Abstract: Abstract
In Bertram (Continuum Mech Thermodyn. doi:10.1007/s00161-014-0387-0, 2015), a mechanical framework for finite gradient elasticity and plasticity has been given. In the present paper, this is extended to thermodynamics. The mechanical theory is only briefly repeated here. A format for a rather general constitutive theory including all thermodynamic fields is given in a Euclidian invariant setting. The plasticity theory is rate-independent and unconstrained. The Clausius–Duhem inequality is exploited to find necessary and sufficient conditions for thermodynamic consistency. The residual dissipation inequality restricts the flow and hardening rules in combination with the yield criterion. PubDate: 2015-03-13

Abstract: Abstract
In this article, an alternative to the classical dynamic equation formulation is presented. To achieve this goal, we need to derive the reciprocal theorem in rates and the principle of virtual work in rates, in a small deformation regime, with which we will be able to obtain an expression for damping force. In this new formulation, some terms that are not commonly considered in the classical formulation appear, e.g., the term that is function of jerk (the rate of change of acceleration). Moreover, in this formulation the term that characterizes material nonlinearity, in dynamic analysis, appears naturally. PubDate: 2015-03-06

Abstract: Abstract
Multi-mechanism models (MM models) have become an important tool for modeling complex material behavior. In particular, two-mechanism models are used. They are applied to model ratcheting in metal plasticity as well as steel behavior during phase transformations. We consider a small-deformation setting. The characteristic trait of multi-mechanism models is the additive decomposition of the inelastic (e.g., plastic or viscoplastic) strain into several parts. These parts are sometimes called mechanisms. In comparison with rheological models, the mechanisms can interact with each other. This leads to new properties and allows to describe important observable effects. Up to now, each mechanism has one kinematic internal variable. As a new feature, we develop multi-mechanism models (in series) with several kinematic variables for each mechanism as well as with several isotropic variables for each flow criterion. We describe this complex situation by three structural matrices which express the mutual relations between mechanisms, flow criteria, kinematic, and isotropic variables. The well-known Chaboche model with a unique inelastic strain and several kinematic variables represents a special case of these general multi-mechanism models. In this work, we also present a matrix-based approach for these new complex MM models. The presented models can form the basis for developing numerical algorithms for simulation and parameter identification. PubDate: 2015-03-01

Abstract: Abstract
A new non-classical Kirchhoff plate model is developed using a modified couple stress theory, a surface elasticity theory and a two-parameter elastic foundation model. A variational formulation based on Hamilton’s principle is employed, which leads to the simultaneous determination of the equations of motion and the complete boundary conditions and provides a unified treatment of the microstructure, surface energy and foundation effects. The new plate model contains a material length scale parameter to account for the microstructure effect, three surface elastic constants to describe the surface energy effect, and two foundation moduli to represent the foundation effect. The current non-classical plate model reduces to its classical elasticity-based counterpart when the microstructure, surface energy and foundation effects are all suppressed. In addition, the newly developed plate model includes the models considering the microstructure dependence or the surface energy effect or the foundation influence alone as special cases and recovers the Bernoulli–Euler beam model incorporating the microstructure, surface energy and foundation effects. To illustrate the new model, the static bending and free vibration problems of a simply supported rectangular plate are analytically solved by directly applying the general formulas derived. For the static bending problem, the numerical results reveal that the deflection of the simply supported plate with or without the elastic foundation predicted by the current model is smaller than that predicted by the classical model. Also, it is observed that the difference in the deflection predicted by the new and classical plate models is very large when the plate thickness is sufficiently small, but it is diminishing with the increase of the plate thickness. For the free vibration problem, it is found that the natural frequency predicted by the new plate model with or without the elastic foundation is higher than that predicted by the classical plate model, and the difference is significant for very thin plates. These predicted trends of the size effect at the micron scale agree with those observed experimentally. In addition, it is shown both analytically and numerically that the presence of the elastic foundation reduces the plate deflection and increases the plate natural frequency, as expected. PubDate: 2015-02-21

