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Journal Club Theme of December 2013: Bio-Integrated Flexible and Stretchable Strain Gauges

Nanshu Lu's picture


Strain gauges are widely used across all engineering fields to measure mechanical deformation of a solid object. The most common type of strain gauges consists of a patterned metal foil on a stiff plastic backing sheet glued to the solid object. Deformation in the object leads to deformation in the foil, thereby causing its electrical resistance to change. The fractional change in resistance, ΔR/R0, is related to the mechanical strain by the gauge factor (GF): GF = (ΔR/R0)/ε. The GF for metallic foils are typically between 2 to 5 [1], due mostly to changes in length and cross-sectional area. Compared to metallic foils, semiconductor devices can exhibit much larger GF due to piezoresistive effects [2] where the resistivity changes rapidly with strain due to the dependence of the bandgap on inter-atomic spacing. For example, the gauge factor of p-type [110] single crystalline silicon can be as high as 200 [2]. As a result, for precision measurements, semiconductor gauges, also called piezoresistors, are preferred over metal foils. These types of devices are widely used as ‘hard’ sensors attached to stiff materials such as metals, concretes and high modulus plastics for structural health monitoring or quantifying specimen deformation. 

Studies of biomechanics, physiology, and kinesiology often require the detection of mechanical deformation of bio-tissues. State-of-the-art strain measurements of soft tissues are based on imaging technologies such as optical cameras, MRI, CT or X-ray. To quantify soft tissue deformation without using sophisticated imaging facilities calls for devices that can conform to the curvilinear surfaces of biological tissues and also accommodate the large deformations that are often associated with them. Ordinary strain gauges made out of silicon slabs are clearly unsuitable for such uses, but so are flexible devices (metal foils or silicon nanomembranes) due to their inability to wrap complex curved objects or to stretch (i.e. respond in a reversible manner to strains much larger than ~1%).  Electrogoniometers and electrotorsiometers made of metal wires can be mounted on human joints to measure, in a bending mode, motions such as human elbow rotation and ankle dorsiflexion, but they cannot map spatial distributions of strain and they also impose unacceptably large mechanical constraints for measuring motions of soft parts of the body, such as the skin [3].  Mercury-in-rubber strain gauges represent one solution, suitable for monitoring blood flow and tissue swelling by local measurements of skin extension [4]. The filling requirements in the fabrication of such devices, however, restrict their geometries and modes of use. For example, most devices provide only single measurement capabilities, in closed loop form for application around approximately cylindrical parts of the body such as toes or legs. Other approaches include platinum (Pt)-based strain gauges for integration onto surfaces of objects such as contact lenses to record changes in the curvature of the cornea for the diagnosis of glaucoma [5]. These and other efforts establish a trend in strain gauge development toward increasingly soft and deformable mechanics, for bio-integrated applications. To monitor the surface strains of human skin due to joint motion, tissue swelling, wound healing, or even emotional expression, a sheet of skin-like, highly sensitive strain gauges that can be directly applied onto the tissue surface would be ideal. Such a system could conformally laminate onto the curvilinear surfaces of human body without any mechanical fixture or adhesives, and with an ability to follow the natural motions of the tissue without delaminating or imposing any mechanical constraint, similar to recently described ‘epidermal’ electronic systems [6].

Polymer-Based Bio-Integrated Strain Gauges

Electrically conductive rubber (ECR) is a promising class of material for this purpose, due to its intrinsically low modulus, low density, elastic mechanics and its pronounced piezoresistivity [7]. ECRs can be prepared by dispersing conductive fillers such as carbon black (CB), carbon nanotubes (CNT) or metallic nanoparticles into elastomers such as poly(dimethylsiloxane) (PDMS). Molding and curing processes can be used to manipulate such materials, which we refer to generally as conductive PDMS (CPDMS), into desired geometries for device integration. The electrical behaviors of CPDMS, such as the conductivity and the piezoresistance, depend strongly on filler concentration and morphology (e.g. particle size and structure) as well as filler–filler and filler–matrix interactions. With similar levels of loading, the sheet resistances of CB-doped PDMS (CB-PDMS) are several orders of magnitude higher than those of PDMS doped with multiwalled CNTs (CNT-PDMS) [8]. The piezoresistive effect is believed to arise from the different compressibilities between the filler and the matrix, such that the application of stress changes in the separations between individual filler elements. Applications of these effects range from tactile sensors [9] to strain gauges [10] and flow sensors [11]. 

