Nanocrystalline metals have many applications in nanodevices, especially nanoscale electronics in aerospace. Their ability to resist fracture under impact produced by environmental stress is the main ...concern of nanodevice design. By carrying out molecular dynamics simulations under different fast loading rates, this work examines the effect of impact load on the fracture behavior of nanocrystalline bcc iron at an atomistic scale. The results show that a crack propagates with intergranular decohesion in nanocrystalline iron. With the increase in impact load, intergranular decohesion weakens, and plastic behaviors are generated by grain boundary activities. Also, the mechanism dominating plastic deformation changes from the atomic slip at the crack tip to obvious grain boundary activities. The grain boundary activities produced by the increase in impact load lead to an increase in the threshold energy for crack cleavage and enhance nanocrystalline bcc iron resistance to fracture. Nanocrystalline bcc iron can keep a high fracture ductility under a large impact load.
•This paper proposed a new modeling to simulate nonlinear hardening plastic materials' deformation for OSPD.•This paper provides a simpler way to simulate linear hardening materials' deformation for ...OSPD.•A new approach to construct yield function based on Von-Mises criterion for state-based peridynamics is developed.•The nonlinear hardening plastic materials' crack initiation and growth is simulated in this paper.
In this paper, a modelling for ordinary state-based peridynamics to simulate plastic deformation is presented. This modelling can simulate nonlinear-hardening plastic mode, what's more, the perfect plastic model and linear-hardening plastic model can also be simulated in a simple way too. The expression of equivalent plastic stress in the formulation of nonlocal ordinary state-based peridynamics is established. The yield function is constructed based on the Von Mises yield criteria. Then the way to calculate the equivalent plastic stress in every step is established. And all the formulations have been discussed both in 2D case and 3D case. The validity of this modelling is established by comparing the results of a plate under tension or pushing simulated by peridynamics and FEM in 2D case, and the plate under tension is the plastic material with power-hardening law, the plate under pushing is the plastic material with linear-hardening law.
•The strain gradient viscoelastic solutions of the Mode-I and Mode-II crack in an infinite quasi-brittle advanced material are proposed based on the strain gradient viscoelasticity theory using the ...Wiener-Hopf method and the correspondence principle in Maxwell's standard linear solid model. The strain gradient viscoelasticity theory are successfully used to explain the fracture of microscale and nanoscale materials with viscosity and size effect.•The stress near the crack tip is time-dependent and size-dependent. The stress near the crack tip is more significant than that based on gradient elasticity theory. Compared with the elastic strain gradient effect, the viscous gradient effect makes the stress field at the crack tip harden.•The location and the value of maximum stress change with time, which differs from the case in strain gradient elasticity theory. The time that the normalized stress takes to stabilize also changes with the distance from the crack tip. When the viscosity effect is neglected or time tends to infinity, the strain gradient viscoelasticity theory can be reduced to the classical strain gradient elasticity theory.
The impacts of size and viscosity become distinctly evident when considering micro- and nano-scale phenomena for advanced materials with micro- and nanostructures. In this study, the mechanical behavior of the advanced material is characterized by using the strain gradient viscoelasticity theory, and a novel solution is presented for the mode-I and mode-II cracks, which is formulated based on the strain gradient viscoelasticity theory, employing the Wiener-Hopf method. Besides, the gradient-dependent viscoelastic crack solutions are directly derived by applying the correspondence principle that aligns strain gradient viscoelasticity with strain gradient elasticity within the Maxwell's standard linear solid model. Relative to the influence of elastic strain gradient effects, the involvement of viscous gradient effects instigates a reinforcement to the stress field around the crack tip, thereby offering a more reasonable representation of advanced materials crack behavior. When the viscosity effect is omitted or as time tends to infinity, the solutions based on strain gradient viscoelasticity theory converges to those on the classical strain gradient elasticity theory.
•The GDH-PD is proposed to address size-dependent effects and fracture problems.•The lower- and higher-order micro-modulus states of GDH-PD are firstly derived.•GDH-PD eliminates zero-energy modes of ...traditional higher-order peridynamics.•HOBCs are applied by constructing quadratic functional on the boundary points.•Nonlocal effects, size effects, strain gradient effects and damage are considered.
