Universal synthesis of conductive liquid network in polymers enabling elastic printed circuit board technology

Stretchable electronics are considered next-generation electronic devices in a broad range of emerging fields, including soft robotics1,2, biomedical devices3,4, human-machine interfaces5,6, and virtual or augmented reality devices7,8. A stretchable printed circuit board (S-PCB) is a basic conductive framework for the facile assembly of system-level stretchable electronics with various electronic components. Since an S-PCB is responsible for electrical communications between numerous electronic components, the conductive lines in S-PCB should strictly satisfy the following features: (i) metallic conductivity, (ii) constant electrical resistance during dynamic stretching, and (iii) tough interface bonding with various components9. Despite recent significant advances in intrinsically stretchable conductors10,11,12, they cannot simultaneously satisfy the above stringent requirements. Here, we present a new concept of conductive liquid network-based elastic conductors. These conductors are based on unprecedented liquid metal particles assembled network (LMPNet) and an elastomer. The unique assembled network structure and reconfigurable nature of the LMPNet conductor enabled high conductivity, high stretchability, tough adhesion, and imperceptible resistance changes under large strains, which enabled the first elastic-PCB (E-PCB) technology. We synthesized LMPNet through an acoustic field-driven cavitation event in the solid state. When an acoustic field is applied, liquid metal nanoparticles (LMPnano) are remarkably generated from original LMPs and assemble into a highly conductive particle network (LMPNet). Finally, we demonstrated a multi-layered E-PCB, in which various electronic components were integrated with tough adhesion to form a highly stretchable health monitoring system. Since our synthesis of LMPNet is universal, we could synthesize LMPNet in various polymers, including hydrogel, self-healing elastomer and photoresist and add new functions to LMPNet.

Orientational arrest in dense suspensions of elliptical particles under oscillatory shear flows

We study the rheological response of dense suspensions of elliptical particles, with an aspect ratio equal to 3, under oscillatory shear flows and imposed pressure by numerical simulations. Like for the isotropic particles, we find that the oscillatory shear flows respect the Cox-Merz rule at large oscillatory strains but differ at low strains, with a lower viscosity than the steady shear and higher shear jamming packing fractions. However, unlike the isotropic cases (i.e., discs and spheres), frictionless ellipses get dynamically arrested in their initial orientational configuration at small oscillatory strains. We illustrate this by starting at two different configurations with different nematic order parameters and the average orientation of the particles. Surprisingly, the overall orientation in the frictionless case is uncoupled to the rheological response close to jamming, and the rheology is only controlled by the average number of contacts and the oscillatory strain. Having larger oscillatory strains or adding friction does, however, help the system escape these orientational arrested states, which are evolving to a disordered state independent of the initial configuration at low strains and ordered ones at large strains.

An Analytic Solution for an Expanding/Contracting Strain-Hardening Viscoplastic Hollow Cylinder at Large Strains and Its Application to Tube Hydroforming Design

This paper presents a semi-analytic rigid/plastic solution for the expansion/contraction of a hollow cylinder at large strains. The constitutive equations comprise the yield criterion and its associated flow rule. The yield criterion is pressure-independent. The yield stress depends on the equivalent strain rate and the equivalent strain. No restriction is imposed on this dependence. The solution is facilitated using the equivalent strain rate as an independent variable instead of the polar radius. As a result, it reduces to ordinary integrals. In the course of deriving the solution above, the transformation between Eulerian and Lagrangian coordinates is used. A numerical example illustrates the solution for a material model available in the literature. A practical aspect of the solution is that it readily applies to the preliminary design of tube hydroforming processes.