We have reported materials and mechanics for an all-elastomer strain measurement device with gauge factor as high as 29 and with Young’s modulus that approaches that of the human epidermis [12] . These systems combine thin, carbon black doped poly(dimethylsiloxane) (CB-PDMS) as the strain gauges due to their high resistivity and strong dependence on strain, with carbon nanotube doped PDMS (CNT-PDMS) as the interconnects due to their comparatively low resistivity and weak dependence on strain.  Devices comprised of molded, straight resistors of CB-PDMS joined by serpentine-shaped interconnects of CNT-PDMS, both in a common matrix substrate of PDMS, have electrical responses that depend almost entirely on the strain in the CB-PDMS.  Integrated structures of this type have Young’s moduli of 224 kPa, which lies within the range of values for the human epidermis. Such sheets can be readily laminated on and form conformal contact to the human skin, with only modest mechanical constraints on natural motions. Strains measured in this mode on the wrist are between 11.2% and 22.6%.

Silicon-Based Bio-Integrated Strain Gauges

Although silicon is an intrinsically stiff and brittle material, flexible and even stretchable strain gauges have been achieved by integrating single crystalline silicon nanomembranes on polyimide substrates [13] and elastomer substrates [14, 15]. While polyimide-supported strain gauges are too stiff to integrate on soft bio-tissues, elastomer-supported silicon gauges have been applied to accurately and repeatedly measure the human finger bending [14] and internal organ motion (e.g. heart beat) [15] for the first time. We notice that even silicon strips with the same thickness, orientation, and doping concentration, when bonded to different types of polymer substrates, the GF and stretchability (the applied strain beyond which silicon ruptures) can vary by orders of magnitude. For example, when polyimide substrates are used, GF obtained from uniaxial tension tests are 43 and the system cannot be stretched beyond 1% [13]. In contrast, when the substrate is elastomer, the measured GF reduced to 0.23 but the system can be stretched beyond 25% without inducing any cracks in silicon [14, 15]. Mechanics models accounting for the silicon length and thickness as well as substrate modulus and thickness need to be developed to explain the discrepancies found in different systems and to guide the rationalized design of future flexible/stretchable silicon-on-polymer strain gauges.

Our recent work has achieved a systematic understanding of the large variance in gauge factor and stretchability of reported flexible/stretchable silicon-on-polymer strain gauges [16] . Finite element and analytically models are established to reveal the effects of the length of the silicon strip, and the thickness and modulus of the polymer substrate. Analytical results for two limiting cases, i.e. infinitely thick substrate and infinitely long strip, have found good agreement with FEM results. We have discovered that strains in silicon resistor can vary by orders of magnitude with different substrate materials whereas strip length or substrate thickness only affects the strain level mildly. While the average strain in silicon reflects the gauge factor, the maximum strain in silicon governs the stretchability of the system. The tradeoff between gauge factor and stretchability of silicon-on-polymer strain gauges has been proposed and discussed.


On the way of pursuing multidirectional, more sensitive, and higher resolution bio-integrated strain gauges, we shall not forget about the tissue-gauge interaction. Any slippage the gauge against the tissue will result in underestimated strains. On the one hand, softer strain gauges will exert lower driving force for slippage; on the other hand, improved gauge-tissue adhesion, especially on wet tissue surfaces, without constraining the normal tissue kinetics will also represent important advancement.


