An FFT based chemo-mechanical framework with fracture: Application to mesoscopic electrode degradation

Misfit stress generated by lattice mismatch between the lithiated and delithiated phases upon ion (de)intercalation plays a key role in cycling-induced mechanical degradation and capacity fading of battery electrodes. As a general phenomenon, misfit stress also leads to interface instability. A well-known example is the stress-induced island growth or the Stranski-Krastanov growth mode of epitaxial thin films, where the misfit strain between thin film and substrate destabilizes the uniform film growth. In this work, we predict that similar phenomenon can also occur during the ion (de)intercalation process in battery compounds, in which the misfit stress triggers the morphological instability of the moving phase boundary. This phenomenon results in non-uniform (de)intercalation, leading to capacity under-utilization and battery degradation and even failure due to stress concentration, and therefore needs to be carefully mitigated to improve battery performance. In our theoretical analysis, we consider the kinetic evolution of a sinusoidal perturbation applied to an initially flat interface between the lithium-rich and lithium-poor phases upon (de)lithiation under constant overpotential or flux conditions. The perturbation growth rate is calculated from the linear stability analysis. For interface-limited phase boundary movement, there exists a critical wavelength above which perturbation will growth. On the other hand, two critical wavelengths are identified for diffusion-limited phase transformation, and only perturbations with wavelengths between them will grow with time. The growth exponents predicted by the linear stability theory agree well with phase-field simulations. Based on the analysis, a stability diagram for lithium (de)intercalation is constructed in the space of particle size, applied overpotential (or intercalation flux) and interface location, as shown in Figure 1. Such diagram provides guidance on the conditions at which stress-induced Li intercalation instability can be avoided. A useful insight from our study is that the interface is most susceptible to instability when it is near the electrode particle surface, i.e. at the beginning of (dis)charge process. Accordingly, we propose a (dis)charging strategy to suppress the instability, in which a high Li flux pulse is applied at the initial (de)lithiation stage to stabilize the interface until it moves into the particles. We compare interface evolution in this (dis)charging protocol against during galvanostatic cycling in phase-field simulations. It shows that the proposed strategy can effectively prevent interface instability, which results in an increase in the (dis)charge capacity and reduction in localized stress hotspots. Figure 1

Simulations at physical quark masses are affected by the critical slowing down of the solvers. Multigrid preconditioning has proved to deal effectively with this problem. Multigrid accelerated simulations at the physical value of the pion mass are being performed to generate Nf = 2 and Nf = 2 + 1 + 1 gauge ensembles using twisted mass fermions. The adaptive aggregation-based domain decomposition multigrid solver, referred to as DD-αAMG method, is employed for these simulations. Our simulation strategy consists of an hybrid approach of different solvers, involving the Conjugate Gradient (CG), multi-mass-shift CG and DD-αAMG solvers. We present an analysis of the multigrid performance during the simulations discussing the stability of the method. This significant speeds up the Hybrid Monte Carlo simulation by more than a factor 4 at physical pion mass compared to the usage of the CG solver.

The aim of the present paper is to propose a phenomenological thermodynamically consistent 3D model for shape memory alloys (SMA) in the finite strain range. In particular, a model able to predict the main features of SMA materials, such as the superelastic and the shape‐memory effects, is proposed. The model is based on the assumption of the local multiplicative split of the deformation gradient into an elastic and a phase transformation part. The governing state and evolutive equations are written in the undeformed configuration. The material parameters of the model are characterized by a clear physical meaning so that they can be determined by simple experimental tests. The finite deformation SMA model is also reformulated in the framework of small strain, linearizing the strain and stress measures in order to obtain a consistent constitutive model preserving the nonlinear material response. A robust algorithm is adopted in order to integrate the nonlinear evolutive equations; 2D and 3D finite elements are implemented in a numerical code considering finite and small deformations. Some numerical applications are carried out showing the performances of the proposed model and the developed numerical procedure to describe the superelastic and the shape‐memory effects of SMA devices. Comparisons of different results obtained by the small and finite strain formulations are reported. Copyright © 2009 John Wiley & Sons, Ltd.

