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• Novel physics-driven neural networks are proposed for nonlinear micromechanics. • No labeled training data is needed for the proposed PDNNs. • Unphysical behaviors are avoided using a kinematic-based loss term. • Our PDNNs are computationally more efficient than the traditional PINNs. Micromechanical problems seek full-field solutions in response to external and/or internal thermal-mechanical loads, which have been increasingly encountered in material property and process assessments. Here we present a machine learning based strategy of solving micromechanics at finite strains. Deep neural networks (DNNs) are trained by employing the elastic energy together with other physical constraints to formulate the loss function. In particular, the crossover of material points, which can be a common issue for similar DNNs when applied to compression-dominant problems, is shown to be effectively addressed by including a kinematic penalty term that forces the DNN to maintain structural integrity and stability and avoid unphysical behavior. The generality and accuracy of the proposed physics-driven neural networks (PDNNs) are demonstrated through various micromechanical problems, including single crystal anisotropy elasticity, Eshelby's inclusion problem, buckling, and elastic homogenization of polycrystals. The effect of the choice of optimizers and hyperparameters on the PDNN training are discussed and the computational efficiency is also analyzed. It is shown that this novel PDNN framework can completely remove the need of labeled training data and exhibit improved performances as compared to the conventional physics-informed neural networks (PINNs) in terms of avoiding unphysical solutions and attaining higher computational efficiency. PDNNs can thus serve as a promising tool to solve some critical challenges associated with a wide range of nonlinear micromechanical problems. [Display omitted] [ABSTRACT FROM AUTHOR]

• Novel mechanical characteristics of metamaterials are studied by theoretical analysis. • Dissipated energy per buckling event is studied. • Static and dynamic(re)programming characteristics are studied. • Potential energy landscape of programmable structure is studied. Metamaterials derive promising properties mainly from an internal micromechanical mechanism, rather than their chemical composition. Many interesting mechanical behaviors can be obtained by orderly assembling buckling elements. Elastic programmable properties, corresponding potential energy landscape and dynamic dissipation mechanism of elastic beam structures are studied in detail. To accomplish this work, a combination of theoretical models and extensive numerical calculations are applied to investigate a single element as well as homogeneous and gradient structures. This comprehensive investigation not only provides insights into the complex internal buckling behaviors and mechanisms of a specific unstable structure but also establishes conclusions that are applicable to other unstable structures having similar buckling behaviors. The potential energy of a serial combination of unstable elements is extremely wiggly, enabling multiple equilibrium configurations and resulting in multistable transformations and energy dissipation with elastic deformation and loading timescale independence. To the best of our knowledge, the most of programming properties investigated in this paper, the complex energy landscape, the deformation of internal elements, and programmable dynamic responses of gradient unstable structures have not been reported in previous papers. [Display omitted] [ABSTRACT FROM AUTHOR]

• Buckling behavior of spherical shells with patterned surface under indentation is investigated. • Shells with discontinuous protrusions exhibit unique multiple snap-through due to local buckling. • Mechanical response and buckling morphology can be controlled by tuning surface patterns. A well understanding of instability mechanics of soft shell structures is key issue due to its important implications in functional shape morphing, flexible electronics, soft robotics, nanotechnology, biological engineering, etc. Despite abundant studies, buckling analysis of flexible shells with patterned surface under indentation is rare, primarily because of the complexities of high nonlinearities in geometry, material, and surface contact. In this paper, buckling behavior of spherical shells with patterned surface under indentation is comprehensively investigated by using experimental, numerical and theoretical analyses. It is found shells with stripes show similar variation in the force-displacement curves and post-buckling morphologies like perfect shells. Unlike perfect ones, shells with discontinuous protrusions exhibit multiple snap-through due to local buckling under indentation. What is more, mechanical response and buckling morphology can be well controlled by tuning shell thickness as well as positions and sizes of protrusions. These results can not only deepen understanding of mechanism of spherical shell buckling under local loads, but also provide a designing guidance for flexible electronics, soft robotics, and other future devices. [Display omitted] [ABSTRACT FROM AUTHOR]