Roadmap on multiscale materials modeling

Modeling and simulation is transforming modern materials science, becoming an important tool for the discovery of new materials and material phenomena, for gaining insight into the processes that govern materials behavior, and, increasingly, for quantitative predictions that can be used as part of a design tool in full partnership with experimental synthesis and characterization. Modeling and simulation is the essential bridge from good science to good engineering, spanning from fundamental understanding of materials behavior to deliberate design of new materials technologies leveraging new properties and processes. This Roadmap presents a broad overview of the extensive impact computational modeling has had in materials science in the past few decades, and offers focused perspectives on where the path forward lies as this rapidly expanding field evolves to meet the challenges of the next few decades. The Roadmap offers perspectives on advances within disciplines as diverse as phase field methods to model mesoscale behavior and molecular dynamics methods to deduce the fundamental atomic-scale dynamical processes governing materials response, to the challenges involved in the interdisciplinary research that tackles complex materials problems where the governing phenomena span different scales of materials behavior requiring multiscale approaches. The shift from understanding fundamental materials behavior to development of quantitative approaches to explain and predict experimental observations requires advances in the methods and practice in simulations for reproducibility and reliability, and interacting with a computational ecosystem that integrates new theory development, innovative applications, and an increasingly integrated software and computational infrastructure that takes advantage of the increasingly powerful computational methods and computing hardware

A discrete, geometrically exact method for simulating nonlinear, elastic and inelastic beams

We present an extension of a discrete, geometrically exact beam formulation based on discrete framed curves and discrete parallel transport originally introduced in the computer graphics community. In combination with variational constitutive updates, our numerical scheme decouples the kinematics from the material behavior, and can handle finite rotations as well as a wide class of constitutive laws depending on the stretching, flexural and torsional strain and strain rates. We demonstrate its capabilities through a suite of benchmark problems involving elastic, viscous and visco-elastic beams. The method fits naturally in existing finite element frameworks and is well suited to engineering applications. It can efficiently and accurately simulate the nonlinear deformation of slender beams featuring complex material behavior, such as those found in the topical design of flexible structural metamaterials

A discrete, geometrically exact method for simulating nonlinear, elastic and inelastic beams

We present an extension of a discrete, geometrically exact beam formulation based on discrete framed curves and discrete parallel transport originally introduced in the computer graphics community. In combination with variational constitutive updates, our numerical scheme decouples the kinematics from the material behavior, and can handle finite rotations as well as a wide class of constitutive laws depending on the stretching, flexural and torsional strain and strain rates. We demonstrate its capabilities through a suite of benchmark problems involving elastic, viscous and visco-elastic beams. The method fits naturally in existing finite element frameworks and is well suited to engineering applications. It can efficiently and accurately simulate the nonlinear deformation of slender beams featuring complex material behavior, such as those found in the topical design of flexible structural metamaterials

A discrete, geometrically exact method for simulating nonlinear, elastic and inelastic beams

We present an extension of a discrete, geometrically exact beam formulation based on discrete framed curves and discrete parallel transport originally introduced in the computer graphics community. In combination with variational constitutive updates, our numerical scheme decouples the kinematics from the material behavior, and can handle finite rotations as well as a wide class of constitutive laws depending on the stretching, flexural and torsional strain and strain rates. We demonstrate its capabilities through a suite of benchmark problems involving elastic, viscous and visco-elastic beams. The method fits naturally in existing finite element frameworks and is well suited to engineering applications. It can efficiently and accurately simulate the nonlinear deformation of slender beams featuring complex material behavior, such as those found in the topical design of flexible structural metamaterials

Resilient 3D hierarchical architected metamaterials.

Hierarchically designed structures with architectural features that span across multiple length scales are found in numerous hard biomaterials, like bone, wood, and glass sponge skeletons, as well as manmade structures, like the Eiffel Tower. It has been hypothesized that their mechanical robustness and damage tolerance stem from sophisticated ordering within the constituents, but the specific role of hierarchy remains to be fully described and understood. We apply the principles of hierarchical design to create structural metamaterials from three material systems: (i) polymer, (ii) hollow ceramic, and (iii) ceramic-polymer composites that are patterned into self-similar unit cells in a fractal-like geometry. In situ nanomechanical experiments revealed (i) a nearly theoretical scaling of structural strength and stiffness with relative density, which outperforms existing nonhierarchical nanolattices; (ii) recoverability, with hollow alumina samples recovering up to 98% of their original height after compression to ≥ 50% strain; (iii) suppression of brittle failure and structural instabilities in hollow ceramic hierarchical nanolattices; and (iv) a range of deformation mechanisms that can be tuned by changing the slenderness ratios of the beams. Additional levels of hierarchy beyond a second order did not increase the strength or stiffness, which suggests the existence of an optimal degree of hierarchy to amplify resilience. We developed a computational model that captures local stress distributions within the nanolattices under compression and explains some of the underlying deformation mechanisms as well as validates the measured effective stiffness to be interpreted as a metamaterial property

Reexamining the mechanical property space of three-dimensional lattice architectures

Lightweight materials that are simultaneously strong and stiff are desirable for a range of applications from transportation to energy storage to defense. Micro- and nanolattices represent some of the lightest fabricated materials to date, but studies of their mechanical properties have produced inconsistent results that are not well captured by existing lattice models. We performed systematic nanomechanical experiments on four distinct geometries of solid polymer and hollow ceramic (Al2O3) nanolattices. All samples tested had a nearly identical scaling of strength (σy) and Young's modulus (E) with relative density (ρ¯), ranging from σy∝ρ¯1.45 to ρ¯1.92 and E∝ρ¯1.41 to ρ¯1.83, revealing that changing topology alone does not necessarily have a significant impact on nanolattice mechanical properties. Finite element analysis was performed on solid and hollow lattices with structural parameters beyond those realized experimentally, enabling the identification of transition regimes where solid-beam lattices diverge from existing analytical theories and revealing the complex parameter space of hollow-beam lattices. We propose a simplified analytical model for solid-beam lattices that provides insight into the mechanisms behind their observed stiffness, and we investigate different hollow-beam lattice parameters that give rise to their aberrant properties. These experimental, computational and theoretical results uncover how architecture can be used to access unique lattice mechanical property spaces while demonstrating the practical limits of existing beam-based models in characterizing their behavior