Graphene oxide (GO) or reduced-GO offer excellent mechanical, electrical and chemical properties. Their nanocomposites have been increasingly explored for attractive applications in diverse fields. However, due to the flexible feature and weak interlayer interactions of GO sheets, flexural mechanical properties of GObased composites especially for the bulk materials are largely restrained, which would hinder their use in real situations. Here inspired by amorphous/crystalline heterophase features within nacreous platelets, we construct a centimetre-sized GO-based bulk, the building blocks of which consist of crystalline GO and amorphous/crystalline MnO2 phases adhered by polymer-based crosslinkers. The GO/MnO2 heterophase layers are stacked and hot-pressed with further crosslinking between the layers to form bulk artificial nacre. The resultant GO/MnO2-based layered (GML) bulk exhibits the highest flexural strength (up to 203.4 MPa) among all of GO-based bulk materials. Moreover, an excellent fracture toughness, a strong impact resistance and light weight are also achieved. Mechanical and simulation analyses corroborate that the highly ordered heterophase structure together with complex crosslinking interactions across multiscale interfaces, lead to superior mechanical properties. We expect that these results provide interesting insights into the design of structural materials and allow the use of high-performance GO-based bulks in engineering and military applications.

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In this paper, a new method, named the Fragile Points Method (FPM), is developed for computer modeling in engineering and sciences. In the FPM, simple, local, polynomial, discontinuous and Point-based trial and test functions are proposed based on randomly scattered points in the problem domain. The local discontinuous polynomial trial and test functions are postulated by using the Generalized Finite Difference method. These functions are only piece-wise continuous over the global domain. By implementing the Point-based trial and test functions into the Galerkin weak form, we define the concept of Point Stiffnesses as the contribution of each Point in the problem domain to the global stiffness matrix. However, due to the discontinuity of trial and test functions in the domain, directly using the Galerkin weak form leads to inconsistency. To resolve this, Numerical Flux Corrections, which are frequently used in Discontinuous Galerkin methods are further employed in the FPM. The resulting global stiffness matrix is symmetric and sparse, which is advantageous for large-scale engineering computations. Several numerical examples of 1D and 2D Poisson equations are given in this paper to demonstrate the high accuracy, robustness and convergence of the FPM. Because of the locality and discontinuity of the Point-basedtrial and test functions, this method can be easily extended to model extreme problems in mechanics, such as fragility, rupture, fracture, damage, and fragmentation. These 2 extreme problems will be discussed in our future studies.

The Fragile Points method (FPM) is an elementarily simple Galerkin meshless method, employing Point-based discontinuous trial and test functions only, without using element-based trial and test functions. In this study, the algorithmic formulations of FPM for linear elasticity are given in detail, by exploring the concepts of point stiffness matrices and numerical flux corrections. Advantages of FPM for simulating the deformations of complex structures, and for simulating complex crack propagations and rupture developments, are also thoroughly discussed. Numerical examples of deformation and stress analyses of benchmark problems, as well as of realistic structures with complex geometries, demonstrate the accuracy, efficiency, and robustness of the proposed FPM. Simulations of crack initiation and propagations are also given in this study, demonstrating the advantages of the present FPM in modeling complex rupture and fracture phenomena. The crack and rupture propagation modeling in FPM is achieved without remeshing or augmenting the trial functions as in standard, extended, or generalized finite element method. The simulation of impact, penetration, and other extreme problems by FPM will be discussed in our future articles.

An explicit solution, considering the interface bending resistance as described by the Steigmann-Ogden interface model, is derived for the problem of a spherical nano-inhomogeneity (nanoscale void/inclusion) embedded in an infinite linear-elastic matrix under a general uniform far-field-stress (including tensile and shear stresses). The Papkovich-Neuber (P-N) general solutions, which are expressed in terms of spherical harmonics, are used to derive the analytical solution. A superposition technique is used to overcome the mathematical complexity brought on by the assumed interfacial residual stress in the Steigmann-Ogden interface model. Numerical examples show that the stress field, considering the interface bending resistance as with the Steigmann-Ogden interface model, differs significantly from that considering only the interface stretching resistance as with the Gurtin-Murdoch interface model. In addition to the size-dependency, another interesting phenomenon is observed: some stress components are invariant to interface bending stiffness parameters along a certain circle in the inclusion/matrix. Moreover, a characteristic line for the interface bending stiffness parameters is presented, near which the stress concentration becomes quite severe. Finally, the derived analytical solution with the Steigmann-Ogden interface model is provided in the supplemental MATLAB code, which can be easily executed, and used as a benchmark for semi-analytical solutions and numerical solutions in future studies.6 of 37 pages ellipsoidal, etc.). More complex loads may also be considered, such as far-field bending.The rest of this paper is organized as follows: In Section 2, the governing equations for the 3D nano-inhomogeneity with Steigmann-Ogden interface are briefly stated. In Section 3, the Papkovich-Neuber solutions and spherical harmonics are detailed. Then using the Steigmann-Ogden interface description and the far-field conditions, the explicit analytical solution to the considered nano-inhomogeneity problem is given in Section 4. In Section 5, we discuss the influences of the interface bending on stress distributions within and around the nano-inhomogeneity(nano-void/inclusion), when the far-field tensile/shear loads are applied. In Section 6, we complete this paper with some concluding remarks.

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