Papers by Coleman Alleman
Microscopy and Microanalysis
International Journal of Fracture
Computer Methods in Applied Mechanics and Engineering
We advance the Schwarz alternating method as a means for concurrent multiscale coupling in finite... more We advance the Schwarz alternating method as a means for concurrent multiscale coupling in finite deformation solid mechanics. We prove that the Schwarz alternating method converges to the solution of the problem on the entire domain and that the convergence rate is geometric provided that each of the subdomain problems is well-posed, i.e. their corresponding energy density functions are quasi-convex. It is shown that the use of a Newton-type method for the solution of the resultant nonlinear system leads to two kinds of block linearized systems, depending on the treatment of the Dirichlet boundary conditions. The first kind is a symmetric block-diagonal linear system in which each diagonal block is the tangent stiffness of each subdomain, i.e. the off-diagonal blocks are all zero and the coupling terms appear only on the right-hand side. The second kind is a nonsymmetric block system with off-diagonal coupling terms. Several variants of the Schwarz alternating method are proposed for the first kind of linear system, including one in which the Schwarz alternating iterations and the Newton iterations are combined into a single scheme. This version of the method is particularly attractive, as it lends itself to a minimally intrusive implementation into existing finite element codes. Finally, we demonstrate the performance of the proposed variants of the Schwarz alternating method on several one-dimensional and three-dimensional examples.
Computer Methods in Applied Mechanics and Engineering
Journal of the Mechanics and Physics of Solids, 2015
Philosophical Magazine, 2014
ABSTRACT This study is aimed at developing a physics-based crystal plasticity finite element mode... more ABSTRACT This study is aimed at developing a physics-based crystal plasticity finite element model for body-centred cubic (BCC) metals, through the introduction of atomic-level deformation information from molecular dynamics (MD) investigations of dislocation motion at the onset of plastic flow. In this study, three critical variables governing crystal plasticity mediated by dislocation motion are considered. MD simulations are first performed across a range of finite temperatures up to 600K to quantify the temperature dependence of critical stress required for slip initiation. An important feature of slip in BCC metals is that it is not solely dependent on the Schmid law measure of resolved shear stress, commonly employed in crystal plasticity models. The configuration of a screw dislocation and its subsequent motion is studied under different load orientations to quantify these non-Schmid effects. Finally, the influence of strain rates on thermal activation is studied by inducing higher stresses during activation at higher applied strain rates. Functional dependence of the critical resolved shear stress on temperature, loading orientation and strain rate is determined from the MD simulation results. The functional forms are derived from the thermal activation mechanisms that govern the plastic behaviour and quantification of relevant deformation variables. The resulting physics-based rate-dependent crystal plasticity model is implemented in a crystal plasticity finite element code. Uniaxial simulations reveal orientation-dependent tension-compression asymmetry of yield that more accurately represents single-crystal experimental results than standard models.
Modelling and Simulation in Materials Science and Engineering, 2010
This paper develops a detailed molecular dynamics (MD) simulation model to study the glass transi... more This paper develops a detailed molecular dynamics (MD) simulation model to study the glass transition temperature (T g) of a finite polystyrene (PS) system in the presence of high pressure carbon dioxide (CO 2). Validated inter-atomic potentials for pure PS and CO 2 are used for these simulations. Specific parameters and combinations rules are introduced to accurately model the intermolecular interactions between PS and CO 2. The intermolecular interaction model has a strong effect on the T g of the PS-CO 2 system. The MD model comprises PS and CO 2 molecules confined in a finite walled system to manifest the effects of high pressure CO 2. The effectiveness of the simulation model is established by comparison with experimental free-volume data from positronium annihilation lifetime spectroscopy (PALS). An important outcome of this study is the identification of clearly demarcated regions for bulk and surface analysis. Physical properties such as density, free volume, segmental motion across the thickness and end group mobility are also studied to gain insight into the polymer dynamics. As is expected, the simulations show that the presence of high pressure CO 2 reduces the T g of PS significantly due to an increase in chain mobility. Additionally, the simulation data show a remarkable effect of CO 2 on the extent and characteristics of the surface layer.
Journal of the Mechanics and Physics of Solids, 2013
ABSTRACT A physically consistent framework for combining pressure-volume-temperature equations of... more ABSTRACT A physically consistent framework for combining pressure-volume-temperature equations of state with crystal plasticity models is developed for the application of modeling the response of single and polycrystals under shock conditions. The particular model is developed for copper, thus the approach focuses on crystals of cubic symmetry although many of the concepts in the approach are applicable to crystals of lower symmetry. We employ a multiplicative decomposition of the deformation gradient into isochoric elastic, thermoelastic dilation, and plastic parts leading to a definition of isochoric elastic Green-Lagrange strain. This finite deformation kinematic decomposition enables a decomposition of Helmholtz free-energy into terms reflecting dilatational thermoelasticity, strain energy due to long-range isochoric elastic deformation of the lattice and a term reflecting energy stored in short range elastic lattice deformation due to evolving defect structures. A model for the single crystal response of copper is implemented consistent with the framework into a three-dimensional Lagrangian finite element code. Simulations exhibit favorable agreement with single and bicrystal experimental data for shock pressures ranging from 3 to 110 GPa.
Journal of Polymer Science Part B: Polymer Physics, 2011
Fabrication of nanoscale polymer-based devices, especially in biomedical applications, is a chall... more Fabrication of nanoscale polymer-based devices, especially in biomedical applications, is a challenging process due to requirements of precise dimensions. Methods that involve elevated temperature or chemical adhesives are not practicable due to the fragility of the device components and associated deformation. To effectively fabricate devices for lab-on-a-chip or drug delivery applications, a process is required that permits bonding at low temperatures. The use of carbon dioxide (CO 2) to assist the bonding process shows promise in reaching this goal. It is now well established that CO 2 can be used to depress the glass transition temperature (T g) of a polymer, allowing bonding to occur at lower temperatures. Furthermore, it has been shown that CO 2 can preferentially soften a polymer surface, which should allow for effective bonding at temperatures even below the bulk T g. However, the impact of this effect on bonding has not been quantified, and the optimal bonding temperature and CO 2 pressure conditions are unknown. In this study, a molecular dynamics model is used to examine the atomic scale behavior of polystyrene in an effort to develop understanding of the physical mechanisms of bonding and to quantify how the process is impacted by CO 2. The final result is the identification of a range of CO 2 pressure conditions which produce the strongest bonding between PS thin films at room temperature.
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Papers by Coleman Alleman