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Abstract: A Correction to this paper has been published: 10.1007/s00161-022-01098-4 PubDate: 2022-05-19
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Abstract: Abstract In this paper, interlaminar stresses in a symmetrical laminated composite plate with a circular hole under uniform heat flux were examined. The analytical solution was achieved based on the boundary-layer theory by Lekhnitskii’s solution. The stress relations related out-of-plane stress components were obtained by variational principle states, the minimum principle of complementary energy, zero-order equilibrium relations and boundary conditions for each layer. The unknown factors in the stress relations were obtained by the equilibrium equation in integral form. This solution prepared a calculation method via adaptability for examining the 3D thermal stresses in perforated laminated with curved boundaries. The results were obtained for \([45/-45]\) s, [0/90]s, \([30/-30]\) s lay-ups made of graphite/epoxy and glass/epoxy materials. PubDate: 2022-05-14
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Abstract: Abstract The article considers an approach for multiscale geomechanical modeling under finite strains. A mathematical model, methods and algorithms for the multiscale numerical estimation of the effective elastic and thermal properties of the preloaded heterogeneous porous materials under finite strains are presented. The developed algorithms were applied to the problem of the estimation of the effective properties of core samples. The digital models obtained from computed tomography scan data of core samples are used. An initial voxel representation of the digital core sample is transformed into an unstructured mesh, thus reducing the number of unknowns by orders of magnitude and requiring computational resources accordingly. The mesh convergence tests demonstrated the efficiency and correctness of the developed algorithms. The calculations of the effective elastic and thermal properties of preloaded porous materials are performed with CAE Fidesys using finite element method. The numerical results demonstrate the significant impact of pre-loading by internal pressure on the effective properties of porous materials. PubDate: 2022-05-12
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Abstract: Abstract We propose, for the first time, a thermodynamically consistent formulation for open system (continuum-kinematics-inspired) peridynamics. In contrast to closed system mechanics, in open system mechanics mass can no longer be considered a conservative property. In this contribution, we enhance the balance of mass by a (nonlocal) mass source. To elaborate a thermodynamically consistent formulation, the balances of momentum, energy and entropy need to be reconsidered as they are influenced by the additional mass source. Due to the nonlocal continuum formulation, we distinguish between local and nonlocal balance equations. We obtain the dissipation inequality via a Legendre transformation and derive the structure and constraints of the constitutive expressions based on the Coleman–Noll procedure. For the sake of demonstration, we present an example for a nonlocal mass source that can model the complex process of bone remodelling in peridynamics. In addition, we provide a numerical example to highlight the influence of nonlocality on the material density evolution. PubDate: 2022-05-10
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Abstract: Abstract This paper presents a semi-analytic rigid/plastic solution for the expansion/contraction of a hollow sphere at large strains. The yield stress depends on the equivalent strain rate and the equivalent strain. No restriction is imposed on this dependence. The solution reduces to a single ordinary differential equation for determining the radial stress. The independent variable in this equation is the equivalent strain. Moreover, the equivalent strain rate is expressed in terms of elementary functions of the equivalent strain, which allows for representing the yield stress as a function of the equivalent strain and a time-like independent variable. In the course of deriving the equations above, the transformation between Eulerian and Lagrangian coordinates is used. A numerical example illustrates the solution for a material model available in the literature. The motivation of this research is that solutions for the expansion/contraction of a hollow sphere are widely used at the micro-level to calculate some material properties at the macro-level. To this end, it is necessary to specify constitutive equations for micromechanical modeling. The accuracy of these equations is questionable. An advantage of the solution found is that it is practically analytic for quite a general material model that accounts for both strain- and rate-hardening. Therefore, it is straightforward to generate a large amount of theoretical data for comparing with measurable quantities at the macro-level. PubDate: 2022-05-05
