What is the Correct Definition of Average Pressure?

Use of a correct definition of average pressure is important in numerical modeling of oil reservoirs and aquifers, where the simulated domain can be very large. Also, the average pressure needs to be defined in the application of pore-network modeling of (two-phase) flow in porous media, as well as in the (theoretical) upscaling of flow equations. Almost always the so-called intrinsic phase-volume average operator, which weighs point pressure values with point saturation values, is employed. Here, we introduce and investigate four other potentially plausible averaging operators. Among them is the centroid-corrected phase-average pressure, which corrects the intrinsic phase-volume average pressure for the distance between the centroid of the averaging volume and the phase. We consider static equilibrium of two immiscible fluids in a homogeneous, one-dimensional, vertical porous medium domain under a series of (static) drainage conditions. An important feature of static equilibrium is that the total potential (i.e., the sum of pressure and gravity potentials) is constant for each phase over the whole domain. Therefore, its average will be equal to the same constant. It is argued that the correct average pressure must preserve the fact that fluid potentials are constant. We have found that the intrinsic phase-volume average pressure results in a gradient in the total phase potential, i.e., the above criterion is violated. In fact, only the centroid-corrected operator satisfies this criterion. However, at high saturations, use of the centroid-corrected average can give rise to negative values of the difference between the average nonwetting and wetting phase pressures. For main drainage, differences among various averaging operators are significantly less because both phases are present initially, such that the difference between the centroids of phases, and the middle of the domain are relatively small.     

What is the Optimal Shape of a Pipe?

We consider an incompressible fluid in a three-dimensional pipe, following the Navier–Stokes system with classical boundary conditions. We are interested in the following question: is there any optimal shape for the criterion “energy dissipated by the fluid”? Moreover, is the cylinder the optimal shape? We prove that there exists an optimal shape in a reasonable class of admissible domains, but the cylinder is not optimal. For that purpose, we define the first order optimality condition, thanks to the adjoint state and we prove that it is impossible that the adjoint state be a solution of this over-determined system when the domain is the cylinder. At last, we show some numerical simulations for that problem.     

Oscillations of the plastic wave front under high‐rate loading

Two models of elastoplastic wave propagation in metals under uniaxial deformation are considered. The first model treats plastic deformation as being due to dislocation motion during heterogeneous formation of dislocations. The second model assumes that plastic deformation occurs by motion of dipoles of partial disclinations. It is shown that in both cases, certain conditions can give rise to damped oscillations of the plastic wave front, which were detected in shock loading experiments with flat specimens made of 28Kh3SNMFA steel.     

Micromorphic approach for gradient-extended thermo-elastic–plastic solids in the logarithmic strain space

The coupled thermo-mechanical strain gradient plasticity theory that accounts for microstructure-based size effects is outlined within this work. It extends the recent work of Miehe et al. (Comput Methods Appl Mech Eng 268:704–734, 2014) to account for thermal effects at finite strains. From the computational viewpoint, the finite element design of the coupled problem is not straightforward and requires additional strategies due to the difficulties near the elastic–plastic boundaries. To simplify the finite element formulation, we extend it toward the micromorphic approach to gradient thermo-plasticity model in the logarithmic strain space. The key point is the introduction of dual local–global field variables via a penalty method, where only the global fields are restricted by boundary conditions. Hence, the problem of restricting the gradient variable to the plastic domain is relaxed, which makes the formulation very attractive for finite element implementation as discussed in Forest (J Eng Mech 135:117–131, 2009) and Miehe et al. (Philos Trans R Soc A Math Phys Eng Sci 374:20150170, 2016).     

A modified Green–Lindsay thermoelasticity with strain rate to eliminate the discontinuity

Probing the mechanism of ultrafast thermoelastic processes is becoming increasingly important with the development of laser-assisted micro/nano machining. Although thermoelastic models containing temperature rate have been historically proposed, the strain rate has not been considered yet. In this work, a generalized thermoelastic model is theoretically established by introducing the strain rate in Green–Lindsay (GL) thermoelastic model with the aid of extended thermodynamics. Numerically, a semi-infinite one-dimensional problem is considered with traction free at one end and subjected to a temperature rise. The problem is solved using the Laplace transform method, and the transient responses, i.e. displacement, temperature and stresses are graphically depicted. Interestingly, it is found that the strain rate may eliminate the discontinuity of the displacement at the elastic and thermal wave front. Also, the present model is compared with Green–Naghdi (GN) models. It is found that the thermal wave speed of the present model is faster than GN model without energy dissipation, and slower than GN model with energy dissipation. In addition, the thermoelastic responses from the present model are the largest. The present model based upon GL model is free of the jump of GL model in the displacement distribution, and is safer in engineering practices than GN model. The present work will benefit the theoretical modeling and numerical prediction of thermoelastic process, especially for those under extreme fast heating.     

An equivalent von Mises stress and corresponding equivalent plastic strain for elastic–plastic ordinary peridynamics

Meccanica - Simple formulas for calculating equivalent von Mises stress and von Mises effective plastic strain in an elastic–plastic ordinary peridynamic analysis are proposed. The equivalent...     