A formulation of the Element-Free Galerkin Method (EFGM) for saturated soil with pore water is presented under Cam-clay model to overcome the difficulties which appear in the FE analysis. A weak form of the set of equations for the equilibrium of total nominal stress rate and the continuity of pore water is derived and its discretization, based on the usual EFGM strategy, e.g., the moving least square method (MLSM), is fumished within the framework of finite strain. Numerical discretization of the weak form leads to an updated Lagrangean scheme. Such a numerical strategy, in which the nonlocal characteristics incorporated is into the discretized continuity equation, is expected to be advantageous in avoiding the dependency of mesh type and size on numerical solution of strain localization problem. The stiffness matrix is numerically evaluated by the fourth order of the Gauss integration, and boundary conditions are treated with the help of the penalty method. To trace the bifurcation phenomena in the relation of load and deflection, several patterns of initial imperfection are given along the surface of soil specimen. Shear banding within a soil specimen can be introduced while avoiding the numerical difficulties which depend on mesh size in the corresponding FE analyses.

A multi-physics, multi-scale and finite strain crystal plasticity-based model for pseudoelastic NiTi shape memory alloy

Topology optimization of finite strain elastoplastic materials using continuous adjoint method: Formulation, implementation, and applications

Topology optimization with a finite strain nonlocal damage model using the continuous adjoint method

This paper presents a thermomechanical model for pseudoelastic shape memory alloys (SMAs) accounting for internal hysteresis effect due to incomplete phase transformation. The model is developed within the finite-strain framework, wherein the deformation gradient is multiplicatively decomposed into thermal dilation, rigid body rotation, elastic and transformation parts. Helmholtz free energy density comprises three components: the reversible thermodynamic process , the irreversible thermodynamic process and the physical constraints of both. In order to capture the multiple internal hysteresis loops in SMA, two internal variables representing the transition points of the forward and reverse phase transformation, $$\phi _s^f$$ and $$\phi _s^r$$ , are introduced to describe the incomplete phase transformation process. Evolution equations of the internal variables are derived and linked to the phase transformation. Numerical implementation of the model features an Euler discretization and a cutting-plane algorithm. After validation of the model against the experimental data, numerical examples are presented, involving a SMA-based vibration system and a crack SMA specimen subjected to partial loading–unloading case. Simulation results well demonstrate the internal hysteresis and free vibration behavior of SMA.

This paper presents a computational performance analysis of a parallel implementation of a conjugate gradient (CG) solver using domain decomposition and distributed memory computers, applied to a 3-D finite element method problem. The results show a superlinear speedup, which is not usually expected. The analysis shows why and how it can happen.

OpenMP is an architecture-independent language for programming in the shared memory model. OpenMP is designed to be simple and powerful in terms of programming abstractions. Unfortunately, the architecture-independent abstractions sometimes come with the price of low parallel performance. This is especially true for applications with an unstructured data access pattern running on distributed shared memory systems (DSM). Here, proper data distribution and algorithmic optimizations play a vital role for performance. In this article, we have investigated ways of improving the performance of an industrial class conjugate gradient (CG) solver, implemented in OpenMP running on two types of shared memory systems. We have evaluated bandwidth minimization, graph partitioning and reformulations of the original algorithm reducing global barriers. By a detailed analysis of barrier time and memory system performance, we found that bandwidth minimization is the most important optimization reducing both L2 misses and remote memory accesses. On a uniform memory system, we get perfect scaling. On a NUMA system, the performance is significantly improved with the algorithmic optimizations leaving the system dependent global reduction operations as a bottleneck.

Comparison of different isotropic elastoplastic models at finite strains used in numerical analysis

While the advances in synchrotron light sources, together with the development of focusing optics and detectors, allow nanoscale ptychographic imaging of materials and biological specimens, the corresponding experiments can yield terabyte-scale volumes of data that can impose a heavy burden on the computing platform. Although graphics processing units (GPUs) provide high performance for such large-scale ptychography datasets, a single GPU is typically insufficient for analysis and reconstruction. Several works have considered leveraging multiple GPUs to accelerate the ptychographic reconstruction. However, most of these works utilize only the Message Passing Interface to handle the communications between GPUs. This approach poses inefficiency for a hardware configuration that has multiple GPUs in a single node, especially while reconstructing a single large projection, since it provides no optimizations to handle the heterogeneous GPU interconnections containing both low-speed (e.g., PCIe) and high-speed links (e.g., NVLink). In this paper, we provide an optimized intranode multi-GPU implementation that can efficiently solve large-scale ptychographic reconstruction problems. We focus on the maximum likelihood reconstruction problem using a conjugate gradient (CG) method for the solution and propose a novel hybrid parallelization model to address the performance bottlenecks in the CG solver. Accordingly, we have developed a tool, called PtyGer (Ptychographic GPU(multiple)-based reconstruction), implementing our hybrid parallelization model design. A comprehensive evaluation verifies that PtyGer can fully preserve the original algorithm’s accuracy while achieving outstanding intranode GPU scalability.