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Abstract: Abstract After the wide premise of Part I, where the equations for Cauchy’s continuum were retrieved through the energy minimization and some differential geometric perspectives were specified, the present paper as Part II outlines the variational derivation of the equilibrium equations for second gradient materials and their transformation from the Eulerian to the Lagrangian form. Volume, face and edge contributions to the inner virtual work were provided through integration by parts and by repeated applications of the divergence theorem extended to curved surfaces with border. To sustain double forces over the faces and line forces along the edges, the role of the third rank hyperstress tensor was highlighted. Special attention was devoted to the edge work, and to the evaluation of the variables discontinuous across the edge belonging to the contiguous boundary faces. The detailed expression of the contact pressures was provided, including multiple products of normal vector components, their gradient and a combination of them: in particular, the dependence on the local mean curvature was shown. The transport of the governing equations from the Eulerian to the Lagrangian configuration was developed according to two diverse strategies, exploiting novel differential geometric formulae and revealing a coupling of terms transversely to the involved domains. PubDate: 2022-05-03
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Abstract: Abstract Some errors exist in the above paper. PubDate: 2022-05-01
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Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract Toward directly simulating pseudo-elastic effects of shape memory alloys, new elastoplastic equations of von Mises type are proposed by correlating the yield surface radius with the yield surface center, thus establishing a new elastoplasticity model characterized by three coupled quantities for isotropic and anisotropic hardening. Within the framework of conventional macroscopic elastoplasticity, it is demonstrated that the new model can exactly reproduce pseudo-elastic hysteresis effects of shape memory alloys, with no need to characterize any microstructural features of solid–solid phase transitions. To this end, explicit expressions for the three hardening quantities introduced are presented in terms of two single-variable functions. Then, exact closed-form solutions are obtained for the uniaxial stress–strain responses in a loading and a subsequent unloading process, and such responses are shown to give rise to a hysteresis loop shaped just by the foregoing two single-variable functions. As such, hysteresis loops of arbitrary shapes can be simulated in a straightforward and accurate manner simply prescribing two single-variable functions shaping such loops. For the first time, cumbersome and time-consuming procedures both for conducting statistical averaging schemes and for identifying numerous unknown parameters may be bypassed with broad applicability. PubDate: 2022-05-01
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Abstract: Abstract A modified form of BGK source terms is proposed for modeling two-phase flows with thermodynamical disequilibrium. The novelty is that three independent time-scales allow to manage the return to the thermodynamical equilibrium while remaining in agreement with the second law of thermodynamics. This is achieved thanks to the definition of a “local-in-time” equilibrium state which tends toward the asymptotic equilibrium state when time increases. The thermodynamical paths of the system are then modified with respect to the classical BGK source terms used for two-phase flow modeling, and the relaxation process of the system toward the asymptotic equilibrium state can be defined with additional degrees of freedom. In a numerical point of view, both the classical and the modified BGK source terms have advantages. The choice between these two forms strongly depends on the numerical strategy used to perform simulations. PubDate: 2022-05-01
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Abstract: Abstract The thermodynamic theory of dislocation/grain boundary interaction, including dislocation pileup against, absorption by, and transfer through the grain boundary, is developed for non-uniform plastic deformations in polycrystals. The case study is carried out on the boundary conditions affecting work hardening of a bicrystal subjected to plane constrained shear for three types of grain boundaries: (i) impermeable hard grain boundary, (ii) grain boundary that allows dislocation transfer without absorption, and (iii) grain boundary that absorbs dislocations and allows them to pass later. PubDate: 2022-05-01
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Abstract: In the original publication of the article, a typo error has been introduced in the appendix section PubDate: 2022-04-19
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Abstract: Abstract The present work is devoted to a study of the generalized poro-thermoelasticity theory and aims to derive the variational principle and continuous dependence results in the context of this theory. The basic field equations are considered for an isotropic and homogeneous fluid-saturated poro-thermoelastic medium. With the concept of incorporating initial conditions into the field equations, an alternative characterization of the present mixed initial-boundary value problem is presented. By taking into account of this alternative characterization, a convolution type variational principle is derived in the context of this generalized poro-thermoelasticity theory. Further, a continuous dependence result of solution on initial data and external supply terms (heat source and body force) is established. Uniqueness of solution of the present problem is also shown to be followed from this result. PubDate: 2022-04-19
