•Stationary variational framework for higher-order unified gradient elasticity theory.•Higher-order boundary value problem and gradient constitutive laws in intrinsic form.•Elimination of recognized ...restrictions typical of nonlocal gradient elasticity model.•Examination of well-posed generalized elasticity theory in nano-mechanics of torsion.•Determination of size-dependent shear modulus of SWCNTs with dissimilar chirality.
The higher-order unified gradient elasticity theory is conceived in a mixed variational framework based on suitable functional space of kinetic test fields. The intrinsic form of the differential and boundary conditions of equilibrium along with the constitutive laws is consistently established. Various forms of the gradient elasticity theory, in the sense of stress or strain gradient models, can be retrieved as particular cases of the introduced generalized elasticity theory. The proposed stationary variational principle can effectively realize the nanoscopic structural effects while being exempt of restrictions typical of the nonlocal gradient elasticity model. The well-posed generalized gradient elasticity theory is invoked to study the mechanics of torsion and the torsional behavior of elastic nano-bars is analytically examined. The closed-form analytical formulae of the size-dependent shear modulus of nano-sized bar is determined and efficiently applied to reconstruct the shear modulus of SWCNTs with dissimilar chirality in comparison with the numerical simulation data. A practical approach to calibrate the characteristic lengths associated with the higher-order unified gradient elasticity theory is introduced. Numerical results associated with the torsion of higher-order unified gradient elastic bars are demonstrated and compared with the counterpart size-dependent elasticity theories. The conceived generalized gradient elasticity theory can beneficially characterize the nanoscopic response of advanced nano-materials.
Shear modulus assumes an important role in characterizing the applicability of different materials in various multi-functional systems and devices, such as deformation under shear and torsional modes ...and vibrational behavior involving torsion, wrinkling, and rippling effects. Lattice-based artificial microstructures have been receiving significant attention from the scientific community over the past decade due to the possibility of developing materials with tailored multifunctional capabilities that are not achievable in naturally occurring materials. In general, the lattice materials can be conceptualized as a network of beams with different periodic architectures, wherein the common practice is to adopt initially straight beams. While shear modulus and multiple other mechanical properties can be simultaneously modulated by adopting an appropriate network architecture in the conventional periodic lattices, the prospect of on-demand global specific stiffness and flexibility modulation has become rather saturated lately due to intense investigation in this field. Thus there exists a strong rationale for innovative design at a more elementary level in order to break the conventional bounds of specific stiffness that can be obtained only by lattice-level geometries. In this article, we propose a novel concept of anti-curvature in the design of lattice materials, which reveals a dramatic capability in terms of enhancing shear modulus in the nonlinear regime while keeping the relative density unaltered. A semi-analytical bottom-up framework is developed for estimating effective shear modulus of honeycomb lattices with the anti-curvature effect in cell walls considering geometric nonlinearity under large deformation. We propose to consider the complementary deformed shapes of cell walls of honeycomb lattices under anti-clockwise or clockwise modes of shear stress as the initial beam-level elementary configuration. A substantially increased resistance against deformation can be realized when such a lattice is subjected to the opposite mode of shear stress, leading to increased effective shear modulus. Within the framework of a unit cell based approach, initially curved lattice cell walls are modeled as programmed curved beams under large deformation. The combined effect of bending, stretching, and shear deformation is considered in the framework of Reddy’s third order shear deformation theory in a body embedded curvilinear frame. Governing equation of the elementary beam problem is derived using variational energy principle based Ritz method. In addition to application-specific design and enhancement of shear modulus, unlike conventional materials, we demonstrate through numerical results that it is possible to achieve non-invariant shear modulus under anti-clockwise and clockwise modes of shear stress. The developed physically insightful semi-analytical model captures nonlinearity in shear modulus as a function of the degree of anti-curvature and applied shear stress along with conventional parameters related to unit cell geometry and intrinsic material property. The concept of anti-curvature in lattices would introduce novel exploitable dimensions in mode-dependent effective shear modulus modulation, leading to an expanded design space including more generic scopes of nonlinear large deformation analysis.
•This article proposes a novel concept of anti-curvature in the design of lattice materials, which reveals a dramatic capability in terms of enhancing shear modulus in the nonlinear regime.•A semi-analytical unit cell-based bottom-up framework is developed for estimating the effective shear modulus of honeycomb lattices with the anti-curvature effect in cell walls under large deformation.•The combined effect of bending, stretching and shear deformation is considered in the framework of Reddy’s third order shear deformation theory in a body embedded curvilinear frame.•We demonstrate through numerical results that it is possible to achieve non-invariant shear modulus under anti-clockwise and clockwise modes of shear stress.•The developed model captures nonlinearity in shear modulus as a function of anti-curvature and applied far-field shear stress along with conventional parameters related to unit cell geometry and intrinsic material property.