Temperature–strain rate deformation conditions of aluminum alloys

This paper presents the results of an experimental study of the deformation and structural parameters of 1561 anisotropic alloy. It has been found that the lowest anisotropy factor corresponds to the formation of an ultrafine-grained equiaxed structure under temperature–strain rate conditions of superplasticity.     

On Aifantis’ strain gradient plasticity theory accounting for plastic spin

This paper examines the effect of codirectionality hypothesis on Aifantis’ distortion gradient plasticity theory. The system of microforces includes microstress, power-conjugate to the Burgers tensor rate. The proposed codirectionality hypothesis assumes, that the flow direction and the plastic microstress are in the same direction. It is obtained that the power expended by the microstress power-conjugate to the Burgers tensor rate, can be additively decomposed to power expended by scalar and vector microscopic stresses power-conjugate to the accumulated plastic distortion rate and gradient of plastic distortion rate respectively. Following the proposed codirectionality hypothesis, it is obtained that the microstress power-conjugate to the Burgers tensor rate is purely energetic. The obtained flow rule accounts for plastic spin and generalizes the Aifantis’ flow rule.     

Tension–torsion fracture experiments—Part I: Experiments and a procedure to evaluate the equivalent plastic strain

Ductile failure experiments on a double notched tube (DNT) specimen subjected to a combination of tensile load and torque that was applied at a fixed ratio is presented. The experimental results extend those in Barsoum and Faleskog (2007a) down to zero stress triaxiality. A new and robust evaluation procedure for such tests is proposed, and a simple relation for the equivalent plastic strain at failure for combined normal and shear deformation, respectively, is developed. Tests were carried out on the medium strength medium hardening steel Weldox 420, and the high strength low hardening steel Weldox 960. The experimental results unanimously show that ductile failure not only depends on stress triaxiality, but is also strongly affected by the type of deviatoric stress state that prevails, which can be quantified by a stress invariant that discriminates between axisymmetric stressing and shear dominated stressing, e.g., the Lode parameter. Additional experiments on round notch bar (RNB) specimens are recapitulated in order to give a comprehensive account on how ductile failure depends on stress triaxiality, ranging from zero to more than 1.6, and the type of stress state for the two materials tested. This provides an extensive experimental data base that will be used to explore an extension of the Gurson model that incorporates damage development in shear presented in Xue et al. (2013) (Part II).     

Q-consciousness: where is the flow?

What can recent research on quantum-consciousness (Q-consciousness) tell us about the connection between quantum level phenomena and human consciousness? Q-consciousness theorists propose and experimenters purport to show evidence linking quantum mechanisms of one kind or another to changes in biologically important atomic and molecular processes that produce and shape 'consciousness.' Several mechanisms are identified. In the studies reviewed, consciousness is not operationally defined. How Q-level events influence or are responsible for the complex performance of consciousness in its environment is not specified. Several problems with specifying causality within and between different temporalities at the biological and quantum level are not addressed. The morphogenic rules that govern the origin, continuous or discontinuous, and spontaneous presenting of an organized consciousness are missing. The literature reviewed shows that there are causal links between quantum events and molecular changes that affect biological processes such as photosynthesis and bird migration. Even so, the connections between the quantum level of reality, biological processes, mind and the diverse flow of consciousness are not well and consistently defined, or characterized and understood in ways useful for conducting research of the morphogenesis of consciousness. No overall experimental direction is Q-consciousness research is discernable. Finally, the preponderance of limited experimental evidence does not point toward a particular Q-consciousness theory. Suggestions are made about how recasting cell doctrine, thinking of consciousness as 'performance,' and nonlinear and complexity theory may provide some guidance relevant to the possible flow of Q-consciousness.     

What are the Longest Ropes on the Unit Sphere?

We consider the variational problem of finding the longest closed curves of given minimal thickness on the unit sphere. After establishing the existence of solutions for any given thickness between 0 and 1, we explicitly construct for each given thickness \({\Theta_n:= {\rm sin}\, \pi/(2n),}\) \({n\in\mathbb{N}}\), exactly \({\varphi(n)}\) solutions, where \({\varphi}\) is Euler’s totient function from number theory. Then we prove that these solutions are unique, and also provide a complete characterisation of sphere filling curves on the unit sphere; that is of those curves whose spherical tubular neighbourhood completely covers the surface area of the unit sphere exactly once. All of these results carry over to open curves as well, as indicated in the last section.     

Shear response of β-SiC bulk dependent on temperature and strain rate

The shear responses of β-SiC are investigated using molecular dynamics simulation with the Tersoff interatomic potential. Results show a clear decreasing trend in critical stress,fracture strain and shear modulus as temperature increases. Above a critical temperature, β-SiC bulk just fractures after the elastic deformation. However, below the critical temperature, an interesting pattern in β-SiC bulk emerges due to the elongation of Si-C bonds before fracture. Additionally, the shear deformation of β-SiC at room temperature is found to be dependent on the strain rate. This study may shed light on the deformation mechanism dependent on temperature and strain rate.     

