Design, inverted vat photopolymerization 3D printing, and initial characterization of a miniature force sensor for localized in vivo tissue measurements

Background Tissue healthiness could be assessed by evaluating its viscoelastic properties through localized contact reaction force measurements to obtain quantitative time history information. To evaluate these properties for hard to reach and confined areas of the human body, miniature force sensors with size constraints and appropriate load capabilities are needed. This research article reports on the design, fabrication, integration, characterization, and in vivo experimentation of a uniaxial miniature force sensor on a human forearm. Methods The strain gauge based sensor components were designed to meet dimensional constraints (diameter ≤3.5mm), safety factor (≥3) and performance specifications (maximum applied load, resolution, sensitivity, and accuracy). The sensing element was fabricated using traditional machining. Inverted vat photopolymerization technology was used to prototype complex components on a Form3 printer; micro-component orientation for fabrication challenges were overcome through experimentation. The sensor performance was characterized using dead weights and a LabVIEW based custom developed data acquisition system. The operational performance was evaluated by in vivo measurements on a human forearm; the relaxation data were used to calculate the Voigt model viscoelastic coefficient. Results The three dimensional (3D) printed components exhibited good dimensional accuracy (maximum deviation of 183μm). The assembled sensor exhibited linear behavior (regression coefficient of R2=0.999) and met desired performance specifications of 3.4 safety factor, 1.2N load capacity, 18mN resolution, and 3.13% accuracy. The in vivo experimentally obtained relaxation data were analyzed using the Voigt model yielding a viscoelastic coefficient τ=12.38sec and a curve-fit regression coefficient of R2=0.992. Conclusions This research presented the successful design, use of 3D printing for component fabrication, integration, characterization, and analysis of initial in vivo collected measurements with excellent performance for a miniature force sensor for the assessment of tissue viscoelastic properties. Through this research certain limitations were identified, however the initial sensor performance was promising and encouraging to continue the work to improve the sensor. This micro-force sensor could be used to obtain tissue quantitative data to assess tissue healthiness for medical care over extended time periods.

FORCE DRIVEN VIBRATIONS OF NONLINEAR PLATES ON A VISCOELASTIC WINKLER FOUNDATION UNDER THE HARMONIC MOVING LOAD

In the present paper, the forced driven nonlinear vibrations of an elastic plate in a viscoelastic medium and resting on a viscoelastic Winkler-type foundation are studied. The damping features of the surrounding medium and foundation are described by the Kelvin-Voigt model and standard linear solid model with fractional derivatives, respectively. The dynamic response of the plate is described by the set of nonlinear differential equations with due account for the fact that the plate is being under the conditions of the internal resonance accompanied by the external resonance. The expressions for the stress function and nonlinear coefficients for different types of boundary conditions are presented.

Existence and long-time behavior of solutions to the velocity-vorticity-Voigt model of the 3D Navier-Stokes equations with damping and memory

In this paper, we study the long-time dynamical behavior of the non-autonomous velocity-vorticity-Voigt model of the 3D Navier-Stokes equations with damping and memory. We first investigate the existence and uniqueness of weak solutions to the initial boundary value problem for above-mentioned model. Next, we prove the existence of uniform attractor of this problem, where the time-dependent forcing term $f \in L^2_b(\mathbb{R}; H^{-1}(\Omega))$ is only translation bounded instead of translation compact. The results in this paper will extend and improve some results in Yue, Wang (Comput. Math. Appl., 2020) in the case of non-autonomous and contain memory kernels which have not been studied before.

