Shear localization as a mesoscopic stress-relaxation mechanism in fused silica glass at high strain rates

Molecular dynamics (MD) simulations of fused silica glass deforming in pressure-shear, while revealing useful insights into processes unfolding at the atomic level, fail spectacularly in that they grossly overestimate the magnitude of the stresses relative to those observed, e. g., in plate-impact experiments. We interpret this gap as evidence of relaxation mechanisms that operate at mesoscopic lengthscales and which, therefore, are not taken into account in atomic-level calculations. We specifically hypothesize that the dominant mesoscopic relaxation mechanism is shear banding. We evaluate this hypothesis by first generating MD data over the relevant range of temperature and strain rate and then carrying out continuum shear-banding calculations in a plate-impact configuration using a critical-state plasticity model fitted to the MD data. The main outcome of the analysis is a knock-down factor due to shear banding that effectively brings the predicted level of stress into alignment with experimental observation, thus resolving the predictive gap of MD calculations

Development of a maximum entropy approach for the thermomecanical modelling of the rotary friction welding process

A multi-physics modelling of rotary friction welding process based on a Maximum Entropy approach is proposed. This approach will be able to solve coupled thermomechanical problems. Because strains are very high locally around the welded area, the remeshing time in a classical finite element method is very important. The use of this meshless method should reduce simulations time and the numerical diffusion phenomena

An optimal-transport finite-particle method for mass diffusion

We formulate a class of velocity-free finite-particle methods for mass transport problems based on a time-discrete incremental variational principle that combines entropy and the cost of particle transport, as measured by the Wasserstein metric. The incremental functional is further spatially discretized into finite particles, i.~e., particles characterized by a fixed spatial profile of finite width, each carrying a fixed amount of mass. The motion of the particles is then governed by a competition between the cost of transport, that aims to keep the particles fixed, and entropy maximization, that aims to spread the particles so as to increase the entropy of the system. We show how the optimal width of the particles can be determined variationally by minimization of the governing incremental functional. Using this variational principle, we derive optimal scaling relations between the width of the particles, their number and the size of the domain. We also address matters of implementation, including the acceleration of the computation of diffusive forces by exploiting the Gaussian decay of the particle profiles and by instituting fast nearest-neighbor searches. {\red Sources, advection, boundary flux and diffusion are accounted for by fractional steps.} We demonstrate the robustness and versatility of the finite-particle method by means of a test problem concerned with the injection of mass into a sphere. There test results demonstrate the meshless character of the method in any spatial dimension, its ability to redistribute mass particles and follow their evolution in time, its ability to satisfy flux boundary conditions for general domains based solely on a distance function, and its robust convergence characteristics

Data-driven fracture mechanics

We present a new data-driven paradigm for variational brittle fracture mechanics. The fracture-related material modeling assumptions are removed and the governing equations stemming from variational principles are combined with a set of discrete data points, leading to a model-free data-driven method of solution. The solution at a given load step is identified as the point within the data set that best satisfies either the Kuhn–Tucker conditions stemming from the variational fracture problem or global minimization of a suitable energy functional, leading to data-driven counterparts of both the local and the global minimization approaches of variational fracture mechanics. Both formulations are tested on different test configurations with and without noise and for Griffith and R-curve type fracture behavior

A Multiscale Approach for Modeling Crystalline Solids

In this paper we present a modeling approach to bridge the atomistic with macroscopic scales in crystalline materials. The methodology combines identification and modeling of the controlling unit processes at microscopic level with the direct atomistic determination of fundamental material properties. These properties are computed using a many body Force Field derived from ab initio quantum-mechanical calculations. This approach is exercised to describe the mechanical response of high-purity Tantalum single crystals, including the effect of temperature and strain-rate on the hardening rate. The resulting atomistically informed model is found to capture salient features of the behavior of these crystals such as: the dependence of the initial yield point on temperature and strain rate; the presence of a marked stage I of easy glide, specially at low temperatures and high strain rates; the sharp onset of stage II hardening and its tendency to shift towards lower strains, and eventually disappear, as the temperature increases or the strain rate decreases; the parabolic stage II hardening at low strain rates or high temperatures; the stage II softening at high strain rates or low temperatures; the trend towards saturation at high strains; the temperature and strain-rate dependence of the saturation stress; and the orientation dependence of the hardening rate.Comment: 25 pages, 15 figures, LaTe

Shear localization as a mesoscopic stress-relaxation mechanism in fused silica glass at high strain rates

Molecular dynamics (MD) simulations of fused silica glass deforming in pressure-shear, while revealing useful insights into processes unfolding at the atomic level, fail spectacularly in that they grossly overestimate the magnitude of the stresses relative to those observed, e. g., in plate-impact experiments. We interpret this gap as evidence of relaxation mechanisms that operate at mesoscopic lengthscales and which, therefore, are not taken into account in atomic-level calculations. We specifically hypothesize that the dominant mesoscopic relaxation mechanism is shear banding. We evaluate this hypothesis by first generating MD data over the relevant range of temperature and strain rate and then carrying out continuum shear-banding calculations in a plate-impact configuration using a critical-state plasticity model fitted to the MD data. The main outcome of the analysis is a knock-down factor due to shear banding that effectively brings the predicted level of stress into alignment with experimental observation, thus resolving the predictive gap of MD calculations

Data-Driven Multiscale Modeling in Mechanics

We present a Data-Driven framework for multiscale mechanical analysis of materials. The proposed framework relies on the Data-Driven formulation in mechanics (Kirchdoerfer and Ortiz 2016), with the material data being directly extracted from lower-scale computations. Particular emphasis is placed on two key elements: the parametrization of material history, and the optimal sampling of the mechanical state space. We demonstrate an application of the framework in the prediction of the behavior of sand, a prototypical complex history-dependent material. In particular, the model is able to predict the material response under complex nonmonotonic loading paths, and compares well against plane strain and triaxial compression shear banding experiments