Exploring the interplay between cellular development and mechanics in the developing human brain

The human brain has a complex structure on both cellular and organ scales. This structure is closely related to the brain's abilities and functions. Disruption of one of the biological processes occurring during brain development on the cellular scale may affect the cortical folding pattern of the brain on the organ scale. However, the link between disruptions in cellular brain development and associated cortical malformation remains largely unknown. From a mechanical perspective, the forces generated during development lead to mechanical instability and, eventually, the mergence of cortical folds. To fully understand mechanism underlying malformations of cortical development, it is key to consider both the events that occur on the cellular scale and the mechanical forces generated on the organ scale. Here we present a computational model describing cellular division and migration on the cellular scale, as well as growth and cortical folding on the tissue or organ scale, in a continuous way by a coupled finite growth and advection-diffusion model. We introduce the cell density as an independent field controlling the volumetric growth. Furthermore, we formulate a positive relation between cell density and cortical layer stiffness. This allows us to study the influence of the migration velocity, the cell diffusivity, the local stiffness, and the local connectivity of cells on the cortical folding process and mechanical properties during normal and abnormal brain development numerically. We show how an increase in the density of the neurons increases the layer's mechanical stiffness. Moreover, weWe validate our simulation results through the comparison with histological sections of the fetal human brain. The current model aims to be a first step towards providing a reliable platform to systematically evaluate the role of different cellular events on the cortical folding process and vice versa

Comparative computational analysis of the Cahn-Hilliard equation with emphasis on C1-continuous methods

The numerical treatment of the fourth-order Cahn–Hilliard equation is nonstandard. Using a Galerkin-method necessitates, for instance, piecewise smooth and globally -continuous basis functions or a mixed formulation. The latter is obtained introducing an auxiliary field which allows to rephrase the Cahn–Hilliard equation as a set of two coupled second-order equations. In view of this, the formulation in terms of the primal unknown appears to be a more intuitive and natural choice but requires a -continuous interpolation. Therefore, isogeometric analysis, using a spline basis, and natural element analysis are addressed in the present contribution. Mixed second-order finite element methods introducing the chemical potential or alternatively a nonlocal concentration as auxiliary field serve as references to which both higher-order methods are compared in terms of accuracy and efficiency

General imperfect interfaces

The objective of this contribution is to develop a thermodynamically consistent theory for general imperfect interfaces and to establish a unified computational framework to model all classes of such interfaces using the finite element method. The interface is termed general imperfect in the sense that it allows for a jump of the temperature as well as for a jump of the normal heat flux across the interface. Conventionally, imperfect interfaces with respect to their thermal behavior are restricted to being either highly-conducting (HC) or lowly-conducting (LC) also known as Kapitza. For a HC interface the temperature is continuous across the interface while the jump of the normal heat flux is admissible. On the contrary, a LC interface does not allow for a jump of the heat flux across the interface but it does allow for a temperature jump. The temperature jump of a LC interface is frequently assumed to be proportional to the average heat flux across the interface. In this contribution we prove that this common assumption is indeed an appropriate condition to (sufficiently and not necessarily) satisfy the second law of thermodynamics.While HC and LC interfaces are generally accepted and well established today, the general imperfect interfaces remain poorly understood. Here we propose a thermodynamically consistent theory of general imperfect interfaces and we show that the dissipative structure of the interface suggests firstly to classify such interfaces as semi-dissipative (SD) and fully-dissipative (FD). Secondly, for a FD interface the interface temperature shall be considered as an independent degree of freedom and a new (constitutive) equation is obtained to calculate the interface temperature using a new interface material parameter i.e. the sensitivity. Furthermore, we show how all types of interfaces are derived from a FD general imperfect interface model. This finding allows us to establish a unified finite element framework to model all classes of interfaces. Full details of the novel numerical scheme are provided. Key features of general imperfect interfaces are then elucidated via a series of three-dimensional numerical examples. In particular, we show that according to the second law the interface temperature may not necessarily be the average of (or even between) the temperatures across the interface. Finally, we recall since the influence of interfaces on the overall response of a body increases as the scale of the problem decreases, this contribution has certain applications to nano-composites

Thermomechanics of solids with general imperfect coherent interfaces

The objective of this contribution is to develop a thermodynamically consistent theory for general imperfect coherent interfaces in view of their thermomechanical behavior and to establish a unified computational framework to model all classes of such interfaces using the finite element method. Conventionally, imperfect interfaces with respect to their thermal behavior are often restricted to being either highly conducting (HC) or lowly conducting (LC) also known as Kapitza. The interface model here is general imperfect in the sense that it allows for a jump of the temperature as well as for a jump of the normal heat flux across the interface. Clearly, in extreme cases, the current model simplifies to HC and LC interfaces. A new characteristic of the general imperfect interface is that the interface temperature is an independent degree of freedom and, in general, is not a function of only temperatures across the interface. The interface temperature, however, must be computed using a new interface material parameter, i.e., the sensitivity. It is shown that according to the second law, the interface temperature may not necessarily be the average of (or even between) the temperatures across the interface. In particular, even if the temperature jump at the interface vanishes, the interface temperature may be different from the temperatures across the interface. This finding allows for a better, and somewhat novel, understanding of HC interfaces. That is, a HC interface implies, but is not implied by, the vanishing temperature jump across the interface. The problem is formulated such that all types of interfaces are derived from a general imperfect interface model, and therefore, we establish a unified finite element framework to model all classes of interfaces for general transient problems. Full details of the novel numerical scheme are provided. Key features of the problem are then elucidated via a series of three-dimensional numerical examples. Finally, we recall since the influence of interfaces on the overall response of a body increases as the scale of the problem decreases, this contribution has certain applications to nano-composites and also thermal interface materials

Magnetic force and torque on particles subject to a magnetic field

Materials that are sensitive to an applied magnetic field are of increased interest and use to industry and researchers. The realignment of magnetizable particles embedded within a substrate results in a deformation of the material and alteration of its intrinsic properties. An increased understanding of the influence of the particles under magnetic load is required to better predict the behaviour of the material. In this work, we examine two distinct approaches to determine the resulting magnetic force and torque generated within a general domain. The two methodologies are qualitatively and quantitatively compared, and we propose scenarios under which one is more suitable for use than the other. We also describe a method to compute the generated magnetic torque. These post-processing procedures utilize results derived from a magnetic scalar-potential formulation for the large deformation magneto-elastic problem. We demonstrate their application in several examples involving a single and two particle system embedded within a carrier matrix. It is shown that, given a chosen set of boundary conditions, the magnetic forces and torques acting on a particle are influenced by its shape, size and location within the carrier

Homogenization of Dispersion-Strengthened Thermoelastic Composites with Imperfect Interfaces by Using Finite Element Technique

The paper describes the homogenization procedure for a two-phase mixture composite that consists of two isotropic thermoelastic materials. It is assumed that the special interface conditions are held on the boundary between the phases, where the stress and the thermal flux jump over the interphase boundary are equal to the surface stresses and thermal flux at the interface. Such boundary conditions are used to describe the nanoscale effects in thermoelastic nanodimensional bodies and nanocomposites. The homogenization problems are solved using the approach of the effective moduli method, the finite element method and the algorithm for generating the representative volume of cubic finite elements with random distribution of element material properties. As a numerical example, a mixture wolfram-copper composite is considered, where the interface conditions are simulated by surface membrane and thermal shell elements