[1] A. L. Window, Strain gauge technology. London, England: Elsevier Applied Science, 1992.

[2] C. S. Smith, "Piezoresistance Effect in Germanium and Silicon," Physical Review, vol. 94, pp. 42-49, 1954.

[3] K. Rome and F. Cowieson, "A reliability study of the universal goniometer, fluid goniometer, and electrogoniometer for the measurement of ankle dorsiflexion," Foot & Ankle International, vol. 17, pp. 28-32, Jan 1996.

[4] G. Bell, P. E. Nielsen, N. A. Lassen, and B. Wolfson, "Indirect measurement of systolic blood pressure in the lower limb using a mercury in rubber strain gauge," Cardiovascular Research, vol. 7, pp. 282-289, 1973.

[5] M. Leonardi, E. M. Pitchon, A. Bertsch, P. Renaud, and A. Mermoud, "Wireless contact lens sensor for intraocular pressure monitoring: assessment on enucleated pig eyes," Acta Ophthalmologica, vol. 87, pp. 433-437, Jun 2009.

[6] D. H. Kim, N. S. Lu, R. Ma, Y. S. Kim, R. H. Kim, S. D. Wang, et al., "Epidermal Electronics ," Science, vol. 333, pp. 838-843, Aug 12 2011.

[7] C. Liu, "Recent developments in polymer MEMS," Advanced Materials, vol. 19, pp. 3783-3790, Nov 19 2007.

[8] L. Bokobza, "Multiwall carbon nanotube elastomeric composites: A review," Polymer, vol. 48, pp. 4907-4920, Aug 10 2007.

[9] D. H. Kim, N. S. Lu, R. Ghaffari, Y. S. Kim, S. P. Lee, L. Z. Xu, et al., "Materials for multifunctional balloon catheters with capabilities in cardiac electrophysiological mapping and ablation therapy ," Nature Materials, vol. 10, pp. 316-323, Apr 2011.

[10] T. Yamada, Y. Hayamizu, Y. Yamamoto, Y. Yomogida, A. Izadi-Najafabadi, D. N. Futaba, et al., "A stretchable carbon nanotube strain sensor for human-motion detection," Nature Nanotechnology, vol. 6, pp. 296-301, May 2011.

[11] A. R. Aiyar, C. Song, S. H. Kim, and M. G. Allen, "An all-polymer airflow sensor using a piezoresistive composite elastomer," Smart Materials & Structures, vol. 18, Nov 2009.

[12] N. S. Lu, C. Lu, S. X. Yang, and J. Rogers, "Highly Sensitive Skin-Mountable Strain Gauges Based Entirely on Elastomers ," Advanced Functional Materials, vol. 22, pp. 4044-4050, Oct 10 2012.

[13] S. M. Won, H. S. Kim, N. S. Lu, D. G. Kim, C. Del Solar, T. Duenas, et al., "Piezoresistive Strain Sensors and Multiplexed Arrays Using Assemblies of Single-Crystalline Silicon Nanoribbons on Plastic Substrates ," Ieee Transactions on Electron Devices, vol. 58, pp. 4074-4078, Nov 2011.

[14] M. Ying, A. P. Bonifas, N. S. Lu, Y. W. Su, R. Li, H. Y. Cheng, et al., "Silicon nanomembranes for fingertip electronics ," Nanotechnology, vol. 23, Aug 31 2012.

[15] D. Kim, R. Ghaffari, N. Lu, S. Wang, S. P. Lee, H. Keum, et al., "Electronic sensor and actuator webs for large-area complex geometry cardiac mapping and therapy ," Proceedings of the National Academy of Sciences, vol. 109, pp. 19910-19915, December 4, 2012 2012.

[16] S. Yang and N. Lu, "Gauge factor and stretchability of silicon-on-polymer strain gauges ," Sensors, vol. 13, pp. 8577-8594, 2013.