Abstract: Abstract
This paper presents a pure complementary energy variational method for solving a general anti-plane shear problem in finite elasticity. Based on the canonical duality–triality theory developed by the author, the nonlinear/nonconvex partial differential equations for the large deformation problem are converted into an algebraic equation in dual space, which can, in principle, be solved to obtain a complete set of stress solutions. Therefore, a general analytical solution form of the deformation is obtained subjected to a compatibility condition. Applications are illustrated by examples with both convex and nonconvex stored strain energies governed by quadratic-exponential and power-law material models, respectively. Results show that the nonconvex variational problem could have multiple solutions at each material point, the complementary gap function and the triality theory can be used to identify both global and local extremal solutions, while the popular convexity conditions (including rank-one condition) provide mainly local minimal criteria and the Legendre–Hadamard condition (i.e., the so-called strong ellipticity condition) does not guarantee uniqueness of solutions. This paper demonstrates again that the pure complementary energy principle and the triality theory play important roles in finite deformation theory and nonconvex analysis. PubDate: 2015-02-21

Abstract: Abstract
It is well known that the crystallisation and melting behaviour of semicrystalline polymers depends in a pronounced manner on the temperature history. If the polymer is in the liquid state above the melting point, and the temperature is reduced to a level below the glass transition, the final degree of crystallinity, the amount of the rigid amorphous phase and the configurational state of the mobile amorphous phase strongly depend on the cooling rate. If the temperature is increased afterwards, the extents of cold crystallisation and melting are functions of the heating rate. Since crystalline and amorphous phases exhibit different densities, the specific volume depends also on the temperature history. In this article, a thermodynamically based phenomenological approach is developed which allows for the constitutive representation of these phenomena in the time domain. The degree of crystallinity and the configuration of the amorphous phase are represented by two internal state variables whose evolution equations are formulated under consideration of the second law of thermodynamics. The model for the specific Gibbs free energy takes the chemical potentials of the different phases and the mixture entropy into account. For simplification, it is assumed that the amount of the rigid amorphous phase is proportional to the degree of crystallinity. An essential outcome of the model is an equation in closed form for the equilibrium degree of crystallinity in dependence on pressure and temperature. Numerical simulations demonstrate that the process dependences of crystallisation and melting under consideration of the glass transition are represented. PubDate: 2015-02-18

Abstract: Abstract
The present paper is devoted to a model for elastic layered prismatic shells which is constructed by means of a suggested in the paper approach which essentially differs from the known approaches for constructing models of laminated structures. Using Vekua’s dimension reduction method after appropriate modifications, hierarchical models for elastic layered prismatic shells are constructed. We get coupled governing systems for the whole structure in the projection of the structure. The advantage of this model consists in the fact that we solve boundary value problems separately for each ply. In addition, beginning with the second ply, we use a solution of a boundary value problem of the preceding ply. We indicate ways of investigating boundary value problems for the governing systems. For the sake of simplicity, we consider the case of two plies, in the zeroth approximation. However, we also make remarks concerning the cases when either the number of plies is more than two or higher-order approximations (hierarchical models) should be applied. As an example, we consider a special case of deformation and solve the corresponding boundary value problem in the explicit form. PubDate: 2015-02-13

Abstract: Abstract
Gurson-type material models are based on concepts of porous materials and have been largely used to describe mechanical degradation under inelastic deformation. In addition to mechanical damage, temperature evolution is also relevant to this class of problems owing to thermal softening effects. This work addresses a finite strain thermo-elastic-plastic formulation fully coupled to the energy conservation equation and investigates the sensitivity of the mechanical response with respect to the temperature evolution based on tensile tests for small to moderate temperatures. The results indicate that the initial temperature, sensitivity of the yield stress to temperature and the heat transfer coefficient at the specimen surface play an important role on the evolution of the void fraction, stress distribution and, ultimately, the load-bearing capacity. PubDate: 2015-02-13

Abstract: Abstract
In this paper, we provide a new example of the solution of a finite deformation boundary-value problem for a residually stressed elastic body. Specifically, we analyse the problem of the combined extension, inflation and torsion of a circular cylindrical tube subject to radial and circumferential residual stresses and governed by a residual-stress dependent nonlinear elastic constitutive law. The problem is first of all formulated for a general elastic strain-energy function, and compact expressions in the form of integrals are obtained for the pressure, axial load and torsional moment required to maintain the given deformation. For two specific simple prototype strain-energy functions that include residual stress, the integrals are evaluated to give explicit closed-form expressions for the pressure, axial load and torsional moment. The dependence of these quantities on a measure of the radial strain is illustrated graphically for different values of the parameters (in dimensionless form) involved, in particular the tube thickness, the amount of torsion and the strength of the residual stress. The results for the two strain-energy functions are compared and also compared with results when there is no residual stress. PubDate: 2015-01-25

