Can Complex Material Behavior be Predicted?

Michael Ortiz, California Institute of Technology

Many engineering systems of interest exhibit complex behavior that challenges our ability to make precise predictions of the behavior of the system. Complex behavior specifically means: that the response of the system takes place over multiple length and time scales, often ranging from the nanoscale to the macroscale; the subscale behavior of the system is stochastic and exhibits fine patterning in space and time; the behavior of the system is irreversible, dissipative and hysteretic; and the system exhibits intricate failure modes. Examples of complex behavior include the formation of fine microstructure in materials such as micromagnetic are martensitic domains and dislocation structures; and dynamic fragmentation of expanding shells. The behavior of complex systems often sets in motion a broad range of diverse physics, both in the form of unit mechanisms and governing equations as well as in the form of statistical and cooperative phenomena. From a mathematical point of view, complex systems are characterized by their multiscale nature (with or without strict separation of lengthscales), by the vast non-uniqueness of solutions at multiple levels (lack of stability or lower-semicontinuity), by the evolutionary and irreversible character of the governing equations, by the lack of strong convergence of solutions (weak convergence of convergence in the sense of averages), and by the existence of failure modes (lack of coerciveness). From an experimental science point of view, many of the systems of interest are characterized by our inability to characterize their behavior fully by means of laboratory testing. This inability may be due to cost, operating conditions that cannot be realized under laboratory conditions, or other constraints. A by-now conventional theoretical response to these challenges is to attempt multiphysics, fully resolved, hero calculations that account for all the relevant physics and scales. This paradigm has led to unprecedented developments in computational power, both in the form of advanced computing platforms as well as high-fidelity physics models and numerical algorithms, many of them led by DoE’s ground-breaking ASCI program. However, more recently a paradigm shift has taken place whereby the aim has moved from performing isolated, or hero, high-fidelity calculations to carrying out exhaustive explorations of parameter space leading, in conjunction with limited experimental testing, to rigorous certification of the performance of complex systems. This new paradigm is sometimes referred to as Predictive Science to emphasize the aim of making precise and rigorous predictions of complex behavior on the basis partial or incomplete experimental data. The Predictive Science paradigm, with its focus on rigorous certification, ratchets the theoretical challenge to unprecedented levels. In my presentation, I plan to review ongoing research aimed at addressing these challenges presently being conducted at Caltech’s Center for the Predictive Modeling and Simulation of High-Energy Density Dynamic Response of Materials.

Abstract Author(s): Michael Ortiz