[Paper Review] A new technique for the characterization of viscoelastic materials: theory, experiments and comparison with DMA

Elena Pierro, Giuseppe Carbone|arXiv (Cornell University)|Jan 1, 2021

Force Microscopy Techniques and Applications25 references17 citations

TL;DR

This paper proposes a low-cost, accurate method for characterizing the viscoelastic complex modulus of materials using free-free suspended beams of varying lengths. By combining an analytical model of beam dynamics with curve fitting of experimental impact response data, the technique optimizes the number of relaxation times to match DMA results across a broad frequency range, demonstrating feasibility and reliability with minimal instrumentation.

ABSTRACT

In this paper we present a theoretical and experimental study aimed at characterizing the hysteretic properties of viscoelastic materials. In the last decades viscoelastic materials have become a reference for new technological applications, which require lightweight, deformable but ultra-tough structures. The need to have a complete and precise knowledge of their mechanical properties, hence, is of utmost importance. The presented study is focused on the dynamics of a viscoelastic beam, which is both experimentally investigated and theoretically characterized by means of an accurate analytical model. In this way it is possible to fit the experimental curves to determine the complex modulus. Our proposed approach enables the optimal fitting of the viscoelastic modulus of the material by using the appropriate number of relaxation times, on the basis of the frequency range considered. Moreover, by varying the length of the beams, the frequency range of interest can be changed/enlarged. Our results are tested against those obtained with a well established and reliable technique as compared with experimental results from the Dynamic Mechanical Analysis (DMA), thus definitively establishing the feasibility, accuracy and reliability of the presented technique.

Motivation & Objective

• To develop a simple, low-cost alternative to Dynamic Mechanical Analysis (DMA) for viscoelastic material characterization.
• To enable broader frequency range coverage by varying beam lengths in experimental setups.
• To optimize the number of relaxation times in the viscoelastic model for accurate fitting across different frequency bands.
• To validate the proposed method against established DMA measurements for reliability and accuracy.
• To demonstrate that inexpensive instrumentation (impact hammer, accelerometer) can yield results comparable to high-end DMA equipment.

Proposed method

• Uses a free-free suspended beam setup with an impact hammer and ICP accelerometer for excitation and response measurement.
• Employs an analytical model based on the generalized Maxwell viscoelastic model with multiple relaxation times.
• Applies Laplace-domain formulation to derive the beam's dynamic response, incorporating the complex modulus E(s) = E0 + Σ(Ek sτk / (1 + sτk)).
• Performs curve fitting of experimental frequency response functions (FRFs) to the analytical model to extract the complex modulus.
• Varies beam length to extend the measurable frequency range, enabling coverage of broader viscoelastic behavior.
• Validates results by comparing fitted viscoelastic modulus with DMA measurements across 0–600 Hz.

Experimental results

Research questions

• RQ1 Can a simple beam vibration setup with minimal instrumentation accurately determine the viscoelastic complex modulus of materials?
• RQ2 How does varying beam length affect the measurable frequency range and accuracy of viscoelastic characterization?
• RQ3 What is the optimal number of relaxation times needed to fit experimental data across different frequency bands?
• RQ4 How does the proposed method compare quantitatively with DMA in terms of accuracy and reliability?
• RQ5 Can the method be extended to cover frequency ranges comparable to those of traditional DMA?

Key findings

• The method achieved excellent agreement with DMA measurements for LUBRIFLON material, validating its accuracy across 0–600 Hz.
• Using beams of different lengths (40 cm and 60 cm) successfully extended the measurable frequency range beyond what a single beam could achieve.
• Optimizing the number of relaxation times significantly improved fitting accuracy, especially in high-damping and transition zones.
• The technique demonstrated that a simple setup with an impact hammer and accelerometer can yield reliable viscoelastic modulus data comparable to DMA.
• The study confirmed that the analytical model incorporating multiple relaxation times accurately captures viscoelastic behavior across wide frequency bands.
• The results suggest that replacing the impact hammer with an electrodynamic shaker could further extend the frequency range, enabling broader applicability.