Abstract: Abstract
We propose a Bhatnagar–Gross–Krook (BGK) kinetic model in which the collision frequency is a linear combination of polynomials in the velocity variable. The coefficients of the linear combination are determined so as to enforce proper relaxation rates for a selected group of moments. The relaxation rates are obtained by a direct numerical evaluation of the full Boltzmann collision operator. The model is conservative by construction. Simulations of the problem of spatially homogeneous relaxation of hard spheres gas show improvement in accuracy of controlled moments as compared to solutions obtained by the classical BGK, ellipsoidal-statistical BGK and the Shakhov models in cases of strong deviations from continuum. PubDate: 2015-01-15

Abstract: Abstract
The intersection between the two concepts of structural control and defectiveness is discussed. Two simple oscillators differently connected by serial spring-dashpot arrangement are used to simply simulate technically relevant cases: dissipatively coupled adjacent free-standing structures, structures equipped by TMD and base-isolated structures. Eigensolution loci of the two classes of systems are tracked against one or more significant parameters to determine the potential benefits realized by different combinations of stiffness and viscosity. In both studied cases, codimension-two manifolds in the four-parameter space corresponding to coalescing eigenvalues are determined by analytical expressions. Conditions to discern semi-simple eigenvalues from defective ones confirm that the latter is the generic case laying in a two-parameter space while the former span a one-parameter subspace. The knowledge of the location of the defective systems in the parameter space permits to determine regions with specific dynamical properties useful for control design purpose. PubDate: 2015-01-14

Abstract: Abstract
This paper deals with modelling of landslide propagation. Its purpose is to present a methodology of analysis based on mathematical, constitutive and numerical modelling, which includes both well-established theories together with some improvements which are proposed herein. Concerning the mathematical model, it is based on Biot–Zienkiewicz equations, from where a depth-integrated model is developed. The main contribution here is to combine a depth-integrated description of the soil–pore fluid mixture together with a set of 1D models dealing with pore pressure evolution within the soil mass. In this way, pore pressure changes caused by vertical consolidation, changes of total stresses resulting from height variations and changes of basal surface permeability can be taken into account with more precision. Most of rheological models used in depth-integrated models are derived either heuristically (the case of Voellmy model, for instance), or from general 3D rheological models. Here, we will propose an alternative way, based on Perzyna’s viscoplasticity. The approach followed for numerical modelling is the SPH method, which we have enriched adding a 1D finite difference grid to each SPH node, in order to improve the description of pore water profiles in the avalanching soil. This paper intends to be a homage to Professor Felix Darve, who has very much contributed to the field of modern geomechanics. PubDate: 2015-01-01

Abstract: Abstract
Instability and stress–strain behavior were investigated for 2D regular assemblies of cylindrical particles. Biaxial shear experiments were performed on three sets of assemblies with regular, albeit increasingly defective structures. These experiments revealed unique instability behavior of these assemblies. Continuum models for the assemblies were then constructed using the granular micromechanics approach. In this approach, the constitutive equations governing the behavior of inter-particle contacts are written in local or microscopic level. The behavior of the RVE is then retrieved by using either kinematic constraint or least squares (static constraint) along with the principle of virtual work to equate the work done by microscopic force–displacement conjugates to that of the macroscopic stress and strain tensor conjugates. The ability of the two continuum approaches to describe the measured stress–strain behavior was evaluated. The continuum models and the local constitutive laws were used to perform instability analyses. The onset of instability and orientation of shear band was found to be well predicted by the instability analyses with the continuum models. Further, macro-scale instability was found to correlate with the instability of inter-particle contacts, although with some variations for the two modeling approaches. PubDate: 2015-01-01

Abstract: Abstract
A major scientific challenge in establishing a micromechanics theory for complex materials is the characterisation and modelling of emergent mesoscopic phenomena. This study demonstrates the key elements of a structural mechanics approach to the modelling of mesoscopic dissipative phenomena in comminution systems where grain breakage and force chain buckling coexist. Given the many degrees of freedom in these systems, there are multitude of possible configurations and configurational transitions accessible even for a small particle cluster (e.g. a particle and its immediate neighbours). Here, we develop a model of the evolution of a 6-particle cluster undergoing breakage and force chain buckling, in sequence. The analysis lays bare the intricate connections between the contact topology, the relative kinematics arising from the interactions of particles at the bonded versus non-bonded contacts, and the collective dynamics of these interactions as the cluster is monotonically compressed under confinement. The stress-displacement response profiles at the cluster scale exhibit qualitatively similar properties to those seen in macroscopic assemblies under confined compression. A parametric analysis is undertaken to explore the effects of grain-scale resistances to breakage and buckling with respect to the overall force-displacement behaviour of the granular cluster. The study casts light on open problems for future research into the micromechanics of emergent cluster behaviour germane to comminution systems. PubDate: 2015-01-01

