**Author details**

318 Viscoelasticity – From Theory to Biological Applications

from the test results, an initial condition that easily converges.

**Figure 17.** Smoothing manipulation for relaxation spectra





Log H i [MPa]



0

**Figure 18.** Examples of measured master curve

1.E-02 1.E+02 1.E+06 1.E+10 1.E+14 Reduction angular velocity ω [rad/sec]

1.E+0

1.E+1

1.E+2

Storage modulus E' [MPa]

1.E+3

1.E+4

the respective format of the input file for Abaqus, Marc, or LS-DYNA.

Smoothed Envelope

calculation. The optimization operation uses the quasi-Newton method. For the quasi-Newton method, it is necessary to set up the initial condition in the vicinity of the optimized value. However, this program incorporates an algorithm that can automatically estimate,

The master curve for epoxy resin material shown in Fig. 8 covers a range of about 12 digits in terms of angular frequency, so the number of terms in the Maxwell model is set to 12. As previously mentioned, positive values for all of Ee, En, and τn are maintained during the calculation. The coefficients of the identified Maxwell model are automatically written into

> 1.E-12 1.E-09 1.E-06 1.E-03 1.E+00 Relaxation Time [sec]

(a) favorable (b) defective

1.E+0

1.E-02 1.E+02 1.E+06 1.E+10 1.E+14 Reduction angular velocity ω [rad/sec]

1.E+1

1.E+2

Storage modulus E' [MPa]

1.E+3

1.E+4

Takaya Kobayashi, Masami Sato and Yasuko Mihara *Mechanical Design & Analysis Corporation, Japan* 

#### **7. References**

	- Yuju, W. & Basaran, C. (2003), Thermomechanical Stress Analysis of Multi-Layered Electronic Packaging, *Journal of Electronic Packaging*, Vol. 125, pp. 134-138.

**Chapter 15** 

© 2012 Ibrahim et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

**An Approach for Dynamic Characterisation** 

**of Passive Viscoelasticity and Estimation** 

**of Anthropometric Inertia Parameters** 

B.S. K. K. Ibrahim, M.S. Huq, M.O. Tokhi and S.C. Gharooni

Functional electrical stimulation (FES) is a promising way to restore mobility to individuals paralyzed due to spinal cord injury (SCI). Modelling and parameter identification of both the passive and active joint properties are needed to improve control of this nonlinear time varying system. In order to develop a suitable control strategy for the FES to move of the leg correctly, a proper model of stimulated muscle has to be used. The muscle is assumed to consist of two components: an active force generator and parallel passive properties. Riener and Edrich (1999) suggested passive muscle properties should be identified separately from active muscle properties because it is easier to consider the passive elastic forces as contributions to the total joint moment. Other researchers such as Zajac (1989) and Pandy et al. (1990) used a musculo-tendon model, in which the passive and the active forces are generated by single muscles. However, such models have too many parameters that cannot be identified non-invasively due to the muscle-joint redundancy of the musculoskeletal

Conventionally the joint passive resistance is modelled as an elastic element like a torsion spring and a viscous element like a rotary damper (Lamb et al., 1991). These two resistances are non-linear, but the viscous resistance is often approached as a linear function of the joint angular velocity (Chizeck et. al., 1999; Mansour and Audu, 1986). These characteristics are important to estimate muscle load or fatigue during motion, especially in the field of biomechanics. Some researchers have shown further that these resistances influence the basis of motion effectively. For example, the resistance imposed by passive joint properties can impede the functionality of FES systems during limb movements (Amankwah, 2001).

and reproduction in any medium, provided the original work is properly cited.

**of Paraplegic's Knee Joint** 

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/45994

system (Riener and Edrich, 1999).

**1. Introduction** 
