research

We develop and demonstrate the first general computational tool for finite deformation static and dynamic dislocation mechanics. A finite element formulation of finite deformation (Mesoscale) Field Dislocation Mechanics theory is presented. The model is a minimal enhancement of classical crystal/J_2 plasticity that fundamentally accounts for polar/excess dislocations at the mesoscale. It has the ability to compute the static and dynamic finite deformation stress fields of arbitrary (evolving) dislocation distributions in finite bodies of arbitrary shape and elastic anisotropy under general boundary conditions. This capability is used to present a comparison of the static stress fields, at finite and small deformations, for screw and edge dislocations, revealing heretofore unexpected differences. The computational framework is verified against the sharply contrasting predictions of geometrically linear and nonlinear theories for the stress field of a spatially homogeneous dislocation distribution in the body, as well as against other exact results of the theory. Verification tests of the time-dependent numerics are also presented. Size effects in crystal and isotropic versions of the theory are shown to be a natural consequence of the model and are validated against available experimental data. With inertial effects incorporated, the development of an (asymmetric) propagating Mach cone is demonstrated in the finite deformation theory when a dislocation moves at speeds greater than the linear elastic shear wave speed of the material.

Paper can be found at link Finite_Deformation_Dislocation_Mechanics.

The Design & Uncertainty Quantification group at The University of Iowa, led by Professor Sharif Rahman, is looking for new Ph.D. students, who are capable of and interested in performing high-quality research on uncertainty quantification and stochastic design optimization. The research, supported by U.S. National Science Foundation, requires building a solid mathematical foundation, devising efficient numerical algorithms, and developing practical computational tools, all associated with stochastic analysis and design of complex materials and structures.

A very interesting recent paper by Dalvi et al. has demonstrated convincingly with adhesion experiments of a soft material with a hard rough material that the simple energy idea of Persson and Tosatti works reasonably well, namely the reduction in apparent work of adhesion is equal to the energy required to achieve conformal contact. We demonstrate here that, in terms of a stickiness criterion, this is extremely close to a criterion we derive from BAM (Bearing Area Model) of Ciavarella, and not very far from that of Violano et al.

https://doi.org/10.1088/1361-651X/ab3b62

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Published in Extreme Mechanics Letters: https://doi.org/10.1016/j.eml.2019.100507. For more than half a century, physicists rejected the existence of two-dimensional (2D) materials since they theoretically underestimated the stability. However, the discovery of one-atom-thick graphene proved the inapplicability of this theory.

One of our studies on linear and nonlinear non-Hermitian metamaterials has been published on the recent special issue of the Journal of the Acoustical Society of America: Non-Reciprocal and Topological Wave Phenomena in Acoustics.

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