Abstract: Abstract
The destabilization effect of damping on a class of general dynamical systems is discussed. The phenomenon of jump in the critical value of the bifurcation parameter, in passing from undamped to damped system, is view in a new perspective, according to which no discontinuities manifest themselves. By using asymptotic analysis, it is proved that all subcritically loaded undamped systems are candidate to become unstable, provided a suitable damping matrix is added. The mechanism of instability is explained by introducing the concept of modal dampings, as the components of the damping forces along the unit vectors of a non-orthogonal eigenvector basis. Such quantities can change sign while the load changes the eigenvectors of the basis, thus triggering instability. A paradigmatic, non-physical, minimal system has been built up, admitting closed-form solutions able to explain the essence of the destabilizing phenomenon. Series expansions carried out on the exact solution give information on how to deal more complex systems by perturbation methods. PubDate: 2015-01-01

Abstract: Abstract
The response of a sandy seabed under wave loading is investigated on the basis of numerical modeling using a multi-scale approach. To that aim, the discrete element method is coupled to a finite volume method specially enhanced to describe compressible fluid flow. Both solid and fluid phase mechanics are upscaled from considerations established at the pore level. Model’s predictions are validated against poroelasticity theory and discussed in comparison with experiments where a sediment analog is subjected to wave action in a flume. Special emphasis is put on the mechanisms leading the seabed to liquefy under wave-induced pressure variation on its surface. Liquefaction is observed in both dilative and compactive regimes. It is shown that the instability can be triggered for a well-identified range of hydraulic conditions. Particularly, the results confirm that the gas content, together with the permeability of the medium are key parameters affecting the transmission of pressure inside the soil. PubDate: 2015-01-01

Abstract: Abstract
This paper proposes a continuum description of the quasi-static processes of non-wetting liquid intrusion into a porous body. The description of such processes is important in the interpretation of mercury porosimetry data, which is commonly used to determine the pore space structure parameters of porous materials. A new macroscopic model of capillary transport of non-wetting liquid in porous material is proposed. It is assumed that a quasi-static process of liquid intrusion takes place in the pore space-pressure continuum and that liquid filling an undeformable porous material forms a macroscopic continuum constituted by a mobile and a capillary liquid which exchange mass and energy. The capillary liquid forms a thin layer on the surface of the liquid filling the porous material that is in contact with the internal surface of the pores. It is immoveable and contains the whole capillary energy. Mass balance equations for both constituents and constitutive relations describing capillary transport in the pore space-pressure continuum are formulated, and a boundary condition on the surface of the porous body is proposed. The equations obtained are solved for the special case of liquid intrusion into a ball of porous material. Analytical expressions are obtained for the saturation distribution of non-wetting liquid in the ball and for the capillary potential curve. Their dependence on parameters of the system is analyzed. PubDate: 2015-01-01

Abstract: Abstract
This paper gives an overview of wind-induced galloping phenomena, describing its manifold features and the many advances that have taken place in this field. Starting from a quasi-steady model of aeroelastic forces exerted by the wind on a rigid cylinder with three degree-of-freedom, two translations and a rotation in the plane of the model cross section, the fluid–structure interaction forces are described in simple terms, yet suitable with complexity of mechanical systems, both in the linear and in the nonlinear field, thus allowing investigation of a wide range of structural typologies and their dynamic behavior. The paper is driven by some key concerns. A great effort is made in underlying strengths and weaknesses of the classic quasi-steady theory as well as of the simplistic assumptions that are introduced in order to investigate such complex phenomena through simple engineering models. A second aspect, which is crucial to the authors’ approach, is to take into account and harmonize the engineering, physical and mathematical perspectives in an interdisciplinary way—something which does not happen often. The authors underline that the quasi-steady approach is an irreplaceable tool, tough approximate and simple, for performing engineering analyses; at the same time, the study of this phenomenon gives origin to numerous problems that make the application of high-level mathematical solutions particularly attractive. Finally, the paper discusses a wide range of features of the galloping theory and its practical use which deserve further attention and refinements, pointing to the great potential represented by new fields of application and advanced analysis tools. PubDate: 2015-01-01