A Data-Driven Memory-Dependent Modeling Framework for Anomalous Rheology: Application to Urinary Bladder Tissue

We introduce a data-driven fractional modeling framework for complex materials, and particularly bio-tissues. From multi-step relaxation experiments of distinct anatomical locations of porcine urinary bladder, we identify an anomalous relaxation character, with two power-law-like behaviors for short/long long times, and nonlinearity for strains greater than 25%. The first component of our framework is an existence study, to determine admissible fractional viscoelastic models that qualitatively describe linear relaxation. After the linear viscoelastic model is selected, the second stage adds large-strain effects to the framework through a fractional quasi-linear viscoelastic approach for the nonlinear elastic response of the bio-tissue of interest. From single-step relaxation data of the urinary bladder, a fractional Maxwell model captures both short/long-term behaviors with two fractional orders, being the most suitable model for small strains at the first stage. For the second stage, multi-step relaxation data under large strains were employed to calibrate a four-parameter fractional quasi-linear viscoelastic model, that combines a Scott-Blair relaxation function and an exponential instantaneous stress response, to describe the elastin/collagen phases of bladder rheology. Our obtained results demonstrate that the employed fractional quasi-linear model, with a single fractional order in the range α = 0.25–0.30, is suitable for the porcine urinary bladder, producing errors below 2% without need for recalibration over subsequent applied strains. We conclude that fractional models are attractive tools to capture the bladder tissue behavior under small-to-large strains and multiple time scales, therefore being potential alternatives to describe multiple stages of bladder functionality.

A component-free Lagrangian finite element formulation for large strain elastodynamics

Standard finite element formulation and implementation in solid dynamics at large strains usually relies upon and indicial-tensor Voigt notation to factorized the weighting functions and take advantage of the symmetric structure of the algebraic objects involved. In the present work, a novel component-free approach, where no reference to a basis, axes or components is made, implied or required, is adopted for the finite element formulation. Under this approach, the factorisation of the weighting function and also of the increment of the displacement field, can be performed by means of component-free operations avoiding both the use of any index notation and the subsequent reorganisation in matrix Voigt form. This new approach leads to a straightforward implementation of the formulation where only vectors and second order tensors in $${\mathbb {R}}^3$$ R 3 are required. The proposed formulation is as accurate as the standard Voigt based finite element method however is more efficient, concise, transparent and easy to implement.

Evidence of a Unique Critical Fabric Surface for Granular Soils

The critical state of granular soils needs to make proper reference to the fabric that develops at critical state. This study substantializes the concept of critical fabric surface (CFS) which attracts the fabric state of granular soils upon continuous shearing. Numerical experiments using discrete element modelling (DEM) are conducted under drained and undrained conditions with varies Lode angles. Fabric tensors are defined based on the normals of all contacts and of the strong force contacts only. Both tensors have their spherical component preserved such that the information of coordination number can be carried. A separate series of low confining pressure undrained test are conducted to probe the fabric states of soils in the post-liquefaction regime. Finally, a single CFS spanning across a wide range of coordination numbers is established based on the DEM results. The CFS concept provides an important reference state for soils sheared to large strains in complementary to the traditionally defined critical state. It provides a new perspective to interpret and model the mechanics of granular soils in both pre- and post- liquefied regimes. The evolution of fabric shows that the normalized strong-contact fabric evolves linearly with the stress ratio even for liquefied or anisotropically consolidated soils.

An Investigation of Surface Stress on the Fracture Mechanics Behavior of Classical and Phase-Separating Planar Electrodes

Although lithium-ion batteries have extensively been used in various applications because of their high energy capacity, fracture and failure, the by-products of large strains and stresses caused by fast charging and discharging need yet to be addressed. The size effects on the mechanical behavior of the nano-sized structures are significant; however, the classical elasticity theory may not consider such effects. On the other hand, surface stress theory, as a robust and potential theory, is suitable in considering size effects in nano-scale structures. Therefore, in this paper, in order to involve the surface stress effects on the fracture behavior of Li-ion batteries, the following steps are taken. Firstly, a phase-field model is used to determine the evolution of the concentration profile. Subsequently, the stress distribution is obtained by using the surface stress theory combined with chemical equations for a planar electrode. Afterward, by using the weight function method for an edge crack in the plate, the stress intensity factor is derived for all time steps and possible crack lengths during the process. It is found that with increasing phase boundary thickness parameter or decreasing phase-separation phenomenon, the surface mechanics parameters become more influential. Furthermore, in the presence of positive surface stress, the diffusion-induced stress distribution decreases, which in turn reduces the stress intensity factor. In addition, in this paper, the two states of surface stress are compared either for elastic or total strain. Concerning stresses and concentrations, the results indicate a big difference at the beginning of the deintercalation process showing, in particular, 2% for stresses, but the differences diminish gradually.