Kejie Zhao's picture

Nanshu, is the strian gauge factor an intrinsic material property, or is it a structural factor? Is there a fundamental reason on it? Should the gauge factor be represented by the local deformation, instead of the average strain field?  Also, if the gauge size is down to submicron, do you expect there is an effect brought by surface?  Thanks.     -Kejie

Nanshu Lu's picture

Kejie, you have brought up a very important concept for stretchable strain gauges, which is the difference between the material instrinsic gauge factor and the system gauge factor. Material instrinsic gauge factor is a material property which does not change with the shape of the material or the substrate it is sitting on whereas system gauge factor is defined as the relative resistance change per unit strain in the substrate, which depends on both the shape of the strain-sensitive resistor and the modulus mismatch between the resistor and the substrate. System gauge factor is more widely used as the strain gauge specs because the strain in the specimen is first transferred to the substrate of the strain gauge.

The difference between intrinsic and system gauge factors is not very big for conventional strain gauge because the modulus mismatch between the metal trace and the plastic substrate is relatively small (i.e. about 10 times). However, when we are using piezoresistive silicon nanomembranes on elastomer substrates, the modulus mismatch can be as large as six orders. As a result, even if the bonding between silicon and elastomer is perfect, as silicon is patterned into a short strip, the strain transfer coefficient from the substrate to silicon is much smaller than 1. Therefore the (system gauge factor) = (strain transfer coeeficient) * (intrinsic gauge factor of silicon). The compromise in gauge factor actually gains the stretchability of the device, which is discussed in more detail in Ref [16] .

Teng Li's picture

Nanshu: this is a very interesting topic and I read with great interest.

I have a follow-up question after Kejie's and your comment. The precision of strain gauges made of silicon that are capable to measure strain beyond silicon's elastic limit will rely on the quantitative determination of the "strain transfer coefficient" as you termed. Such a coefficient should strongly depend on the strain gauge structural design. Further complicacy will come from the possible nonlinear response of the structurally designed strain gauge as well as their anisotropic nature under different load and deformation states. I wonder if there is some general guideline in this regard to guarantee the preciesion of stretchable Si-based strain gauges.   

Nanshu Lu's picture

Teng, thank you for raising another two important issues of stretchable strain gauges: anisotropy and shape of silicon and nonlinearity of the structure. Since [110] silicon exhibits much higher piezoresistive coefficient compared to other orientations, we prefer to use long and narrow silicon strips whose longitudinal direction is along the [110] direction. It is narrow in the transverse direction so that we can minimize the strain transfer due to tranverse Poisson's strain in the substrate. To measure the three independent in-plane strain components, we have manufactured and simulated silicon-based strain rossetts each of which consists of three narrow silicon strips: two orthoganal [110] silicon strips and one [100] silicon strip in the 45 degree direction, which can be found in Ref [15] .

Nonlinearity of the silicon-on-polymer structure is another outstanding problem under large deformation, especially at the edge of silicon strips where both geometric and material discontinuity present. As a result, we had to turn on the nonlinear geometry function in the FEM simulation in Ref [16] . In our semi-analytical models for extreme cases, instead of diving into nonlinearity, we simply fitted the proportional coefficients out of FEM results when strip length is much smaller than the substrate thickness (L/H<<1); when L/H>>1, a simple linear elastic superposition method has been proved effective of capturing the average and maximum strains inside silicon.

Lihua Jin's picture

Nanshu, thanks for bringing this interesting topic. You mainly mentioned two mechanisms of strain gauges: resistance change due to the deformation of metals and piezoresistive effect in semiconductors. Can strain gauges be realized by other mechanisms, such as piezoelectric effect? How big can those strain gauge factors be?

Chao Chen's picture

Dear Nashu, thank you for introducing the interesting direction of soft strain gauges. As you mentioned in the last part, the strength of delamination determines the accuracy of strain measurement. So how do people prevent delamination or slip in the current soft strain gauge's setup for both gauge types, while the adhesion is still biocompatible?


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