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Whereas various simplistic microplane models of limited applicability, defined by stress–strain curves on the microplane, can function as either explicit or implicit, the explicit‐to‐implicit conversion of realistic versatile microplane models for plain or fiber‐reinforced concrete, shale and composites has remained a challenge for quarter century. The reason is that these realistic models use microplane stress–strain boundaries defined by inequalities. Here, we show how the conversion can be easily achieved on the microplane level and then transferred to a tangent stiffness tensor or an inelastic stiffness tensor to be used in Newton–Raphson iterations within a loading step. To ensure convergence, a minor adjustment in the M7 algorithm is introduced to achieve continuity. Power‐law convergence, almost quadratic in most cases, is also demonstrated. Seven examples of crack‐band finite element simulations of challenging laboratory tests document nearly identical implicit and explicit results, as well as good match of test data. Three of them, including the vertex effect in compression‐torsion tests, pure Mode II shear fracture, and the "gap test" of the crack‐parallel compression effect on Mode I load‐deflection curve, have not been reproduced by other models before. The coding of implicit M7 subroutine, usable in, for example, UMAT of ABAQUS, is posted for a free download. [ABSTRACT FROM AUTHOR]

The line crack models, including linear elastic fracture mechanics (LEFM), cohesive crack model (CCM), and extended finite element method (XFEM), rest on the century-old hypothesis of constancy of materials' fracture energy. However, the type of fracture test presented here, named the gap test, reveals that, in concrete and probably all quasibrittle materials, including coarse-grained ceramics, rocks, stiff foams, fiber composites, wood, and sea ice, the effective mode I fracture energy depends strongly on the crack-parallel normal stress, in-plane or out-of-plane. This stress can double the fracture energy or reduce it to zero. Why hasn't this been detected earlier? Because the crack-parallel stress in all standard fracture specimens is negligible, and is, anyway, unaccountable by line crack models. To simulate this phenomenon by finite elements (FE), the fracture process zone must have a finite width, and must be characterized by a realistic tensorial softening damage model whose vectorial constitutive law captures oriented mesoscale frictional slip, microcrack opening, and splitting with microbuckling. This is best accomplished by the FE crack band model which, when coupled with microplane model M7, fits the test results satisfactorily. The lattice discrete particle model also works. However, the scalar stress-displacement softening law of CCM and tensorial models with a single-parameter damage law are inadequate. The experiment is proposed as a standard. It represents a simple modification of the three-point-bend test in which both the bending and crack-parallel compression are statically determinate. Finally, a perspective of various far-reaching consequences and limitations of CCM, LEFM, and XFEM is discussed. [ABSTRACT FROM AUTHOR]

The fishnet probabilistic model was recently developed to characterize the strength distribution of nacre-like biomimetic materials. It reveals that the unique fishnet-like connectivity of the material microstructure brings about enormous safety gain at the extremely low failure probability level of one out of a million, desired for engineering structures. The gist of the theory is that the material microstructure plays a determining role in its failure probability tail. Therefore, a carefully designed connectivity for a material microstructure not only enhances its mean strength but also significantly reduces its marginal failure risk. Here, we first show that the initially introduced series expansion and the newer formulation based on order statistics are, in the fishnet model, essentially equivalent. From that we develop a neat general form of the fishnet statistics. Then, we extend our theoretical approach to the strength distributions of architected nanomaterials such as the printed octet-truss carbon nanolattices, as well as to quasibrittle particulate composites such as concrete, and formulate a unified general fishnet statistics. We demonstrate that the octet-truss system can be physically seen and statistically treated as a union of three fishnets with three mutually orthogonal orientations. We show that the three-dimensional assembly of fishnets further enhances the tail strength at the 10-6 probability quantile, compared to two-dimensional (2D) fishnet statistics. We compare the performance of different statistical strength models by fitting of the simulated and experimental histograms data for the octet-truss nanolattice. Finally, we argue that, at the extreme lower tail of failure probability, quasibrittle materials such as concrete or fiber composites should partially exhibit the fishnet-type statistical behavior. [ABSTRACT FROM AUTHOR]