Showing papers on "Continuum mechanics published in 2021"

State-of-the-Art Review on the Progressive Failure Characteristics of Geomaterials in Peridynamic Theory

Abstract: Peridynamic (PD) theory is an integral-type nonlocal continuum mechanics theory that reformulates the equation of motion in local continuum mechanics as an integrodifferential equation. PD ...

Bond-Based Peridynamics with Stretch and Rotation Kinematics for Opening and Shearing Modes of Fracture

Abstract: This study presents a new bond-based peridynamic approach for modeling the elastic deformation of isotropic materials with bond stretch and rotation, thus removing the constraint on the Poisson’s ratio The resulting PD equilibrium equations derived under the assumption of small deformation are solved by employing implicit techniques The bond constants associated with stretch and rotation kinematic are directly related to the constitutive relations of stress and strain components in continuum mechanics Also, the expressions for the critical stretch and critical relative rotation are derived in terms of mode I and mode II critical energy release rates, respectively Lastly, it does not require a surface correction procedure, and the displacement and traction type boundary conditions are directly imposed without introducing fictitious regions in the domain The capability of this approach is first demonstrated by capturing the correct deformation of plate type structures under general loading conditions Subsequently, its capability for failure prediction is established by simulating the response of a double cantilever beam (DCB) under mode I type loading and compact shear specimen under mode II type loading

Microstructural-dependent nonlinear stability analysis of random checkerboard reinforced composite micropanels via moving Kriging meshfree approach

Abstract: In the present study, through matching the moving Kriging meshfree formulations with the third-order shear flexible shell model together with the modified strain gradient continuum mechanics, the microstructural-dependent nonlinear stability behavior of micropanels under axial compression is explored. The micropanels are made of composites containing graphene nanoplatelets dispersed in random checkerboard pattern. The associated material characteristics are evaluated via a probabilistic-based homogenization scheme. Afterward, proper meshfree functions are implemented to enforce the essential boundary conditions at the considered nodding system accurately. It is highlighted that the stiffening characters of the microstructural gradient tensors cause to rise the critical stability load as well as the critical shortening of composite micropanels. Also, these stiffening characters make an enhancement in the minimum snap-through postbuckling compression, and shift it to lower values of the panel deflection and end shortening. Additionally, it is demonstrated that among different microstructural gradient tensors, the stiffening character of rotation gradient is more than deviatoric stretch gradient, the stiffening character of the later is more significant than the dilatation gradient tensor.

Modeling of electro–viscoelastic dielectric elastomer: A continuum mechanics approach

Abstract: The present study deals with the rheological behavior modeling of a dielectric elastomeric (DE) material class. The DE materials are commonly used to develop soft actuators and energy harvesters in soft robotics. DE is a class of electroactive polymers that produces large strains with an electrically induced load application. In this article, a micro mechanics-based thermodynamically consistent rheological model is derived to capture the electro–viscoelastic behavior of the DE material class. A multiplicative deformation gradient decomposition into elastic and viscous parts is incorporated to attain a transitional configuration. The decomposition is being used for setting up the constitutive evolution equations for an electro–viscoelastic deformation. The derived rheological model agrees well with existing experimental results. We succeed here to enable the effect of viscosity and electric field on the deformation simultaneously with a micro mechanics-based analytical finding with the least possible material parameters.

Variable-order approach to nonlocal elasticity: theoretical formulation, order identification via deep learning, and applications

Abstract: This study presents the formulation of the variable-order continuum mechanics theory and its application to the analysis of nonlocal heterogeneous solids. The variable-order continuum theory enables a unique approach to model the response of solids exhibiting position-dependent nonlocal behavior. The formulation also guarantees frame-invariance provided that proper constraints on the functional definition of the variable-order are imposed. The study also presents a deep learning approach to identify the variable-order distribution describing the behavior of the medium. This methodology presents a very promising route for the practical application of the variable-order theory to real-world problems, especially when the microstructure is not known a priori and must be inferred from the physical response of the medium. The capabilities of the variable-order theory are illustrated by numerically simulating the static response of nonlocal beams having either a porous or a functionally graded core. The reduced-order variable fractional model shows excellent accuracy and significant computational efficiency when compared with a reference solution produced by a 3D finite element model that fully resolves the beam geometry.

