The Isotropic Material Design of In-Plane Loaded Elasto-Plastic Plates

This paper puts forward a new version of the Isotropic Material Design method for the optimum design of structures made of an elasto-plastic material within the Hencky-Nadai-Ilyushin theory. This method provides the optimal layouts of the moduli of isotropy to make the overall compliance minimal. Thus, the bulk and shear moduli are the only design variables, both assumed as non-negative fields. The trace of the Hooke tensor represents the unit cost of the design. The yield condition is assumed to be independent of the design variables, to make the design process as simple as possible. By eliminating the design variables, the optimum design problem is reduced to the pair of the two mutually dual Linear Constrained Problems (LCP). The solution to the LCP stress-based problem directly determines the layout of the optimal moduli. A numerical method has been developed to construct approximate solutions, which paves the way for constructing the final layouts of the elastic moduli. Selected illustrative solutions are reported, corresponding to various data concerning the yield limit and the cost of the design. The yield condition introduced in this paper results in bounding the values of the optimal moduli in the places of possible stress concentration, such as reentrant corners.

Analysis of Cohesion in Fast-spinning Small Bodies

In this paper, the structural stability of a fast-spinning small body is investigated. In particular, a nonlinear yield condition in tensile stress is applied to estimate the required cohesion in a fast-spinning small body. The least upper bound of required cohesion is investigated for both ellipsoid and irregular shape models. The stress state of a fast-spinning ellipsoid is discussed analytically, and the effects of spin rates and size ratios are analyzed. For an irregularly shaped body, an element average stress method is developed to estimate the range of stress of any element in the body, where only self-gravity and centrifugal force are considered. The maximum tensile stress in the whole body is used to solve the required cohesion. Finally, the proposed methods are applied to different asteroid shape models. The result shows that the least upper bound of cohesion is mainly determined by the spin rate and length of the major axis, but an irregular shape will change the stress distribution and cause a stressed surface. The required cohesion of a fast-spinning small body varies between tens to 1000 Pa. The methods developed in this paper can rapidly provide a conservative lower bound on the cohesion in a fast-spinning body and qualitatively show the distribution of stress, which provides an effective way to study the structural stability of fast-spinning bodies of those bodies.

Viscoplastic plates

An asymptotic model is constructed to describe the bending of thin sheets, or plates, of viscoplastic fluid described by the Herschel–Bulkley constitutive law, which incorporates the von Mises yield condition and a nonlinear viscous stress. The model reduces to a number of previous ones from plasticity theory and viscous fluid mechanics in various limits. It is characterized by a yield criterion proposed by Ilyushin which compactly combines the effect of the bending moment and in-plane stress tensors through three particular invariants. The model is used to explore the bending of loaded flat plates, the deflection of impulsively driven circular plates, and the tension-controlled deflection of loaded beams.

Comprehensive Assessment from Optimum Biodiesel Yield to Combustion Characteristics of Light Duty Diesel Engine Fueled with Palm Kernel Oil Biodiesel and Fuel Additives

Biodiesel is considered as a key prospective renewable energy source in India. Hence, a study was carried out for the improvement of palm kernel oil biodiesel production using a transesterification process at different molar ratios. This study comprehensively examined all aspects of biodiesel from optimum production to the effect of additives on its combustion behavior. The optimum yield condition was validated with the MINITAB-17 software and analyzed using the Taguchi method. Two different additives, 5% diethyl ether (DEE) and 2000 ppm Butylated hydroxyltoluene (BHT), were also experimented. Engine experiments were conducted at constant speed (1500 rpm) and five different engine loads (0, 25, 50, 75 and 100%) on a single-cylinder direct injection diesel engine. Heat release rate, brake specific fuel consumption, brake thermal efficiency, engine emissions, such as CO, HC, NOx, and smoke opacity were analyzed. The maximum palm kernel oil (PKO) biodiesel yields, obtained at 55 °C, for the KOH and NaOH catalysts were 86.69% and 75.21% at the molar ratio of 6:1. B20BHT combustion showed 4.6% higher brake thermal efficiency (BTE). NOx emission was reduced by 19.4%, compared to the diesel fuel values. DEE resulted in higher CO and HC emissions compared to diesel fuel values by 39.2% and 7.6%, respectively, whereas smoke emission was improved by 11.5%.

