A thermo-chemo-mechanically coupled model for cathode particles in lithium-ion batteries

As the demand for lithium-ion batteries increases, a better understanding of the complex phenomena involved in their operation becomes crucial. In this work, we propose a coupled thermo-chemo-mechanical model for electrode particles of Li-ion batteries. To this end, we start with a general finite strain continuum framework for the coupled thermo-chemo-mechanical problem and then narrow it down to cathode active particles of Li-ion batteries, particularly to lithium manganese oxide particles. Electrochemical kinetics at the surface of the particle and also heat generation due to current exchange are taken into account. Next, the numerical treatment of the problem using the finite element method is presented. Specific line elements are needed to evaluate the flux of ions at the surface of the particle. Finally, the performance of the proposed model is evaluated using a few representative boundary value problems.Deutsche ForschungsgemeinschaftProjekt DEA

On the Influence of Ferroelectric Polarization States on the Magneto-electric Coupling in Two-phase Composites

Of particular attention in a variety of novel technical applications is the coupling between magnetic and electric field quantities. Materials that show magneto-electric (ME) coupling could enable new smart devices in the area of electric-field-controlled magnetic-data storage or highly sensitive magnetic-field sensors. In general, ME materials exhibit both a spontaneous magnetization and a spontaneous polarization. In this respect, they feature two ferroic states at the same time and are thus termed magneto-electric multiferroics. However, all natural and most of the synthesized ME multiferroics do not show an interaction between magnetization and electric polarization in the technically relevant temperature range. Thus, there is need for alternative realizations for ME coupling materials. A promising idea lies in the design and manufacturing of ME composites. These materials consist of a magnetostrictive and a piezoelectric phase and generate the ME coupling as a strain-induced product property. Since there exists a wealth of stable magnetostrictive and piezoelectric materials at ambient temperature, such composites yield the desired ME coupling also in a technically useful temperature range. In any case, the effective ME coupling is driven by microscopic interactions between the individual phases and thus highly depends on the microstructure of the composite. This calls for powerful homogenization methods that are able to predict the effective coupling for arbitrary microstructural morphologies. Motivated by that, we apply a two-scale computational homogenization framework for magneto-electro-mechanically coupled boundary value problems, which allows us to analyze the ME composite structures and calculate the effective ME-coefficient. Furthermore, by using a non-linear ferroelectric material model on the micro-level, we are able to simulate the polarization process of the ferroelectric phase. We show that this has a significant impact on the obtainable ME-coefficient

Magneto-electric coupling in terms of magnetically induced polarization from Analytical estimation of non-local deformation-mediated magneto-electric coupling in soft composites

Plots of magnetically induced polarizations and associated magneto-electric sensitivitie

Magneto-electric coupling in terms of magnetically induced polarization from Analytical estimation of non-local deformation-mediated magneto-electric coupling in soft composites

Plots of magnetically induced polarizations and associated magneto-electric sensitivitie

Magneto-electric coupling in terms of magnetically induced polarization from Analytical estimation of non-local deformation-mediated magneto-electric coupling in soft composites

Plots of magnetically induced polarizations and associated magneto-electric sensitivitie

Effect of satellite system impairments on a multilevel coding system for satellite broadcasting

In this paper, we evaluate a multilevel coding (MLC) scheme with multistage decoding (MSD) designed for satellite broadcasting communications. The impact of three different satellite system impairments on the decoding performance is analyzed. First, the influence of errors introduced by the channel estimation is discussed, assuming a typical data-aided (DA) channel estimator with different pilot lengths. Second, the impact of the residual phase noise present after the phase recovery is investigated using a model based on a normal distribution. Finally, the degradation introduced by the non-linearities of the satellite power amplifiers is also analyzed. The impact of these effects is investigated via the mutual information. Besides, bit error rate (BER) simulations are performed for each impairment effect. The considered MLC scheme is compared to a classical bit-interleaved coded modulation (BICM) scheme, showing that the MLC scheme provides different grades of robustness for each level

