Synthesis of auxetic structures using optimization of compliant mechanisms and a micropolar material model

Aim of this work is the synthesis of auxetic structures using a topology optimization approach for micropolar (or Cosserat) materials. A distributed compliant mechanism design problem is formulated, adopting a SIMP–like model to approximate the constitutive parameters of 2D micropolar bodies. The robustness of the proposed approach is assessed through numerical examples concerning the optimal design of structures that can expand perpendicularly to an applied tensile stress. The influence of the material characteristic length on the optimal layouts is investigated. Depending on the inherent flexural stiffness of micropolar solids, truss–like solutions typical of Cauchy solids are replaced by curved beam–like material distributions. No homogenization technique is implemented, since the proposed design approach applies to elements made of microstructured material with prescribed properties and not to the material itself

Auxetic materials for MEMS: modeling, optimization and additive manufacturing

Auxetic materials are of interest because of enhanced material properties related to negative Poisson’s ratio, such as increased shear modulus, indentation resistance, fracture toughness, energy absorption, porosity/permeability variation with strain and synclastic curvature. In addition, the Poissons ratio does not depend on scale: deformation can take place at the nano- (molecular), [1], micro-[2], or even at the macro-level, [3]; the only requirement is the right combination of the geometry and the deformation mechanism. The most popular feature of auxetic structures is that it can expand in the direction perpendicular to an externally exerted tension. This property makes auxetic structures strongly appealing for MEMS applications (i.e. motion conversion and resonators) [4]. Here we present a full study of a re-entrant honeycomb structure which can be used in MEMS devices as motion conversion spring. The design of the proposed structure is obtained from a Matlab optimization procedure targeted to reach a Poisson’s ratio equal to -1. An additional nonlinear numerical simulation (see [5]) is done to verify the behavior of the structure under large deformations regime, which is the one required by the MEMS applications and then, a 3D-printed model (see [6]) of the optimized structure is obtained. Finally, a topology optimization is performed to obtain an auxetic structure that, in principle, can amplify the motion in the direction othogonal to the driving one. With this procedure there is no need to create an input structure from which the optimization procedure can start. Also for one of these optimized auxetic structures, an additional nonlinear numerical simulation is done

Analysis of frequency stability and thermoelastic effects for slotted tuning fork MEMS resonators

MicroElectroMechanical Systems (MEMS) resonators are attracting increasing interest because of their smaller size and better integrability as opposed to their quartz counterparts. However, thermal drift of the natural frequency of silicon structures is one of the main issues that has hindered the development of MEMS resonators. Extensive investigations have addressed both the fabrication process (e.g., introducing heavy doping of the silicon) and the mechanical design (e.g., exploiting proper orientation of the device, slots, nonlinearities). In this work, starting from experimental data published in the literature, we show that a careful design can help reduce the thermal drift even when slots are inserted in the devices in order to decrease thermoelastic losses. A custom numerical code able to predict the dynamic behavior of MEMS resonators for different materials, orientations and doping levels is coupled with an evolutionary optimization algorithm and the possibility to find an optimal mechanical design is demonstrated on a tuning-fork resonator

Integrated structure for a resonant micro-gyroscope and accelerometer

This paper presents the study of the mechanical behavior of a microstructure designed to detect acceleration and angular velocity simultaneously. The new resonant micro-sensor proposed, fabricated by the ThELMA© surface-micromachining technique, bases detection of two components of external acceleration (one in-plane component and one out-of plane component) and two components of angular velocity (roll and yaw) on the variation of frequency of several elements set in resonance. The device, despite its small dimensions, provides a differential decoupled detection of four external quantities thanks to the presence of four slender beams resonating in bending and four torsional resonators

Analysis of frequency stability and thermoelastic effects for slotted tuning fork MEMS resonators

MicroElectroMechanical Systems (MEMS) resonators are attracting increasing interest because of their smaller size and better integrability as opposed to their quartz counterparts. However, thermal drift of the natural frequency of silicon structures is one of the main issues that has hindered the development of MEMS resonators. Extensive investigations have addressed both the fabrication process (e.g., introducing heavy doping of the silicon) and the mechanical design (e.g., exploiting proper orientation of the device, slots, nonlinearities). In this work, starting from experimental data published in the literature, we show that a careful design can help reduce the thermal drift even when slots are inserted in the devices in order to decrease thermoelastic losses. A custom numerical code able to predict the dynamic behavior of MEMS resonators for different materials, orientations and doping levels is coupled with an evolutionary optimization algorithm and the possibility to find an optimal mechanical design is demonstrated on a tuning-fork resonator

3D auxetic single material periodic structure with ultra-wide tunable bandgap

The design and the combination of innovative metamaterials are attracting increasing interest in the scientific community because of their unique properties that go beyond the ones of natural materials. In particular, auxetic materials and phononic crystals are widely studied for their negative Poisson's ratio and their bandgap opening properties, respectively. In this work, auxeticity and phononic crystals bandgap properties are properly combined to obtain a single phase periodic structure with a tridimensional wide tunable bandgap. When an external tensile load is applied to the structure, the auxetic unit cells change their configurations by exploiting the negative Poisson's ratio and this results in the tuning, either hardening or softening, of the frequencies of the modes limiting the 3D bandgap. Moreover, the expansion of the unit cell in all the directions, due to the auxeticity property, guarantees a fully 3D bandgap tunability of the proposed structure. Numerical simulations and analytical models are proposed to prove the claimed properties. The first experimental evidence of the tunability of a wide 3D bandgap is then shown thanks to the fabrication of a prototype by means of additive manufacturing

Self-induced parametric amplification arising from nonlinear elastic coupling in a micromechanical resonating disk gyroscope

Parametric amplification, resulting from intentionally varying a parameter in a resonator at twice its resonant frequency, has been successfully employed to increase the sensitivity of many micro- and nano-scale sensors. Here, we introduce the concept of self-induced parametric amplification, which arises naturally from nonlinear elastic coupling between the degenerate vibration modes in a micromechanical disk-resonator, and is not externally applied. The device functions as a gyroscope wherein angular rotation is detected from Coriolis coupling of elastic vibration energy from a driven vibration mode into a second degenerate sensing mode. While nonlinear elasticity in silicon resonators is extremely weak, in this high quality-factor device, ppm-level nonlinear elastic effects result in an order-of-magnitude increase in the observed sensitivity to Coriolis force relative to linear theory. Perfect degeneracy of the primary and secondary vibration modes is achieved through electrostatic frequency tuning, which also enables the phase and frequency of the parametric coupling to be varied, and we show that the resulting phase and frequency dependence of the amplification follow the theory of parametric resonance. We expect that this phenomenon will be useful for both fundamental studies of dynamic systems with low dissipation and for increasing signal-to-noise ratio in practical applications such as gyroscopes