Elastic Simulation of Joints with Particle-Based Fluid

Skinning, which is used in skeletal simulations to express the human body, has been weighted between bones to enable muscle-like motions. Weighting is not a form of calculating the pressure and density of muscle fibers in the human body. Therefore, it is not possible to express physical changes when external forces are applied. To express a similar behavior, an animator arbitrarily customizes the weight values. In this study, we apply the kernel and pressure-dependent density variations used in particle-based fluid simulations to skinning simulations. As a result, surface tension and elasticity between particles are applied to muscles, indicating realistic human motion. We also propose a tension yield condition that reflects Tresca’s yield condition, which can be easily approximated using the difference between the maximum and minimum values of the principal stress to simulate the tension limit of the muscle fiber. The density received by particles in the kernel is assumed to be the principal stress. The difference is calculated by approximating the moment of greatest force to the maximum principal stress and the moment of least force to the minimum principal stress. When the density of a particle increases beyond the yield condition, the object is no longer subjected to force. As a result, one can express realistic muscles.

Explicit form of yield conditions dual to a class of dissipation potentials dependent on three invariants

In the paper, a pragmatic approach to finding the dual formulation for isotropic perfectly plastic materials given a dissipation potential dependent on three cylindrical invariants and involving the Ottosen shape function is proposed and illustrated by examples. The main goal is to provide instructions on how to perform the Legendre transformation used when passing from a dissipation potential to its conjugate yield condition and offer some suggestions regarding calibration for particular potentials dependent on the trace of the strain rate tensor and the product of the norm of its deviator and the Ottosen shape function, which covers a wide class of engineering materials. The classic framework for constitutive modelling of thermodynamically consistent materials within the small deformation theory is used. First, general formulae connecting a dissipation potential dependent on three invariants of the strain rate tensor to the coupled yield condition are derived. Then, they are narrowed down for the aforementioned case of dissipation functions dependent on the Lode angle in a way proposed by Ottosen. Finally, three examples are given involving classical potentials: Beltrami’s, Drucker–Prager’s and Mises–Schleicher’s generalised potential using the shape function. Detailed calculations exposing the introduced technique are performed. Also, a method of the calibration of such potentials leading to explicit mathematical formulae is demonstrated, based on the typical tests located on the tension and compression meridians.

Extending the Shields criterion to erosion of weakly cemented granular soils

This contribution tackles the issue of incipient conditions for initiation of erosion by a fluid flow at the surface of cohesive materials. To this end, a typical assessment procedure consists of subjecting a soil sample to progressive hydrodynamic stresses induced by a submerged impinging jet flow whose injection velocity is gradually increased. This paper presents the results of an extensive use of this protocol both in experiments and numerical simulations, the latter being based on a coupled DEM and LBM approach. Here we consider the specific case of weakly cemented soils, either made experimentally of glass beads bonded by solid bridges or modelled numerically by a solid bond rheology with a parabolic yield condition involving the micromechanical traction, shearing and bending of the bonds. The results show that, as expected, the hydrodynamic stress for erosion onset substantially increases with solid cohesion as compared to cohesionless cases but can, however, be satisfactorily predicted by a simple extension of the usual Shields criterion that only applies for cohesion-less granular sediments. This extension includes a cohesion number, the granular Bond number, with a simple definition based on tensile yield values.

The tensile strength: The most fundamental mechanical characteristics of concrete

Concrete is an inhomogeneous building material. It has a considerable and reliable compressive strength and a relative low tensile strength which can be even exhausted locally under unfortunate conditions. It is quite obvious that the concrete tensile strength was always reprehended as the most unreliable concrete property. A simple relationship between tensile- and compressive strength is introduced. The mechanical background of the relation tensile- to compressive strength in case of ‘normal’ and high strength concretes is elucidated. Mechanical bond, too, relies completely on the tensile strength. In the design of structural concrete members the tension fields are more characteristic than the compression fields. Effective concrete strengths are not successful. Tensile strength can be applied as ‘yield condition’ for the lower bound solution in the theory of plasticity. The paper intends to contribute to the acceptance of the tensile strength as the more fundamental concrete characteristics.

Plastic response of conical shells with stiffeners to blast loading

The inelastic response of circular conical shells to the blast loading is studied. The impact loading is applied at the initial time moment and it is removed at a certain instant of time. The load intensity depends of the coordinate of the shell. The material of the shell is a perfect plastic one obeying the Johansen yield condition and the associated flow law. It is assumed that the frustum of the cone is furnished with ring stiffeners made of the same material. A theoretical method for the evaluation of the stress strain state of the shell and for determination of maximal residual deflections is developed.