166
J. Hochhalter et al.
Recently, the importance of CP-based models for engineering applications has
been highlighted, especially in aerospace applications where increased demands on
efficiency and speed are driving increased complexity in structural configuration
and reductions in thickness for fracture-critical components [31, 36]. While this
change in paradigm is exciting and is enabling a new era in aerospace vehicles,
it also defines specific challenges for researchers. A major challenge currently
is that traditional standard practice models for material constitutive behavior and
crack growth rates become invalidated for these next-generation applications. For
example, the application of traditional fracture mechanics approaches does not
apply when crack growth is in the microstructurally small regime throughout life
with only several grains through thickness.
At the center of these engineering challenges is CP-based modeling for grainscale constitutive and cracking behavior. An ultimate goal of the Integrated Computational Materials Engineering community is to provide physics-based models for
materials, enabled through multiscale modeling of fundamental material behavior,
propagated to a continuum representation of a material. However, until CP model
parameters can be provided without a need for any experimental measurements,
calibration will play a fundamental role in the application of CP models for
engineering applications.
Simply put, parameter calibration is an inverse problem that aims to determine
a set of material model parameters that minimize some measure of error between
a model, which is a function of the parameters, and measured data. The field of
applying inverse problem methodologies for the calibration of material parameters is
broad. Many of the approaches to date are based on the same variational and virtual
work principles upon which the fundamental principles of continuum solid mechanics are based, such as the reciprocity gap or error in constitutive equations methods.
For an overview of the more general area of inverse problem methodologies applied
to material parameter calibration, see [3]. For understanding the work in this chapter,
it is important to identify the additional complexities imposed by working with CP
models specifically. As the material model becomes more complex or requires more
parameters, which is characteristic of CP models, the computational demand of
calibration increases. Additionally, more data is required in such cases to mitigate
issues of uniqueness. This notion becomes especially important upon consideration
of the need to identify distributions of material parameters, where it is expected that
the parameters are not single deterministic values.
The current literature, pertaining to discussion in this chapter, typically involves
a hybrid approach to CP model parameter calibration, in which local strains from
digital image correlation (DIC) and global (homogenized) stresses from testing are
combined to form a cost function. An interesting approach to calibration using
such data is the integrated DIC (IDIC) method. Early work of Leclerc et al. [24]
formulated a two-stage process, whereby the correlation and parameter identification optimization was solved simultaneously. While the formulation is general, that
work studied identification of elastic material parameters and presented a study of
the effect of signal-to-noise ratio on the calibrated parameters. That initial work
was later extended to the calibration of elastic-plastic material model parameters,
J. Hochhalter et al.
Recently, the importance of CP-based models for engineering applications has
been highlighted, especially in aerospace applications where increased demands on
efficiency and speed are driving increased complexity in structural configuration
and reductions in thickness for fracture-critical components [31, 36]. While this
change in paradigm is exciting and is enabling a new era in aerospace vehicles,
it also defines specific challenges for researchers. A major challenge currently
is that traditional standard practice models for material constitutive behavior and
crack growth rates become invalidated for these next-generation applications. For
example, the application of traditional fracture mechanics approaches does not
apply when crack growth is in the microstructurally small regime throughout life
with only several grains through thickness.
At the center of these engineering challenges is CP-based modeling for grainscale constitutive and cracking behavior. An ultimate goal of the Integrated Computational Materials Engineering community is to provide physics-based models for
materials, enabled through multiscale modeling of fundamental material behavior,
propagated to a continuum representation of a material. However, until CP model
parameters can be provided without a need for any experimental measurements,
calibration will play a fundamental role in the application of CP models for
engineering applications.
Simply put, parameter calibration is an inverse problem that aims to determine
a set of material model parameters that minimize some measure of error between
a model, which is a function of the parameters, and measured data. The field of
applying inverse problem methodologies for the calibration of material parameters is
broad. Many of the approaches to date are based on the same variational and virtual
work principles upon which the fundamental principles of continuum solid mechanics are based, such as the reciprocity gap or error in constitutive equations methods.
For an overview of the more general area of inverse problem methodologies applied
to material parameter calibration, see [3]. For understanding the work in this chapter,
it is important to identify the additional complexities imposed by working with CP
models specifically. As the material model becomes more complex or requires more
parameters, which is characteristic of CP models, the computational demand of
calibration increases. Additionally, more data is required in such cases to mitigate
issues of uniqueness. This notion becomes especially important upon consideration
of the need to identify distributions of material parameters, where it is expected that
the parameters are not single deterministic values.
The current literature, pertaining to discussion in this chapter, typically involves
a hybrid approach to CP model parameter calibration, in which local strains from
digital image correlation (DIC) and global (homogenized) stresses from testing are
combined to form a cost function. An interesting approach to calibration using
such data is the integrated DIC (IDIC) method. Early work of Leclerc et al. [24]
formulated a two-stage process, whereby the correlation and parameter identification optimization was solved simultaneously. While the formulation is general, that
work studied identification of elastic material parameters and presented a study of
the effect of signal-to-noise ratio on the calibrated parameters. That initial work
was later extended to the calibration of elastic-plastic material model parameters,