The SANISAND constitutive model has been widely employed for the simulation of sands cyclic behavior. The shear modulus constant (G0) in SANISAND should be theoretically estimated from maximum shear ...modulus of soil (Gmax). To estimate G0, however, majority of calibration studies have used triaxial tests data in the shear strain levels larger than those associated with Gmax. This technical note aims to demonstrate how the selection criteria forG0 parameter affects the SANISAND model predictions , particularly in terms of G-reduction (shear modulus -shear strain) curve of sands. First, experimental G-reduction curves for four sands are compared with SANISAND predictions based on the values of G0 parameter estimated from triaxial tests. Then, a new calibration set of SANISAND for a single sand is proposed based on the G0 value estimated from Gmax, obtained from resonant column tests. The results confirm that the numerical shear stiffness values fall significantly lower than the experimental values in small strain ranges when the G0 constant is estimated from triaxial tests. However, the G0 constant estimated from Gmax appropriately predicts the experimental G-reduction curve of the sand in a wide shear strain range.
•The selection criteria for G0 parameter significantly affects SANISAND model predictions.•SANISAND calibration set is proposed for a sand based on resonant column tests.•Comparison is made for predicted G-reduction curves based on the G0 estimated from triaxial and resonant column tests.•Calibrations based on G0 parameter from triaxial tests in large strains can produce biased predictions.
The nonlinear, in-plane, shear modulus of re-entrant hexagonal honeycombs under large deformation is analytically derived by studying the mechanical behavior of cell structures, which is later ...verified by numerical simulations. A nonlinear, modified factor is proposed to characterize the difference of the honeycomb's shear modulus under large and small deformation, revealing its independence from the honeycomb's relative density. The effects of both strain and cell geometry on the honeycomb's shear modulus are investigated, exhibiting that the honeycomb's shear modulus increases with shear strain but decreases with the cell-wall-length ratio. For the effect of cell-wall angle, the re-entrant honeycomb's shear modulus decreases gradually with the cell-wall angle until reaching a minimum and then increases, which is highly different from the monotonically increasing relationship of conventional hexagonal honeycombs. When keeping the honeycomb's relative density constant, the re-entrant honeycomb's shear modulus monotonously increases with the cell-wall angle and reaches a maximum at h/l ≈ 3.25. Finally, the shear modulus of the re-entrant honeycombs is compared with that of conventional honeycombs. In contrast to the predictions of the classical continuum theory, the present study shows that the shear modulus of the re-entrant honeycomb with a negative Poisson's ratio is not always higher than that of the conventional honeycomb with a positive Poisson's ratio, which is dominated by the geometry of the cell structure.
It is of great significance to study the nonlinear evolution law of the small strain shear modulus of expansive soil for analyzing the deformation behavior of soil or geotechnical structure and the ...seismic site response. Existing studies rarely discuss the damage mechanism of the small strain shear modulus of expansive soil, and the corresponding damage model describing the small strain stiffness decay law is lacking. In this study, a series of resonance column tests were carried out to investigate the effects of mean effective stress, loading and unloading stress paths and vibration cycles on the nonlinear decay law of small strain shear modulus of expansive soil, and the damage mechanism was discussed in detail. Subsequently, a novel damage model describing the decay law of small strain shear modulus of expansive soil was proposed and verified by the results of resonant column tests. The results show that the decay process of the small strain shear modulus with the shear strain is essentially the damage of the soil structure, which can be characterized mathematically by damage model. The mean effective stress and the larger overconsolidation ratio caused by the unloading process can inhibit the damage, while the vibration cycles can cause small reduction in small strain shear modulus and promote the damage. The proposed damage model with clear physical meaning can well describe the evolution law of small strain shear modulus of expansive soil, and has higher accuracy than the traditional model.
•The effects of various factors on the small strain shear modulus of expansive soil are investigated.•The damage mechanism of small strain shear modulus of expansive soil is analyzed.•A novel damage model describing the decay law of small strain shear modulus of expansive soil is proposed.
A total of 153 cyclic triaxial tests were performed on 19 sand-gravel mixtures over the strain range of 10
-5
-10
-2
, which shows that the particle characteristics have significant influence on the ...small-strain shear-modulus G
0
, shear modulus reduction G/G
0,
and damping ratio λ. An improved Hardin's equation for the G
0
was proposed to consider the effects of particle characteristics and consolidation state. Furthermore, the KZM model correlation was improved to characterize the G/G
0
curve. A four-parameter equation of λ with parent rock type, particle gradation, and consolidation condition was also introduced to characterize the λ curve.
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