On the plastic wave speeds in rate-independent elastic–plastic materials with anisotropic elasticity

This paper presents a theoretical study of the speeds of plastic waves in rate-independent elastic–plastic materials with anisotropic elasticity. It is shown that for a given propagation direction the plastic wave speeds are equal to or lower than the corresponding elastic speeds, and a simple expression is provided for the bound on the difference between the elastic and the plastic wave speeds. The bound is given as a function of the plastic modulus and the magnitude of a vector defined by the current stress state and the propagation direction. For elastic–plastic materials with cubic symmetry and with tetragonal symmetry, the upper and lower bounds on the plastic wave speeds are obtained without numerically solving an eigenvalue problem. Numerical examples of materials with cubic symmetry (copper) and with tetragonal symmetry (tin) are presented as a validation of the proposed bounds. The lower bound proposed here on the minimum plastic wave speed may also be used as an efficient alternative to the bifurcation analysis at early stages of plastic deformation for the determination of the loss of ellipticity.     

The surface-forming energy release rate based fracture criterion for elastic–plastic crack propagation

The J-integral based criterion is widely used in elastic–plastic fracture mechanics. However, it is not rigorously applicable when plastic unloading appears during crack propagation. One difficulty is that the energy density with plastic unloading in the J-integral cannot be defined unambiguously. In this paper, we alternatively start from the analysis on the power balance, and propose a surface-forming energy release rate (ERR), which represents the energy available for separating the crack surfaces during the crack propagation and excludes the loading-mode-dependent plastic dissipation. Therefore the surface-forming ERR based fracture criterion has wider applicability, including elastic–plastic crack propagation problems. Several formulae are derived for calculating the surface-forming ERR. From the most concise formula, it is interesting to note that the surface-forming ERR can be computed using only the stress and deformation of the current moment, and the definition of the energy density or work density is avoided. When an infinitesimal contour is chosen, the expression can be further simplified. For any fracture behaviors, the surface-forming ERR is proven to be path-independent, and the path-independence of its constituent term, so-called J_s-integral, is also investigated. The physical meanings and applicability of the proposed surface-forming ERR, traditional ERR, J_s-integral and J-integral are compared and discussed. Besides, we give an interpretation of Rice paradox by comparing the cohesive fracture model and the surface-forming ERR based fracture criterion.     

Ellipticity loss analysis for tangent moduli deduced from a large strain elastic–plastic self-consistent model

In order to investigate the impact of microstructures and deformation mechanisms on the ductility of materials, the criterion first proposed by Rice is applied to elastic–plastic tangent moduli derived from a large strain micromechanical model combined with a self-consistent scale-transition technique. This approach takes into account several microstructural aspects for polycrystalline aggregates: initial and induced textures, dislocation densities as well as softening mechanisms such that the behavior during complex loading paths can be accurately described.     

Determination of the microscale stress–strain curve and strain gradient effect from the micro-bend of ultra-thin beams

A simple method is established to determine the microscale uniaxial stress–strain curve from the load and deflection data for a doubly clamped beam. The method is based on the fact that, for beam deflection much larger than the beam thickness, the axial stretching dominates the deformation in the doubly clamped beam and the doubly clamped beam behaves like a simple plastic hinge. The microscale uniaxial stress–strain curve, together with the cantilever beam experiments, is used to determine the strain gradient effect in Au thin beams. The effect of finite rotation is also discussed.     

Elastic–plastic behavior of steel sheets under in-plane cyclic tension–compression at large strain

Elastic–plastic behavior of two types of steel sheets for press-forming (an aluminum-killed mild steel and a dual-phase high strength steel of 590 MPa ultimate tensile strength) under in-plane cyclic tension–compression at large strain (up to 25% strain for mild steel and 13% for high strength steel) have been investigated. From the experiments, it was found that the cyclic hardening is strongly influenced by cyclic strain range and mean strain. Transient softening and workhardening stagnation due to the Bauschinger effect, as well as the decrease in Young's moduli with increasing prestrain, were also observed during stress reversals. Some important points in constitutive modeling for such large-strain cyclic elasto-plasticity are discussed by comparing the stress–strain responses calculated by typical constitutive models of mixed isotropic–kinematic hardening with the corresponding experimental observations.     

Fourier-BEM: or What To Do if No Fundamental Solution is Available?

The application of boundary element methods (BEM) to soil-structure interaction problems is still restricted to cases where fundamental solutions are known. Hence, a large number of engineering problems cannot be solved by the BEM. Therefore, an alternative approach is presented here which establishes new boundary integral equations (BIEs) for the computation of the entries of the BEM matrices by means of the spatial Fourier transform.For these alternative BIEs, we need only the transform of the fundamental solution and not the fundamental solution itself. The former is always available as long as the underlying differential operator is linear and has constant coefficients. The approach is possible for all variants of the BEM. For Galerkin approaches, the double integrations over the boundary panels are replaced by single integrations over the infinite domain.