental use only until their official release. These capabilities include, but are not limited to, novel discretization approaches such as the conforming reproducing kernel (CRK) method, numerical fracture and failure modeling aids such as the extended finite element method (XFEM) and J-integral, explicit time step control techniques, dynamic mesh rebalancing, as well as a variety of new material models and finite element formulations.

Brittle material failure in high consequence systems can appear random and unpredictable at subcritical stresses. Gaps in our understanding of how structural flaws and environmental factors (humidity, temperature) impact fracture propagation need to be addressed to circumvent this issue. A combined experimental and computational approach composed of molecular dynamics (MD) simulations, numerical modeling, and atomic force microscopy (AFM) has been undertaken to identify mechanisms of slow crack growth in silicate glasses. AFM characterization of crack growth as slow as 10^-13 m/s was observed, with some stepwise crack growth. MD simulations have identified the critical role of inelastic relaxation in crack propagation, including evolution of the structure during relaxation. A numerical model for the existence of a stress intensity threshold, a stress intensity below which a fracture will not propagate, was developed. This transferrable model for predicting slow crack growth is being incorporated into mission-based programs.

Analytical relations for the mechanical response of single polymer chains are valuable for modeling purposes, on both the molecular and the continuum scale. These relations can be obtained using statistical thermodynamics and an idealized single-chain model, such as the freely jointed chain model. To include bond stretching, the rigid links in the freely jointed chain model can be made extensible, but this almost always renders the model analytically intractable. Here, an asymptotically correct statistical thermodynamic theory is used to develop analytic approximations for the single-chain mechanical response of this model. The accuracy of these approximations is demonstrated using several link potential energy functions. This approach can be applied to other single-chain models, and to molecular stretching in general.

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