Work

Extension of the beam theory for polymer bio-transducers with low aspect ratios and viscoelastic characteristics

Year: 2010

Type: article

Abstract: Polydimethylsiloxane (PDMS)-based micropillars (or microcantilevers) have been used as bio-transducers for measuring cellular forces on the order of pN to µN. The measurement accuracy of these sensitive devices depends on appropriate modeling to convert the micropillar deformations into the corresponding reaction forces. The traditional approach to calculating the reaction force is based on the Euler beam theory with consideration of a linear elastic slender beam for the micropillar. However, the low aspect ratio in geometry of PDMS micropillars does not satisfy the slender beam requirement. Consequently, the Timoshenko beam theory, appropriate for a beam with a low aspect ratio, should be used. In addition, the inherently time-dependent behavior in PDMS has to be considered for accurate force conversion. In this paper, the Timoshenko beam theory, along with the consideration of viscoelastic behavior of PDMS, was used to model the mechanical response of micropillars. The viscoelastic behavior of PDMS was characterized by stress relaxation nanoindentation using a circular flat punch. A correction procedure was developed to determine the load–displacement relationship with consideration of ramp loading. The relaxation function was extracted and described by a generalized Maxwell model. The bending of rectangular micropillars was performed by a wedge indenter tip. The viscoelastic Timoshenko beam formula was used to calculate the mechanical response of the micropillar, and the results were compared with measurement data. The calculated reaction forces agreed well with the experimental data at three different loading rates. A parametric study was conducted to evaluate the accuracy of the viscoelastic Timoshenko beam model by comparing the reaction forces calculated from the elastic Euler beam, elastic Timoshenko beam and viscoelastic Euler beam models at various aspect ratios and loading rates. The extension of modeling from the elastic Euler beam theory to the viscoelastic Timoshenko beam theory has improved the accuracy for the conversion of the PDMS micropillar deformations to forces, which will benefit the polymer-based micro bio-transducer applications.

Source: Journal of Micromechanics and Microengineering

DOI: 10.1088/0960-1317/20/9/095016

Authors: Ping Du, I-Kuan Lin, Hongbing Lu, Xin Zhang

Institutions: Boston University, The University of Texas at Dallas

Language: English

Topic: Cellular Mechanics and Interactions

Subfield: Cell Biology

Field: Biochemistry, Genetics and Molecular Biology

Domain: Life Sciences

Open Access status: bronze

Funders: National Science Foundation, Division of Civil, Mechanical and Manufacturing Innovation

Awards: Mechanical Behavior of Amorphous Plasma-Enhanced Chemical Vapor Deposited Silicon Oxide Films for MEMS Applications, Collaborative Research: Measurements of Yield Strength and Local Viscoelastic Properties Using Nanoparticle Embedment Methods, CAREER: Creating Nanostructured Gratings on Microstructures for Residual Strain/Stress Measurement in NEMS/MEMS and Traction Force Measurement in Cells, Collaborative Research: Elastic and Viscoelastic Characterization and Modeling of Polymer Based Structures for Biological Applications, Collaborative Research: Elastic and Viscoelastic Characterization and Modeling of Polymer based Structures for Biological Applications