In this paper, we propose the implicit stabilized dual-horizon peridynamics-based strain gradient damage model (GDH-PD) to describe the cross-scale fracture behavior of materials. To this end, firstly, the strain energy density function of GDH-PD is reformulated by considering the energy compensation to eliminate zero-energy modes of the traditional higher-order peridynamics. And then, the constitutive force state of GDH-PD is derived and explicitly expressed with the help of the proposed special dimension reduction of the nonlocal higher-order tensors. To solve the steady-state crack propagation problems, the implicit GDH-PD is developed by deriving the lower- and higher-order micro-modulus double state, such that the linearization of the equilibrium equation of GDH-PD is established. At last, the bond length-dependent energy-based failure criterion is used to characterize the cross-scale fracture in the form of bond breakage. The effectiveness of GDH-PD to characterize microstructure size effects and macrostructure strain gradient effects are investigated by numerical simulations. The numerical results are in good agreement with the analytical solutions or the available experimental results. We believe that the proposed GDH-PD may pave the way to an increased application of peridynamics to be used in the cross-scale fracture predictions for the advanced material.
The peridynamic correspondence model (PDCM) provides the stress–strain relation that can introduce many classical constitutive models, however, the high computational consumption and zero-energy mode ...of PDCM certainly limit its further application to practical engineering crack problems. To solve these limitations and exploit the advantage of PDCM, we propose a simple and effective method that adaptively couples dual-horizon peridynamic element (DH-PDE) with finite element (FE) to simulate the quasi-static fracture problems. To this end, a stabilized dual-horizon peridynamic element for DH-PDCM is firstly developed that the peridynamic strain matrices for the bond and material point are constructed respectively. The nonlocal ordinary and correctional peridynamic element stiffness matrices are derived in detail and calculated by the proposed dual-assembly algorithm. Subsequently, a unified variational weak form of this adaptive coupling of DH-PDE and FE is proposed based on the convergence of peridynamics to the classical model in the limit of vanishing horizon. Therefore, the integrals of the peridynamic element and finite element in this coupling method are completely decoupled in the viewpoint of numerical implementation, which makes it easier to realize the proposed adaptive coupling by switching integral element. Moreover, the proposed adaptive coupling is implemented in Abaqus/UEL to optimize the calculational efficiency and real-time visualization of calculated results, which has potential for dealing with the engineering crack problems. Two-dimensional numerical examples involving mode-I and mixed-mode crack problems are used to demonstrate the effectiveness of this adaptive coupling in addressing the quasi-static fracture of cohesive materials.
•A new CMD-DHPD approach to address interface oxidation-induced cracking in TBCs.•Derivation of a dual-horizon peridynamic diffusion-reaction equation and its linearization.•Advancement of BFGS ...Quasi-Newton algorithm for solving coupled equations.•Demonstration with multiple delamination cracks and their interactions within the TGO layer.
The interface oxidation-induced cracking process in thermal barrier coatings (TBCs) is rather complex. It involves the material changes of chemical reactions, dynamic migration and diffusion of BC/TGO (bond coat/thermally grown oxide) interface, delamination of TC (top coat)/TGO and BC/TGO interfaces, multiple delamination cracks and their interactions within the TGO layer, etc. The complex process presents significant difficulties and challenges to simulation. To explore the comprehensive cracking mechanisms induced by the interface oxidation, we propose the coupled chemo-mechanical-damage model in a dual-horizon peridynamic framework (CMD-DHPD). The corresponding governing equations and their linearized forms are derived in the form of integral coupled equations for CMD-DHPD. The dual-horizon peridynamic diffusion-reaction equation and its linearization are derived based on the dual-horizon peridynamic correspondence principle. The nonlocal crack phase-field and interface phase-field are presented to address the geometric discontinuity of bulk materials and the material discontinuity in the region of the TC/TGO interface, respectively. In order to ensure convergence and accuracy, the BFGS Quasi-Newton algorithm is further enhanced to solve for the integral equations arising from the coupled chemo-mechanical-damage processes. The proposed CMD-DHPD captures the TGO growth pattern, interface cracks initiation, propagation and their interactions as observed in experiments. Therefore, it is extremely suitable for solving the interface oxidation-induced cracking process in thermal barrier coatings.
