Non-deterministic Calibration
175
g ∗
s , respectively. Therefore, the set of calibration parameters involved in the current
work include g o , m, G o , and g ∗
s .
The CP model presented in this section is used throughout the remainder of the
chapter. First, the model is used to represent a collection of grains, Sect. 4.2, within
a Taylor model where the grains deform independently. Subsequently, in Sects. 4.3
and 4.4, these equations are implemented within a finite element framework for
higher-fidelity modeling of the interaction among grains in a polycrystal. This
aggregation of the deformation of multiple grains with varying crystallographic
orientations leads to an anisotropic behavior with heterogeneous stress and strain
fields throughout the continuum. As discussed in the subsequent sections, these
heterogeneities are important aspects of the calibration process.
Finally, model selection is an important preliminary step to calibrating parameters. In other words, no calibration process can function adequately if an inaccurate
or invalid model is selected. Consequently, care should be taken in identifying an
appropriate model, before the calibration process is considered. In this chapter,
simulated experiments are completed to serve as a surrogate for physical test data.
As such, the model selection is inherently prescribed, which allows for a focus on
issues regarding non-deterministic calibration (and not model selection).
4 Calibration
In this section, an overview of the general methods for CP material model calibration
is provided in the context of local and global, measured and computed, data.
Subsequently, in Sect. 6, issues of uniqueness and precision are illustrated through
application of several calibration methods, using a simulated experiment.
4.1 General Process
The core of model calibration is the inference of model parameters, θ , adjusted to
match some set of measured data. The inference is centered on the comparison of
the predicted model response and measured response, where the model is subjected
to some measured loading (see the flowchart in Fig. 3). To put this in context of the
uncertainty quantification framework, which is described in Sect. 5, the comparison
is used in the calculation of the likelihood of a set of calibration parameters.
The measurements, model, and comparison parts of the process are where
customization for a particular calibration method are made. The experimental
measurements, which provide loading and geometry input to the model, can be
global, local, or a combination. Similarly, the model itself can be global, local, or
a combination in its scale. The comparison of the model and measured response
can be either deterministic or non-deterministic in its formulation. In this section,
a discussion of available experimental measurement and modeling approaches are
175
g ∗
s , respectively. Therefore, the set of calibration parameters involved in the current
work include g o , m, G o , and g ∗
s .
The CP model presented in this section is used throughout the remainder of the
chapter. First, the model is used to represent a collection of grains, Sect. 4.2, within
a Taylor model where the grains deform independently. Subsequently, in Sects. 4.3
and 4.4, these equations are implemented within a finite element framework for
higher-fidelity modeling of the interaction among grains in a polycrystal. This
aggregation of the deformation of multiple grains with varying crystallographic
orientations leads to an anisotropic behavior with heterogeneous stress and strain
fields throughout the continuum. As discussed in the subsequent sections, these
heterogeneities are important aspects of the calibration process.
Finally, model selection is an important preliminary step to calibrating parameters. In other words, no calibration process can function adequately if an inaccurate
or invalid model is selected. Consequently, care should be taken in identifying an
appropriate model, before the calibration process is considered. In this chapter,
simulated experiments are completed to serve as a surrogate for physical test data.
As such, the model selection is inherently prescribed, which allows for a focus on
issues regarding non-deterministic calibration (and not model selection).
4 Calibration
In this section, an overview of the general methods for CP material model calibration
is provided in the context of local and global, measured and computed, data.
Subsequently, in Sect. 6, issues of uniqueness and precision are illustrated through
application of several calibration methods, using a simulated experiment.
4.1 General Process
The core of model calibration is the inference of model parameters, θ , adjusted to
match some set of measured data. The inference is centered on the comparison of
the predicted model response and measured response, where the model is subjected
to some measured loading (see the flowchart in Fig. 3). To put this in context of the
uncertainty quantification framework, which is described in Sect. 5, the comparison
is used in the calculation of the likelihood of a set of calibration parameters.
The measurements, model, and comparison parts of the process are where
customization for a particular calibration method are made. The experimental
measurements, which provide loading and geometry input to the model, can be
global, local, or a combination. Similarly, the model itself can be global, local, or
a combination in its scale. The comparison of the model and measured response
can be either deterministic or non-deterministic in its formulation. In this section,
a discussion of available experimental measurement and modeling approaches are