Micromechanics-Based Prediction Models and Experimental Validation on Elastic Modulus of Recycled Aggregate Concrete

Elastic modulus is one of the most important mechanical properties of concrete (including recycled aggregate concrete), and it has a notable guiding significance for engineering. There is a lack of micromechanical research on the elastic modulus of recycled aggregate concrete. This paper adopts four models based on micromechanics, including the Voigt model, Reuss model, Eshelby method, and Mori–Tanaka method, to predict the elastic modulus of recycled aggregate concrete. The optimal model is determined by comparing the results of the four models with the experimental data. On this basis, some previous prediction methods for the elastic modulus of concrete are employed to be compared with the most satisfactory models in this paper. Several experimental data from the open literature are also utilized to better illustrate the reliability of the prediction models. It is concluded that the Mori–Tanaka method unfailingly produces more accurate predictions compared to other models. It gives the best overall approximation for various data and has extensive effects in predicting the elastic modulus of RAC. This work may be helpful in promoting the development of micromechanics research in recycled aggregate concrete.

Review on Vibration Analysis of Cracked Cantilever Beam

A unique feature of fiber-reinforced composite materials is that it allows structural tailoring for favorable dynamic performance, due to the directional nature of composite materials. Because of the directed character, material coupling occurs, resulting in coupled vibration modes and complicating dynamic analysis. A transverse triangular force impulse modulated by a harmonic motion excites the beam. For the substance of the beam, the Kelvin–Voigt model is employed. The fractured beam is represented by two sub-beams linked by a massless elastic rotating spring. The beams are designed to function in wet environments, which cause rusting. Corrosion causes cracks to form in beams, altering their inherent frequency and mode shape. The present paper examines the different investigations that have been done to investigate the impact of fracture on the dynamic properties of beams. The researchers provided a comprehensive evaluation of the impact of crack design factors (crack depth, crack location) on cantilever beam transverse and torsional frequencies. It is also given the analytical approach, numerical method, and experimental methods for studying the impact of fracture on vibration characteristics. Keywords: Cantilever Beam, Crack dimensions, Damage, Kelvin–Voigt model.

Effective Acoustic Equations for a Layered Material Described by the Fractional Kelvin-Voigt Model

The paper is devoted to the construction of effective acoustic equations for a two-phase layered viscoelastic material described by the Kelvin–Voigt model with fractional time derivatives. For this purpose, the theory of two-scale convergence and the Laplace transform with respect to time are used. It is shown that the effective equations are partial integro-differential equations with fractional time derivatives and fractional exponential convolution kernels. In order to find the coefficients and the convolution kernels of these equations, several auxiliary cell problems are formulated and solved

Mechanical Models of Pattern and Form in Biological Tissues: The Role of Stress–Strain Constitutive Equations

Mechanical and mechanochemical models of pattern formation in biological tissues have been used to study a variety of biomedical systems, particularly in developmental biology, and describe the physical interactions between cells and their local surroundings. These models in their original form consist of a balance equation for the cell density, a balance equation for the density of the extracellular matrix (ECM), and a force-balance equation describing the mechanical equilibrium of the cell-ECM system. Under the assumption that the cell-ECM system can be regarded as an isotropic linear viscoelastic material, the force-balance equation is often defined using the Kelvin–Voigt model of linear viscoelasticity to represent the stress–strain relation of the ECM. However, due to the multifaceted bio-physical nature of the ECM constituents, there are rheological aspects that cannot be effectively captured by this model and, therefore, depending on the pattern formation process and the type of biological tissue considered, other constitutive models of linear viscoelasticity may be better suited. In this paper, we systematically assess the pattern formation potential of different stress–strain constitutive equations for the ECM within a mechanical model of pattern formation in biological tissues. The results obtained through linear stability analysis and the dispersion relations derived therefrom support the idea that fluid-like constitutive models, such as the Maxwell model and the Jeffrey model, have a pattern formation potential much higher than solid-like models, such as the Kelvin–Voigt model and the standard linear solid model. This is confirmed by the results of numerical simulations, which demonstrate that, all else being equal, spatial patterns emerge in the case where the Maxwell model is used to represent the stress–strain relation of the ECM, while no patterns are observed when the Kelvin–Voigt model is employed. Our findings suggest that further empirical work is required to acquire detailed quantitative information on the mechanical properties of components of the ECM in different biological tissues in order to furnish mechanical and mechanochemical models of pattern formation with stress–strain constitutive equations for the ECM that provide a more faithful representation of the underlying tissue rheology.