Since the beginning of the industrial age,
material performance and design have been in the midst
of innovation of many disruptive technologies. Today's
electronics, space, medical, transportation, and other
industries are enriched by development, design and
deployment of composite, heterogeneous and
multifunctional materials. As a result, materials
innovation is now considerably outpaced by other
aspects from component design to product cycle. In
this article, we review predictive nonlinear theories
for multiscale modeling of heterogeneous materials.
Deeper attention is given to multiscale modeling in
space and to computational homogenization in
addressing challenging materials science questions.
Moreover, we discuss a state-of-the-art platform in
predictive image-based, multiscale modeling with
co-designed simulations and experiments that executes
on the world's largest supercomputers. Such a modeling
framework consists of experimental tools,
computational methods, and digital data strategies.
Once fully completed, this collaborative and
interdisciplinary framework can be the basis of Virtual
Materials Testing standards and aids in the
development of new material formulations. Moreover, it
will decrease the time to market of innovative
products.
Although existing
computational science and engineering capabilities for
modeling nonlinear material behavior are impressive, it
is unclear how much impact they have had on materials
engineering and design in general. Moreover, an
integrated vision and/or framework that would be widely
usable in multiscale computational materials engineering
is lacking. Therefore, establishing
microstructure-statistics-property relations underpinned
by Integrated Computational Materials Engineering based
on an image-based (datadriven) multiscale modeling
framework with co-designed simulations and experiments
has the potential to transform the materials science and
engineering field. Such a framework would ultimately
lead to Virtual Materials Testing standards and aid in
the development of new material formulations as well as
decrease the time to market of innovative products.
In spite of the progress made over
the past decades, a lot of work still remains to be
done, and several technological barriers have to be
mitigated to make integrated computational materials
engineering a reality for a broad spectrum of materials
applications. Among the ongoing challenges and expected
trends the following ones are outlined:
- Fully coupled hierarchical and concurrent
multiscale models in 3D
Without any
doubt, three-dimensional multiscale simulations (both
hierarchical and concurrent) that resolve all essential
length (and time) scales are needed. Fully coupled
multiscale simulations of realistic devices/components
(test specimen) with complex physics are still uncommon
and multiscale modeling is accomplished by the input and
output of stand-alone codes mostly in twodimensions
only. The progress to be made here is evidently coupled
to the next item on Advances in Computing Capabilities.
- Advances in computing
capabilities
Exponential growth in computer performance over the last
several decades is one of the factors in integrated
computational materials engineering feasibility.
Moreover, high performance computing has had a dramatic
effect on multiscale computational materials
engineering. If current computer resources can do X, we
envision that exascale machines will provide O(1000 X)
improvement in terms of larger multiscale problems being
solved, more physics being included, etc. Therefore,
development and application of modern parallel
computational methods will be paramount in the
deployment of integrated computational materials
engineering and utilization of the next generation of
supercomputers (see Section 6).
- Intelligent model reduction -- whether applied
to computational or experimental data
Large 3D
parallel simulations and experimental/imaging materials
characterizations will necessitate the intelligent
reduction of information required for the next level of
materials integration. Mathematical/Statistical (e.g.
machine learning) methods that seek meaningful
low-dimensional structures hidden in high-dimensional
multiscale data (both computational and experimental)
will be important for a variety of tasks, i.e.
multiscale solution accelerators, visualization,
decision making, uncertainty quantification, reduced
order model construction (see Section 7).
- Co-designed simulations and experiments in 3D
This review
article has clearly illustrated the need for growing
interaction with materials science. Materials science
provides not only the required insight in the physical
and mechanical behavior at small scales, but also the
necessary quantitative data (parameters and models) on
which any multiscale method relies. If the quality of
this data is inadequate, not well understood or physical
parameters are not reliable, then multiscale methods
cannot possibly yield predictive results. Proper
characterization of materials at small scales relies on
strong collaboration between mechanics of materials
experts with materials scientists. Cutting-edge research
areas in 3D nondestructive experimental techniques with
in situ measurements are not mature yet, but show a
promising path for validation. Experimental measurements
co-designed with simulations will have a profound impact
on filling gaps in theoretical understanding and
calibrating and validating computational methods. This
can only be achieved by joining the expertise in
experimental mechanics, computational mechanics and
materials science.
- Verification, validation and uncertainty
quantification
Verification and
Validation in computational science and engineering have
been accepted as a key part of modern physics simulation
codes and this trend must continue. Verification in a
multiscale setting (i.e. how to efficiently construct
verified solutions) is still an open area of work, and
validation is linked to the discussion above on
Co-designed Simulations and Experiments. Uncertainty is
a complex issue with pervasive effects that deserves its
own attention. Although UQ is a large and richly
developed area of research in the context of computer
modeling, applications of multiscale UQ techniques in
materials science are still quite limited. Epistemic
uncertainty in parameters of macroscopic models (i.e.
global models) can be properly linked though multiscale
simulations to aleatoric uncertainty of the microscopic
(i.e. fine scale) models. Therefore, uncertainty
quantification, propagation, mitigation and management,
which are all relatively recent research areas in
multiscale computational science and engineering, have
to be further investigated (see Section 8).
- Multiscale versus multi-level description
Damage and
fracture is one of the challenging problems that
hierarchically cascades across all length scales, for
example. Although multiscale modeling and multi-level
materials design are related, these two endeavors are
distinct. Multiscale techniques pertain to data and
systems representing two or more distinct spatial and/or
temporal scales whereas multi-level approaches aim at
data and systems representing multiple levels of
material arrangements. In the perspective of integrated
computational materials engineering, multiscale modeling
(both hierarchical and concurrent) is contributing to
progress in multi-level materials design.
A lot more
attention has to be given to temporal scales and to
spatial-temporal coupling. Many physical time scales in
diffusion and small-scale deformation mechanisms cannot
be accelerated. Likewise several small-scale processes
happen very quickly, e.g. in many chemical reactions.
Scale separation limitations and micro-inertia effects
are also areas of interest. Therefore, capturing fully
transient regimes and extreme spectra of temporal
processes still remains a challenge.
- Cultural barriers, education and workforce
readiness
If integrated
computational materials engineering is to become part of
the industrial design chain, a cultural change in the
engineering and science disciplines is needed and will
require the integration of computational science and
engineering into curriculum at all levels (from
baccalaureate to doctoral). Skills from statistics,
mechanics, physics, chemistry, applied mathematics,
scientific computing, data science, materials science,
are all needed and will have to enrich traditional
single-discipline curricula.
KM and AG were supported in part by
the Department of Energy, National Nuclear Security
Administration, under Award Number DE-NA0002377 as part
of the Predictive Science Academic Alliance Program II.
We would also like to acknowledge computational
resources from the 2015 ASCR Leadership Computing
Challenge (ALCC) under project number CSC188. KM would
like to thank his former graduate research assistant, M.
Mosby, for his numerous contributions to the multiscale
modeling work presented in this review article. The
research of MG has received funding from the European
Research Council under the European Union's Seventh
Framework Programme (FP7/2007-2013) / ERC grant
agreement no [339392].