Efficient and reliable phase‐field simulation of brittle fracture using a nonsmooth multigrid solution scheme

In the last decades the phase‐field approach to fracture [1–3] has gained wide popularity due to advantages such as straight‐forward modeling of complex crack patterns and crack branching while allowing standard finite‐element discretizations. Time‐discrete phase‐field models of brittle fracture are typically formulated in terms of biconvex minimization problems for which a standard monolithic Newton‐Raphson scheme usually fails to converge. Solutions can be found by using operator‐splitting methods [2] or predictor‐corrector schemes [4]. Such methods come at the cost of high computational efforts. Furthermore, models incorporating the thermodynamically consistent local irreversibility of the damage phase‐field contain nonsmooth terms [2]. To improve the stability and to reduce the computational costs originating from the biconvexity and the nonsmoothness of the energy functional, we employ a nonsmooth multigrid method that can solve such problems roughly in the time of one equivalent linear problem [5] and which has been shown to be globally convergent [5]. We will demonstrate the computational speed of the proposed solution scheme by means of a classical benchmark problem of brittle fracture

An affine microsphere approach to modeling strain-induced crystallization in rubbery polymers

Upon stretching a natural rubber sample, polymer chains orient themselves in the direction of the applied load and form crystalline regions. When the sample is retracted, the original amorphous state of the network is restored. Due to crystallization, properties of rubber change considerably. The reinforcing effect of the crystallites stiffens the rubber and increases the crack growth resistance. It is of great importance to understand the mechanism leading to strain-induced crystallization. However, limited theoretical work has been done on the investigation of the associated kinetics. A key characteristic observed in the stress-strain diagram of crystallizing rubber is the hysteresis, which is entirely attributed to strain-induced crystallization. In this work, we propose a micromechanically motivated material model for strain-induced crystallization in rubbers. Our point of departure is constructing a micromechanical model for a single crystallizing polymer chain. Subsequently, a thermodynamically consistent evolution law describing the kinetics of crystallization on the chain level is proposed. This chain model is then incorporated into the affine microsphere model. Finally, the model is numerically implemented and its performance is compared to experimental data

A phase-field model for transversely isotropic ferroelectrics

We propose an electro-mechanically coupled phase-field model for ferroelectric materials that show cubic–tetragonal phase transition. The cubic phase is idealized by an isotropic formulation, and the tetragonal phase is idealized by a transversely isotropic formulation. We consider a classical phase-field model with Ginzburg–Landau-type evolution of the order parameter. The order parameter drives the transition of all involved moduli tensors such as elastic, dielectric and piezoelectric moduli, which in turn maintain their typical features and stability as a result of a selected phase-transition function. The model is described in coordinate-invariant form and implemented into a finite element framework with implicit time integration of the evolution equation. Representative numerical examples in two and three dimensions demonstrate the main features of the constitutive model and the numerical stability of the formulation

An invariant formulation for phase field models in ferroelectrics

This paper introduces an electro-mechanically coupled phase field model for ferroelectric domain evolution based on an invariant formulation for transversely isotropic piezoelectric material behavior. The thermodynamic framework rests upon Gurtin’s notion of a micro-force system in conjunction with an associated micro-force balance. This leads to a formulation of the second law, from which a generalized Ginzburg–Landau evolution equation is derived. The invariant formulation of the thermodynamic potential provides a consistent way to obtain the order parameter dependent elastic stiffness, piezoelectric, and dielectric tensor. The model is reduced to 2d and implemented into a finite element framework. The material constants used in the simulations are adapted to meet the thermodynamic condition of a vanishing micro-force. It is found that the thermodynamic potential taken from the literature has to be extended in order to avoid a loss of positive definiteness of the stiffness and the dielectric tensor. The small-signal response is investigated in the presence and in the absence of the additional regularizing terms in the potential. The simulations show the pathological behavior of the model in case these terms are not taken into account. The paper closes with microstructure simulations concerning a ferroelectric nanodot subjected to an electric field, a cracked single crystal, and a ferroelectric bi-crystal