Elementary Micromechanics of Heterogeneous Media

A Focus on Dynamic Modulus: Effects of External and Internal Morphological Features

The present work examines the effects of external and internal morphological features on the dynamic elastic modulus and its measure. It consists of two parts. The first part considers the effect of geometrical features of probes and shows the key role of roughness as source of a systematic error leading to the underestimation of the Young’s modulus. The second one is focused on the effect of porosity. Several models which consider the porosity as an ideal regular microstructure and the relative equations describing the Young’s modulus vs. porosity have been reviewed and critically discussed. The values of the relative modulus Er predicted by different models are similar for materials with low porosity (p < 0.2) and isolated pores whereas they strongly diverge if p > 0.2 and interconnected pores are present. Moreover, such models fail to describe the elastic behavior of materials correctly also with low porosity (p ≈ 0.1) such as sintered steels in the case of pores with a preferred orientation and an irregular shape.

2D Electrets of Ultrathin MoO2 with Apparent Piezoelectricity

Since graphene, a variety of 2D materials have been fabricated in a quest for a tantalizing combination of properties and desired physiochemical behavior. 2D materials that are piezoelectric, i.e., that allow for a facile conversion of electrical energy into mechanical and vice versa, offer applications for sensors, actuators, energy harvesting, stretchable and flexible electronics, and energy storage, among others. Unfortunately, materials must satisfy stringent symmetry requirements to be classified as piezoelectric. Here, 2D ultrathin single-crystal molybdenum oxide (MoO₂ ) flakes that exhibit unexpected piezoelectric-like response are fabricated, as MoO₂ is centrosymmetric and should not exhibit intrinsic piezoelectricity. However, it is demonstrated that the apparent piezoelectricity in 2D MoO₂ emerges from an electret-like behavior induced by the trapping and stabilization of charges around defects in the material. Arguably, the material represents the first 2D electret material and suggests a route to artificially engineer piezoelectricity in 2D crystals. Specifically, it is found that the maximum out-of-plane piezoresponse is 0.56 pm V^-1 , which is as strong as that observed in conventional 2D piezoelectric materials. The charges are found to be highly stable at room temperature with a trapping energy barrier of ≈2 eV.

An upper bound on the particle-laden dependency of shear stresses at solid–fluid interfaces

In modern advanced manufacturing processes, such as three-dimensional printing of electronics, fine-scale particles are added to a base fluid yielding a modified fluid. For example, in three-dimensional printing, particle-functionalized inks are created by adding particles to freely flowing solvents forming a mixture, which is then deposited onto a surface, which upon curing yields desirable solid properties, such as thermal conductivity, electrical permittivity and magnetic permeability. However, wear at solid–fluid interfaces within the machinery walls that deliver such particle-laden fluids is typically attributed to the fluid-induced shear stresses, which increase with the volume fraction of added particles. The objective of this work is to develop a rigorous strict upper bound for the tolerable volume fraction of particles that can be added, while remaining below a given stress threshold at a fluid–solid interface. To illustrate the bound’s utility, the expression is applied to a series of classical flow regimes.

Local fields and effective conductivity tensor of ellipsoidal particle composite with anisotropic constituents

An accurate semi-analytical solution of the conductivity problem for a composite with anisotropic matrix and arbitrarily oriented anisotropic ellipsoidal inhomogeneities has been obtained. The developed approach combines the superposition principle with the multipole expansion of perturbation fields of inhomogeneities in terms of ellipsoidal harmonics and reduces the boundary value problem to an infinite system of linear algebraic equations for the induced multipole moments of inhomogeneities. A complete full-field solution is obtained for the multi-particle models comprising inhomogeneities of diverse shape, size, orientation and properties which enables an adequate account for the microstructure parameters. The solution is valid for the general-type anisotropy of constituents and arbitrary orientation of the orthotropy axes. The effective conductivity tensor of the particulate composite with anisotropic constituents is evaluated in the framework of the generalized Maxwell homogenization scheme. Application of the developed method to composites with imperfect ellipsoidal interfaces is straightforward. Their incorporation yields probably the most general model of a composite that may be considered in the framework of analytical approach.

Highly stretchable polymer semiconductor films through the nanoconfinement effect

Soft and conformable wearable electronics require stretchable semiconductors, but existing ones typically sacrifice charge transport mobility to achieve stretchability. We explore a concept based on the nanoconfinement of polymers to substantially improve the stretchability of polymer semiconductors, without affecting charge transport mobility. The increased polymer chain dynamics under nanoconfinement significantly reduces the modulus of the conjugated polymer and largely delays the onset of crack formation under strain. As a result, our fabricated semiconducting film can be stretched up to 100% strain without affecting mobility, retaining values comparable to that of amorphous silicon. The fully stretchable transistors exhibit high biaxial stretchability with minimal change in on current even when poked with a sharp object. We demonstrate a skinlike finger-wearable driver for a light-emitting diode.

Modeling electrical power absorption and thermally-induced biological tissue damage

This work develops a model for thermally induced damage from high current flow through biological tissue. Using the first law of thermodynamics, the balance of energy produced by the current and the energy absorbed by the tissue are investigated. The tissue damage is correlated with an evolution law that is activated upon exceeding a temperature threshold. As an example, the Fung material model is used. For certain parameter choices, the Fung material law has the ability to absorb relatively significant amounts of energy, due to its inherent exponential response character, thus, to some extent, mitigating possible tissue damage. Numerical examples are provided to illustrate the model's behavior.

Memory effects for the heat conductivity of random suspensions of spheres

The presence of a particulate phase defines the effective response of a suspension to changes of the average heat flux. Using the random-point approximation we show that within the first order in the concentration, one needs to solve the problem for the temperature field created by a single inclusion in a matrix subject to an unsteady temperature gradient at infinity. We solve this problem by means of Laplace transform and use the solution as the first-order kernel in the functional expansion. From this kernel, we find the statistical average for the heat flux, which turns out to be a memory integral of the spatially averaged time-dependent temperature gradient. Thus, we discover that the constructive relationship between the average flux and averaged temperature gradient is not local in time, but rather involves a convolution integral that represents the memory due to the heterogeneity of the system. This is a novel result, which inter alia gives a rigorous justification to the usage of generalizations of the heat conduction law involving fractional time derivatives. The decay of the kernel is very close to t −1/2 for dimensionless times lesser than one and abruptly changes to t −3/2 for larger times.

Explicit relations between elastic and conductive properties of materials containing annular cracks

The impact of annular cracks on the effective elastic and conductive properties of a material is analysed. The compliance contribution tensor of an annular crack - the quantity that determines the increase in compliance of a solid due to introduction of such a crack - is derived analytically. The resistivity contribution tensor of an annular crack is calculated numerically. It is shown that an effective circular crack, i.e. a crack which yields the same change in elastic/conductive properties of a material as the given annular crack, can be chosen to match both of these tensors. Using this result, the explicit relation between elastic and conductive properties of a material containing annular cracks is obtained. The relation is derived using a non-interaction approximation. Applicability of the derived formulae to real materials (to plasma-sprayed coatings, in particular) is discussed.