In the field of optimal structural design, topology optimization has been shown to be one of the most powerful methodologies. For a given domain under known loading conditions, topology optimization seeks to find the layout of material that optimizes a performance metric. Much of…
We present effective numerical algorithms for recovering unknown governing differential equations from measurement data. Upon recasting the problem into a function approximation problem, we discuss several important aspects for accurate recovery/approximation. Most notably, we discuss the importance of using a large number of short…
Modern machine learning (ML) techniques, in conjunction with simulation-based methods, present remarkable potential for various engineering applications. Within the materials science field, these data-based methods can be used to build efficient structure-property linkages that can be further integrated within multiscale simulations to speed-up communication…
We develop a general framework for a data-driven approximation to input-output maps between infinite dimensional spaces by utilizing the recent success of deep learning. For a class of such maps and a suitably chosen probability measure on the inputs, we prove generalization bounds and…
We present an approach for assessing the impact of epistemic uncertainty arising in damage theory models brittle fracture. The incomplete information about the distribution of the yield stress in the material is modeled by a random damage field. Parameters of this random field are…
As Kolsky Bars (Split Hopkinson Pressure Bars) have grown in popularity, so too has the need for high rate material characterization. To achieve higher rates in excess of 10,000 strain per second, smaller samples and therefore smaller bars are needed. These smaller bars, approximately…
Material optimization (e.g., texture optimization) and multi-scale modeling (e.g., FE^2) of materials requires numerous instances (realizations) of the same calculations. The governing equations of these problems are highly non-linear (because of the complex material behavior and microstructure) and requires enormous computational power and time…
Phase-field models have become an efficient and flexible solution for simulating the evolution of microstructure and phase separation at the mesoscale, whose applications can be easily extended by coupling to other physical systems to simulate multi-physics phenomenon. The physical-informed neural network is a recent…
We use a phase field method to study fracture problems. Within this framework, the linear momentum equations are coupled with a diffusion type equation, which describes the evolution of the fracture variable. The coupled nonlinear system of partial differential equations are solved in a…
Ramp-driven experiments offer possibilities to explore material response under conditions distinct from those accessed by shock-driven loading conditions. Use of the data from ramp-driven experiments is challenging in a variety of ways. The resistance of material to distortional deformation can be assessed from velocimetry…
