Efficient and robust constitutive integrators for single-crystal plasticity modeling

Simulations of the dynamic deformations of metal samples require elastic-plastic constitutive updates of the material behavior to be performed over a small time step between updates, as dictated by the Courant condition. Depending on the deformation conditions, the converged time step becomes short (~$10^{-9} s$ or less). If an implicit constitutive update is applied to this class of simulation, the benefit of the implicit update is negated, and the integration is prohibitively slow. The present work recasts an implicit update algorithm into an explicit form, for which each update step is five to six times faster, and the compute time required for a plastic update approaches that needed for a fully-elastic update. For dynamic loading conditions, the explicit model is found to perform an entire simulation up to 50 times faster than the implicit model. The performance of the explicit model is enhanced by adding a subcycling algorithm to the explicit model, by which the maximum time step between constitutive updates is increased an order of magnitude. These model improvements do not significantly change the predictions of the model from the implicit form, and provide overall computation times significantly faster than the implicit form over finite-element meshes. These modifications are also applied to polycrystals via Taylor averaging, where we also see improved model performance.Comment: 27 pages, 21 figure

Investigation of the role of Ti oxide layer in the size-dependent superelasticity of NiTi pillars: Modeling and simulation

Recent compression tests of NiTi pillars of a wide range of diameters have shown significant size dependency in the strain recovered upon unloading. In this paper, we propose a numerical model supporting the previously proposed explanation that the external Ti oxide layer may be responsible for the loss of superelasticity in the small pillars. The shape memory alloy at the center of the pillar is described using a nonlocal superelastic model, whereas the Ti oxide layer is modeled as elastoplastic. Voigt average analysis and finite element calculations are compared to experiments for the available range of pillar sizes. The simulation results also suggest a size-dependent strain hardening due to the constraint on the phase transformation effected by the confining Ti oxide layer.United States. Army Research Office (DAAD-19–02-D-0002

An extended constitutive correspondence formulation of peridynamics based on nonlinear bond-strain measures

An extension of the constitutive correspondence framework of peridynamics is proposed. The main motivation is to address unphysical deformation modes which are shown to be permitted in the original constitutive formulation. The specific problem of matter interpenetration observed in numerical discretizations of peridynamics has usually been treated by adding short-range forces between neighboring particles in the discretization. Here, we propose a solution that is rooted directly within the nonlocal theory. The basic approach is to introduce generalized nonlocal peridynamic strain tensors based on corresponding bond-level Seth–Hill strain measures which inherently avoid violations of the matter interpenetration constraint. Several analytic examples are used to show that the modified theory avoids issues of matter interpenetration in cases where the original theory fails. The resulting extended constitutive correspondence framework supports general classic constitutive laws as originally intended and is also shown to be ordinary.Massachusetts Institute of Technology. Institute for Soldier Nanotechnologies ( DAAD-19-02-D-0002)United States. Office of Naval Research (N00014-07-1-0764

A discontinuous Galerkin method for nonlinear shear-flexible shells

In this paper, a discontinuous Galerkin method for a nonlinear shear-flexible shell theory is proposed that is suitable for both thick and thin shell analysis. The proposed method extends recent work on Reissner–Mindlin plates to avoid locking without the use of projection operators, such as mixed methods or reduced integration techniques. Instead, the flexibility inherent to discontinuous Galerkin methods in the choice of approximation spaces is exploited to satisfy the thin plate compatibility conditions a priori. A benefit of this approach is that only generalized displacements appear as unknowns. We take advantage of this to craft the method in terms of a discrete energy minimization principle, thereby restoring the Rayleigh–Ritz approach. In addition to providing a straightforward and elegant derivation of the discrete equilibrium equations, the variational character of the method could afford numerous advantages in terms of mesh adaptation and available solution techniques. The proposed method is exercised on a set of benchmarks and example problems to assess its performance numerically, and to test for shear and membrane locking. Keywords: Shells; Discontinuous Galerkin; Locking; VariationalUnited States. Army Research Office (Contract DAAD-19-02-D-0002)United States. Office of Naval Research (Grant N00014-07-1-0764

