Yang Yang

Bio: Yang Yang is an academic researcher from China University of Geosciences (Wuhan). The author has contributed to research in topics: Galerkin method & Granular material. The author has an hindex of 4, co-authored 4 publications receiving 343 citations. Previous affiliations of Yang Yang include University of Kansas.

Higher-Order Continuum Theory Applied to Fracture Simulation of Nanoscale Intergranular Glassy Film

Abstract: Complex grain-boundary structures such as the 1–2 nm thick intergranular glassy films (IGF) play a prominent role in the failure behavior of nanophased ceramics. The IGF plays the role of an imperfection and serves as the location of strain localization and failure. This paper describes recently performed theoretical mechanical loading experiments on very large atomic models of IGF in silicon nitride using ab initio simulation to obtain their failure behavior. The ab initio simulations yield characteristic postpeak softening accompanied by strain localization zone. This paper applies microstructural granular mechanics-based higher-order continuum theory to model the failure behavior of these types of material systems. The results obtained from the ab initio simulations are compared with those predicted by the higher-order continuum theory.

Higher-Order Stress-Strain Theory for Damage Modeling Implemented in an Element-free Galerkin Formulation

Abstract: Gradient theories have found wide applications in modeling of strain softening phenomena. This paper presents a higher order stress-strain theory to describe the damage behavior of strain softening materials. In contrast to most conventional gradient approaches for damage modeling, the present higher order theory considers strain gradients and their conjugate higher-order stress such that stable numerical solutions may be achieved. We have described the derivation of the required constitutive relationships, the governing equations and its weak form for this higher-order theory. The constitutive coefficients were obtained from a granular media approach such that the internal length scale parameter reflects the natural granularity of the underlying microstructure. The weak form was discretized using an element-free Galerkin (EFG) formulation that readily admits approximation functions of higher-order continuity. We have also discussed the implementation of essential boundary conditions and linearization of the derived discrete equations. Finally, the applicability of the derived model is demonstrated through two examples with different imperfections designed to initiate dislocation bands and shear bands, respectively.

At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topical contribution of Gabrio Piola

Abstract: Gabrio Piola’s scientific papers have been underestimated in mathematical physics literature. Indeed, a careful reading of them proves that they are original, deep and far-reaching. Actually, even ...

At the origins and in the vanguard of peri-dynamics, non-local and higher gradient continuum mechanics. An underestimated and still topical contribution of Gabrio Piola

Abstract: Gabrio Piola's scientific papers have been underestimated in the mathematical-physics literature. Indeed a careful reading of them proves that they are original, deep and far reaching. Actually -even if his contribution to mechanical sciences is not completely ignored- one can undoubtedly say that the greatest part of his novel contributions to mechanics, although having provided a great impetus and substantial influence on the work of many preminent mechanicians, is in fact generally ignored. It has to be remarked that authors [10] dedicated many efforts to the aim of unveiling the true value of Gabrio Piola as a scientist; however, some deep parts of his scientific results remain not yet sufficiently illustrated. Our aim is to prove that non-local and higher gradient continuum mechanics was conceived already in Piola's works and to try to explain the reasons of the unfortunate circumstance which caused the erasure of the memory of this aspect of Piola's contribution. Some relevant differential relationships obtained in Piola [Piola, 1845-6] are carefully discussed, as they are still nowadays too often ignored in the continuum mechanics literature and can be considered the starting point of Levi-Civita's theory of Connection for Riemannian manifolds.

Large deformations of planar extensible beams and pantographic lattices: Heuristic homogenization, experimental and numerical examples of equilibrium

Abstract: The aim of this paper is to find a computationally efficient and predictive model for the class of systems that we call ‘pantographic structures’. The interest in these materials was increased by the possibilities opened by the diffusion of technology of three-dimensional printing. They can be regarded, once choosing a suitable length scale, as families of beams (also called fibres) interconnected to each other by pivots and undergoing large displacements and large deformations. There are, however, relatively few ‘ready-to-use’ results in the literature of nonlinear beam theory. In this paper, we consider a discrete spring model for extensible beams and propose a heuristic homogenization technique of the kind first used by Piola to formulate a continuum fully nonlinear beam model. The homogenized energy which we obtain has some peculiar and interesting features which we start to describe by solving numerically some exemplary deformation problems. Furthermore, we consider pantographic structures, find the corresponding homogenized second gradient deformation energies and study some planar problems. Numerical solutions for these two-dimensional problems are obtained via minimization of energy and are compared with some experimental measurements, in which elongation phenomena cannot be neglected.

Mechanical metamaterials: a state of the art:

Abstract: In this paper, we give a review of the state of the art in the study of mechanical metamaterials. The very attractive property of having a microstructure capable of determining exotic and specifica...