Fundamentals - Preventive Biomechanics - page 121

Fig. 3.28 System identification block diagram: a Real System (RS), b Simulation Model (SM)

Table 3.4 Stepwise strategy in constitutive model development

Step Description

1. Modelling concept Determination of model requirements:

specification of the loading range to be simulated and definition of the
observation scale (macro-, meso-, micro-)
characterization of basic existing phenomena (nonlinearity,
viscoelasticity, damage, …)
uncertainties of experimental data (errors, scattering, inappropriate
loading ranges and technical requirements)

2. Mathematical
modelling

Formulation of constitutive equations aiming at qualitative
description of the physical effects, and introduction of material
parameters x i

3. Material parameter
identification

Parameter identification based on comparison of simulated output and
measured data D 1

4. Model verification Investigation of the quality and adequacy of the employed material

model to simulate the experimental findings D 1

5. Model validation Investigation of the quality and adequacy of the employed material

model to simulate the experimental findings D 2

approach on the macro level, such a simulation model is based on constitutive
material models which incorporate parameters (phenomenological constants).
Generally, the parameters are unknown and must be determined from experimental
data. Figure 3.28 illustrates the general process of system modelling (Santamarina
and Fratta 2005).
The real process, Fig. 3.28 a, can be numerically simulated to solve the gov-
erning equations (or the mathematical model) using a numerical method, as
illustrated in Fig. 3.28 b. Considering a mechanical system, the input signals
(control variables or causes) represent the system excitation, e.g. the mechanical
loading. The output signals (system response of effects), such as displacement or
deflection, are determined by the present state of the system, the input signals and
the employed material models. The parameter vector p 2 E n summarizes a set of
material parameters, where the superscript n represents the number of parameters.

A general procedure for the development of constitutive models following the
concept introduced in Mahnken (2004) is shown in Table 3.4 . The material