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Abstract: Abstract The paper aims to study, using the finite element method, the elastic behavior of a cylinder made by a material with micropolar structure, containing (as the results of the processing or introduced intentionally) voids. To study such a type of problem, a theoretical model of a continuous solid body with voids in the material is presented, after which, in order to determine the effect that these voids have, a model with finite elements is made, using Lagrange’s equations. This model can be applied to any type of elastic solid with voids. In the paper study the elastic response of a hollow cylinder made by a material with voids. Finally, comparative results are obtained to show the influence of voids on the elastic behavior of the body in some classic cases. These results are compared with the values obtained in the literature by experimental methods. It is found that a small percentage of voids can lead to significant variations on the mechanical properties. PubDate: 2022-04-11
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Abstract: Abstract The main laws of the processes of creep and long-term strength of polycrystalline structural alloys are considered. From the viewpoint of continuum damaged media (CDM), a mathematical model is developed that describes the processes of viscoplastic deformation and damage accumulation under creep. The problem of determining material parameters and scalar functions of the developed constitutive relations based on the results of specially set basic experiments is discussed. An experimental–theoretical methodology for determining material parameters of the derived constitutive relations of CDM is developed based on analyzing the viscoplastic deformation and failure processes of laboratory specimens in the conditions of soft loading (stress controlled). Experimental results of short-term creep of the VZh-159 heat-resistant alloy are presented. The obtained numerical results are compared with the test data using the numerical modeling method of experimental processes. Qualitative and quantitative agreement between numerical results and experimental data is shown. It is concluded that the developed constitutive relations are reliable, and that the proposed methodology accurately determines the material parameters of the model under degradation of initial strength properties of structural materials according to the long-term strength mechanism. PubDate: 2022-04-09
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Abstract: Abstract In material modeling, when dealing with diffusion at large deformations, there are usually two different variants for the diffusion flux: an isotropic law in the current placement and an isotropic law in the reference placement. The first one causes diffusion behavior, which is independent from the initial shape of the body, i.e., it causes a deformation-independent behavior. The second one relates the diffusion solely to the initial shape of the body, which results in a deformation-dependent behavior in the current state. In most of the works in the literature, one of these two possible formulations is chosen arbitrarily. While the modern description of diffusion at large deformations mostly evolved in the last two decades, to our best knowledge, there are no works which discuss or motivate the choice for one of these two versions really in detail. In the present article, we approach the motivation for the choice of the two different types of diffusion flux formulations. We illustrate their characteristics and discuss their application under different circumstances. It is important to note that the deformation dependency which arises from choosing the isotropic reference placement formulation is quite specific and strongly differs from the actual behavior of many materials. We investigate such a case with a more individual deformation dependency based on a very simple artificial microstructure. We determine the properties on the macroscale using representative volume elements within numerical homogenization. PubDate: 2022-03-22
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Abstract: Abstract In this study, the time-dependent mechanics of multilayered thick hyperelastic beams are investigated for the first time using five different types of shear deformation models for modelling the beam (i.e. the Euler–Bernoulli, Timoshenko, third-order, trigonometric and exponential shear deformable models), together with the von Kármán geometrical nonlinearity and Mooney–Rivlin hyperelastic strain energy density. The laminated hyperelastic beam is assumed to be resting on a nonlinear foundation and undergoing a time-dependent external force. The coupled highly nonlinear hyperelastic equations of motion are obtained by considering the longitudinal, transverse and rotation motions and are solved using a dynamic equilibrium technique. Both the linear and nonlinear time-dependent mechanics of the structure are analysed for clamped–clamped and pinned–pinned boundaries, and the impact of considering the shear effect using different shear deformation theories is discussed in detail. The influence of layering, each layer’s thickness, hyperelastic material positioning and many other parameters on the nonlinear frequency response is analysed, and it is shown that the resonance position, maximum amplitude, coupled motion and natural frequencies vary significantly for various hyperelastic and layer properties. The results of this study should be useful when studying layered soft structures, such as multilayer plastic packaging and laminated tubes, as well as modelling layered soft tissues. PubDate: 2022-03-09 DOI: 10.1007/s00161-022-01090-y
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