•The unified peridynamic correspondence principle is proposed on the basis of the energy compensation method.•A new peridynamic deformation gradient, shape matrix and force state are derived and ...redefined.•The nonlocal phase field damage constitutive model is developed in the context of peridynamics.•The linearization method of the peridynamics-based phase-field model (PD-PFM) is first presented.•The PD-PFM not only solves the zero-energy mode of the conventional peridynamic correspondence principle, but also provides the rational criterion for the breakage of the peridynamic bond.
The peridynamic correspondence model is a promising and attractive candidate for the modeling of localized failure in solids, in that it can incorporate many local classical damage constitutive models through introducing a nonlocal averaged deformation gradient. However, the zero-energy mode and the limited bond breaking criterion greatly restrict the potential applications of this correspondence model. To address these two problems, a unified nonlocal peridynamics-based phase-field damage theory is proposed within the framework of thermodynamics. Firstly, the unified correspondence principle for the displacement field is developed on the basis of the energy compensation method in such a way that a new peridynamic deformation gradient, shape matrix and force state are derived and redefined. And then, the proposed principle is applied to derive the nonlocal phase-field damage constitutive model that the general nonlocal phase-field flux, phase-field flow state and phase-field internal force are defined. Moreover, we propose a mixed variational derivative method to obtain the coupled equilibrium governing equation and present the general linearization approach of the proposed peridynamics-based phase-field model (PD-PFM), where the double states for the coupled displacement and phase fields are derived in detail. It will be found that PD-PFM can not only resolve the zero-energy mode existed in the conventional peridynamic correspondence model, but also provide a rational criterion for the breakage of the peridynamic bond. Some representative numerical examples including mixed mode fracture of single-material media and interface fracture of ceramic coating systems are presented for the validation of PD-PFM. The satisfactory results show both quantitative and qualitative agreement with the available experiment.
Background： To investigate the effects of dietary crude protein（CP） restriction on muscle fiber characteristics and key regulators related to protein deposition in skeletal muscle, a total of 18 ...growing-finishing pigs（62.30 ± 0.88 kg）were allotted to 3 groups and fed with the recommended adequate protein（AP, 16 % CP） diet, moderately restricted protein（MP, 13 % CP） diet and low protein（LP, 10 % CP） diet, respectively. The skeletal muscle of different locations in pigs, including longissimus dorsi muscle（LDM）, psoas major muscle（PMM） and biceps femoris muscle（BFM） were collected and analyzed.Results： Results showed that growing-finishing pigs fed the MP or AP diet improved（P 〈 0.01） the average daily gain and feed： gain ratio compared with those fed the LP diet, and the MP diet tended to increase（P = 0.09） the weight of LDM. Moreover, the ATP content and energy charge value were varied among muscle samples from different locations of pigs fed the reduced protein diets. We also observed that pigs fed the MP diet up-regulated（P 〈 0.05） muscular m RNA expression of all the selected key genes, except that myosin heavy chain（My HC） IIb,My HC IIx, while m RNA expression of ubiquitin ligases genes was not affected by dietary CP level. Additionally, the activation of mammalian target of rapamycin complex 1（m TORC1） pathway was stimulated（P 〈 0.05） in skeletal muscle of the pigs fed the MP or AP diet compared with those fed the LP diet.Conclusion： The results suggest that the pigs fed the MP diet could catch up to the growth performance and the LDM weight of the pigs fed the AP diet, and the underlying mechanism may be partly due to the alteration in energy status, modulation of muscle fiber characteristics and m TORC1 activation as well as its downstream effectors in skeletal muscle of different locations in growing-finishing pigs.
Summary
Mammalian skeletal muscles are composed of two major fibre types (I and II) that differ in terms of size, metabolism and contractile properties. In general, slow‐twitch type I fibres are rich ...in mitochondria and have a greater insulin sensitivity than fast‐twitch type II skeletal muscles. Although not widely appreciated, a forced induction of the slow skeletal muscle phenotype may inhibit the progress of obesity and diabetes. This potentially forms the basis for targeting slow/oxidative myofibers in the treatment of obesity. In this context, a better understanding of the molecular basis of fibre‐type specification and plasticity may help to identify potential therapeutic targets for obesity and diabetes.