A fully-coupled computational framework for large-scale simulation of fluid-driven fracture propagation on parallel computers

The propagation of cracks driven by a pressurized fluid emerges in several areas of engineering, including structural, geotechnical, and petroleum engineering. We present a robust numerical framework to simulate fluid-driven fracture propagation that addresses the challenges emerging in the simulation of this complex coupled nonlinear hydro-mechanical response. We observe that the numerical difficulties stem from the strong nonlinearities present in the fluid equations as well as those associated with crack propagation, from the quasi-static nature of the problem, and from the a priori unknown and potentially intricate crack geometries that may arise. An additional challenge is the need for large scale simulation owing to the mesh resolution requirements and the expected 3D character of the problem in practical applications. To address these challenges we model crack propagation with a high-order hybrid discontinuous Galerkin / cohesive zone model framework, which has proven massive scalability properties, and we model the lubrication flow inside the propagating cracks using continuous finite elements, furnishing a fully-coupled discretization of the solid and fluid equations. The parallel approach for solving the linearized coupled problem consists of standard iterative solvers based on domain decomposition. The resulting computational approach provides the ability to conduct highly-resolved and quasi-static simulations of fluid-driven fracture propagation with unspecified crack path. We conduct a series of numerical tests to verify the computational framework against known analytical solutions in the toughness and viscosity dominated regimes and we demonstrate its performance in terms of robustness and parallel scalability, enabling simulations of several million degrees of freedom on hundreds of processors

Dynamic fragmentation of a brittle plate under biaxial loading: strength or toughness controlled?

The fragmentation of a brittle plate subjected to dynamic biaxial loading is investigated via numerical simulations. The aim is to extend our understanding of the dynamic processes affecting fragment size distributions. A scalable computational framework based on a hybrid cohesive zone model description of fracture and a discontinuous Galerkin formulation is employed. This enables large-scale simulations and, thus, the consideration of rich distributions of defects, as well as an accurate account of the role of stress waves. We study the dependence of the fragmentation response on defect distribution, material properties, and strain rate. A scaling law describing the dependence of fragment size on the parameters is proposed. It is found that fragmentation exhibits two distinct regimes depending on the loading rate and material defect distribution: one controlled by material strength and the other one by material toughness. At low strain rates, fragmentation is controlled by defects, whereas at high strain rates energy balance arguments dominate the fragmentation respons

A Discontinuous Galerkin Formulation of Kirchhoff-Love Shells: From Linear Elasticity to Finite Deformations

Spatially-discontinuous Galerkin methods constitute a generalization of weak formulations, which allow for discontinuities of the problem unknowns in its domain interior [1]. When considering problems involving high-order derivatives, discontinuous Galerkin methods can also be seen as a means of enforcing higher-order continuity requirements in a weak manner [2,3]. Recently, the authors [4] have proposed a DG formulation for Kirchhoff-Love shell theory for which both the membrane and the bending response of the shell are considered. The proposed one-field formulation takes advantage of the weak enforcement in such a way that the displacements are the only discrete unknowns, while the C1 continuity is enforced weakly. The consistency, stability and rate of convergence of the numerical method are demonstrated for the case of a linear elastic material. In this work, this method is extended to shell problems involving finite displacements and finite deformations

A Finite Element Study of Electromagnetic Riveting

Electromagnetic riveting, used in some aerospace assembly processes, involves rapid deformation, leading to the finished rivet configuration. Analysis of this process is described for the case of an aluminum rivet joining typical aluminum structural elements. The analysis is based on a finite element method that includes the effects of heating, due to rapid plastic deformation of the material, on the material properties. Useful details of material deformation and thermal history and the final rivet and structure configuration and states of stress and strain are obtained. These results have significant implications in the design, implementation, and improvement of practical fastening processes in the aerospace industry