Assembly free FEM bypasses the assembly step and solves the system of linear equations at the element level using Conjugate Gradient (CG) type iterative solver. The smaller dense Matrix-vector Products (MvPs) are encapsulated within the CG solver and are computed either at element level or degree of freedom (DoF) level. Both these strategies exploit the computing power of GPU effectively, but the performance is lagging due to the uncoalesced global memory access on GPU. This paper proposes an improved MvP strategy in assembly free FEM, which improves the performance by coalesced global memory access using on-chip faster shared memory and using the texture cache memory on GPU. Since GPU has limited shared memory (in few KBs), the proposed technique suffers from a problem known as low occupancy. Despite the low occupancy issue, the proposed strategy outperforms both element based and DoF based MvP strategies on GPU. Numerical experiments compared with element level and DoF level strategies on GPU and found that, GPU instance of proposed MvP outperforms both strategies approximately by factor of 7 and 1.5 respectively.

Materials in growth have specific features such that changing their own configuration in a particular direction while reorganizing themselves to fit the surroundings. Growth can therefore be viewed as some irreversible anisotropic local structural rearrangement for which more material of the same type is squizzed in the same particle- entering the general theory of such rearrangements in the finite-strain framework. Accordingly, a thermodynamically admissible model of volumetric growth is contemplated which exploits the notion of material transplant (or local structural rearrangement). The associated driving force appears to be the Mandel stress (a part of the Eshelby stress tensor or energy-momentum tensor). Anisotropy of growth is characterized by a vector field slaved to the principal directions of that tensor. The model obtained is one of anisotropic visco-elasticity in finite strains. It is applicable to self-organization or adaptation. The validity of the model is assessed in terms of (i) circumferential (monotonic) growth/resorption behavior, (ii) stress induction in a ring, and (iii) dynamical effects (repeated alternate loading) on the material growth in a cantilever beam.

The kinetics of electrochemical intercalation and electrosorption processes are often limited by the solid-state diffusion of ions inside the lattice of the host material. While some of these limitations can be mitigated by nanostructuring of the electrode material, there is a large interest in the electrochemical energy storage community to find materials with structural motifs that allow for intrinsically fast ion diffusion, even in bulk-sized particles.In this presentation, it will be highlighted how interlayer properties, such as interlayer distance and interlayer chemistry, affect electrochemical ion intercalation and electrosorption processes in layered host materials. Using the examples of hydrogen titanates1 and Ti3C2Tx MXenes2, it is demonstrated that the presence of structural interlayer atoms or molecules can increase the accessibility of ions to the interlayer space. In the model layered host material TiS2, it is shown that increased interlayer spacing and reduced deformation during ion intercalation can lead to a change from diffusion-limited to non-diffusion limited (or pseudocapacitive) charge storage behavior,3 providing some of the most compelling experimental evidence of the intimate relationship between deformation, interlayer distance, and intercalation kinetics in layered host materials.This contribution will emphasize the importance of interlayer properties of layered and 2D materials for electrochemical ion intercalation and electrosorption processes and provide perspectives and design strategies for next generation ion insertion hosts with fast kinetics for high power energy storage. Fleischmann, S. et al. Interlayer separation in hydrogen titanates enables electrochemical proton intercalation. J. Mater. Chem. A 8, 412–421 (2020).Liang, K. et al. Engineering the Interlayer Spacing by Pre-Intercalation for High Performance Supercapacitor MXene Electrodes in Room Temperature Ionic Liquid. Adv. Funct. Mater. 31, 2104007 (2021).Fleischmann, S., Shao, H., Taberna, P.-L., Rozier, P. & Simon, P. Electrochemically Induced Deformation Determines the Rate of Lithium Intercalation in Bulk TiS2. ACS Energy Lett. 6, 4173–4178 (2021).