312 research outputs found
Rigorous bounds on the effective moduli of composites and inhomogeneous bodies with negative-stiffness phases
We review the theoretical bounds on the effective properties of linear
elastic inhomogeneous solids (including composite materials) in the presence of
constituents having non-positive-definite elastic moduli (so-called
negative-stiffness phases). We show that for statically stable bodies the
classical displacement-based variational principles for Dirichlet and Neumann
boundary problems hold but that the dual variational principle for traction
boundary problems does not apply. We illustrate our findings by the example of
a coated spherical inclusion whose stability conditions are obtained from the
variational principles. We further show that the classical Voigt upper bound on
the linear elastic moduli in multi-phase inhomogeneous bodies and composites
applies and that it imposes a stability condition: overall stability requires
that the effective moduli do not surpass the Voigt upper bound. This
particularly implies that, while the geometric constraints among constituents
in a composite can stabilize negative-stiffness phases, the stabilization is
insufficient to allow for extreme overall static elastic moduli (exceeding
those of the constituents). Stronger bounds on the effective elastic moduli of
isotropic composites can be obtained from the Hashin-Shtrikman variational
inequalities, which are also shown to hold in the presence of negative
stiffness
A variational constitutive model for slip-twinning interactions in hcp metals: application to single- and polycrystalline magnesium
We present a constitutive model for hcp metals which is based on variational constitutive updates of plastic slips and twin volume fractions and accounts for the related lattice reorientation mechanisms. The model is applied to single- and polycrystalline pure magnesium. We outline the finite-deformation plasticity model combining basal, pyramidal, and prismatic dislocation activity as well as a convexification-based approach for deformation twinning. A comparison with experimental data from single-crystal tension-compression experiments validates the model and serves for parameter identification. The extension to polycrystals via both Taylor-type modeling and finite element simulations shows a characteristic stress-strain response that agrees well with experimental observations for polycrystalline magnesium. The presented continuum model does not aim to represent the full details of individual twin-dislocation interactions; yet, it is sufficiently efficient to allow for finite element simulations while qualitatively capturing the underlying microstructural deformation mechanisms
Exploiting Microstructural Instabilities in Solids and Structures: From Metamaterials to Structural Transitions
Instabilities in solids and structures are ubiquitous across all length and time scales, and engineering design principles have commonly aimed at preventing instability. However, over the past two decades, engineering mechanics has undergone a paradigm shift, away from avoiding instability and toward taking advantage thereof. At the core of all instabilities—both at the microstructural scale in materials and at the macroscopic, structural level—lies a nonconvex potential energy landscape which is responsible, e.g., for phase transitions and domain switching, localization, pattern formation, or structural buckling and snapping. Deliberately driving a system close to, into, and beyond the unstable regime has been exploited to create new materials systems with superior, interesting, or extreme physical properties. Here, we review the state-of-the-art in utilizing mechanical instabilities in solids and structures at the microstructural level in order to control macroscopic (meta)material performance. After a brief theoretical review, we discuss examples of utilizing material instabilities (from phase transitions and ferroelectric switching to extreme composites) as well as examples of exploiting structural instabilities in acoustic and mechanical metamaterials
Inverse-design of nonlinear mechanical metamaterials via video denoising diffusion models
The accelerated inverse design of complex material properties - such as
identifying a material with a given stress-strain response over a nonlinear
deformation path - holds great potential for addressing challenges from soft
robotics to biomedical implants and impact mitigation. While machine learning
models have provided such inverse mappings, they are typically restricted to
linear target properties such as stiffness. To tailor the nonlinear response,
we here show that video diffusion generative models trained on full-field data
of periodic stochastic cellular structures can successfully predict and tune
their nonlinear deformation and stress response under compression in the
large-strain regime, including buckling and contact. Unlike commonly
encountered black-box models, our framework intrinsically provides an estimate
of the expected deformation path, including the full-field internal stress
distribution closely agreeing with finite element simulations. This work has
thus the potential to simplify and accelerate the identification of materials
with complex target performance.Comment: 21 pages, 3 figure
An infinitely-stiff elastic system via a tuned negative-stiffness component stabilized by rotation-produced gyroscopic forces
An elastic system containing a negative-stiffness element tuned to produce positive-infinite system stiffness, although statically unstable as is any such elastic system if unconstrained, is proved to be stabilized by rotation-produced gyroscopic forces at sufficiently high rotation rates. This is accomplished in possibly the simplest model of a composite structure (or solid) containing a negative-stiffness component that exhibits all these features, facilitating a conceptually and mathematically transparent, completely closed-form analysis
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Modeling of Flexible Beam Networks and Morphing Structures by Geometrically Exact Discrete Beams
Abstract
We demonstrate how a geometrically exact formulation of discrete slender beams can be generalized for the efficient simulation of complex networks of flexible beams by introducing rigid connections through special junction elements. The numerical framework, which is based on discrete differential geometry of framed curves in a time-discrete setting for time- and history-dependent constitutive models, is applicable to elastic and inelastic beams undergoing large rotations with and without natural curvature and actuation. Especially, the latter two aspects make our approach a versatile and efficient alternative to higher-dimensional finite element techniques frequently used, e.g., for the simulation of active, shape-morphing, and reconfigurable structures, as demonstrated by a suite of examples.</jats:p
Physics-Informed Neural Networks for Shell Structures
The numerical modeling of thin shell structures is a challenge, which has
been met by a variety of finite element (FE) and other formulations -- many of
which give rise to new challenges, from complex implementations to artificial
locking. As a potential alternative, we use machine learning and present a
Physics-Informed Neural Network (PINN) to predict the small-strain response of
arbitrarily curved shells. To this end, the shell midsurface is described by a
chart, from which the mechanical fields are derived in a curvilinear coordinate
frame by adopting Naghdi's shell theory. Unlike in typical PINN applications,
the corresponding strong or weak form must therefore be solved in a
non-Euclidean domain. We investigate the performance of the proposed PINN in
three distinct scenarios, including the well-known Scordelis-Lo roof setting
widely used to test FE shell elements against locking. Results show that the
PINN can accurately identify the solution field in all three benchmarks if the
equations are presented in their weak form, while it may fail to do so when
using the strong form. In the thin-thickness limit, where classical methods are
susceptible to locking, training time notably increases as the differences in
scaling of the membrane, shear, and bending energies lead to adverse numerical
stiffness in the gradient flow dynamics. Nevertheless, the PINN can accurately
match the ground truth and performs well in the Scordelis-Lo roof benchmark,
highlighting its potential for a drastically simplified alternative to
designing locking-free shell FE formulations.Comment: 24 pages, 16 figure
Dynamics of periodic mechanical structures containing bistable elastic elements: From elastic to solitary wave propagation
We investigate the nonlinear dynamics of a periodic chain of bistable elements consisting of masses connected by elastic springs whose constraint arrangement gives rise to a large-deformation snap-through instability. We show that the resulting negative-stiffness effect produces three different regimes of (linear and nonlinear) wave propagation in the periodic medium, depending on the wave amplitude. At small amplitudes, linear elastic waves experience dispersion that is controllable by the geometry and by the level of precompression. At moderate to large amplitudes, solitary waves arise in the weakly and strongly nonlinear regime. For each case, we present closed-form analytical solutions and we confirm our theoretical findings by specific numerical examples. The precompression reveals a class of wave propagation for a partially positive and negative potential. The presented results highlight opportunities in the design of mechanical metamaterials based on negative-stiffness elements, which go beyond current concepts primarily based on linear elastic wave propagation. Our findings shed light on the rich effective dynamics achievable by nonlinear small-scale instabilities in solids and structures
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