Correction to: Isogeometric small-scale-dependent nonlinear oscillations of quasi-3D FG inhomogeneous arbitrary-shaped microplates with variable thickness

Abstract: The current investigation deals with proposing a numerical analysis for the geometrically nonlinear large-amplitude vibrations of arbitrary-shaped microplates having variable thickness with various patterns in the presence of couple stress type of microstructural size dependency. To accomplish this purpose, the isogeometric analysis (IGA) is employed to achieve exact geometrical description as well as higher-order efficient smoothness with no meshing difficulty. On the other hand, the modified couple stress continuum mechanics is applied to a refined quasi-3D plate model having the capability to take the thickness stretching into consideration with only four variables. The microplates are assumed made of functionally graded (FG) composites, the material properties of which are changed continuously through the variable thickness. The variation of microplate thickness obeys three different schemes including linear, concave, and convex ones. It is highlighted that by changing the pattern of the thickness variation from convex type to linear one, and then from linear type to concave one, the both classical and couple stress continuum-based nonlinear frequency of the microplates having different shapes increases due to a higher value of the average plat thickness. On the other hand, by considering this change in the thickness variation pattern, it is seen that the significance of the couple stress size effect increases. For this reason, the significance of the stiffening scheme associated with the gradient of rotation gets lower through increment of the material gradient index of a FG composite microplate.

Fluid-solid interaction in the rate-dependent failure of brain tissue and biomimicking gels.

Abstract: Brain tissue is a heterogeneous material, constituted by a soft matrix filled with cerebrospinal fluid. The interactions between, and the complexity of each of these components are responsible for the non-linear rate-dependent behaviour that characterises what is one of the most complex tissue in nature. Here, we investigate the influence of the cutting rate on the fracture properties of brain, through wire cutting experiments. We also present a computational model for the rate-dependent behaviour of fracture propagation in soft materials, which comprises the effects of fluid interaction through a poro-hyperelastic formulation. The method is developed in the framework of finite strain continuum mechanics, implemented in a commercial finite element code, and applied to the case of an edge-crack remotely loaded by a controlled displacement. Experimental and numerical results both show a toughening effect with increasing rates, which is linked to the energy dissipated by the fluid–solid interactions in the region surrounding the crack tip.

Out-of-Plane Deformations Determined Mechanics of Vanadium Disulfide (VS2) Sheets.

Abstract: The rapid development of two-dimensional (2D) materials has significantly broadened the scope of 2D science in both fundamental scientific interests and emerging technological applications, wherein the mechanical properties play an indispensably key role. Nevertheless, particularly challenging is the ultrathin nature of 2D materials that makes their manipulations and characterizations considerably difficult. Herein, thanks to the excellent flexibility of vanadium disulfide (VS2) sheets, their susceptibility to out-of-plane deformation is exploited to realize the controllable loading and enable the accurate measurements of mechanical properties. In particular, the Young's modulus is estimated to be 44.4 ± 3.5 GPa, approaching the lower limit for 2D transition metal dichalcogenides (TMDs). We further report the first measurement of thickness-dependent bending rigidity of VS2, which deviates from the prediction of the classical continuum mechanics theory. Additionally, a deeper understanding of the mechanics within two dimensions also facilitates the modulation of strain-coupled physics at the nanoscale. Our Raman measurements showed the Gruneisen parameters for VS2 were determined for the first time to be γE2g1 ≈ 0.83 and γA1g ≈ 0.32.

Dynamic analysis of FG nanobeam reinforced by carbon nanotubes and resting on elastic foundation under moving load

Abstract: In the context of nonclassical continuum mechanics, the nonlocal strain gradient theory is employed to develop a nonclassical size dependent model to investigate the dynamic behavior of a CNTs rein...

A dynamic hybrid local/nonlocal continuum model for wave propagation

Abstract: In this work, we develop a dynamic hybrid local/nonlocal continuum model to study wave propagations in a linear elastic solid. The developed hybrid model couples, in the dynamic regime, a classical continuum mechanics model with a bond-based peridynamic model using the Morphing coupling method that introduced in a previous study (Lubineau et al., J Mech Phys Solids 60(6):1088–1102, 2012). The classical continuum mechanical model is known as a local continuum model, while the peridynamic model is known as a nonlocal continuum model. This dynamic hybrid model aims to introduce the nonlocal model into the key structural domain, in which the dispersions or crack nucleations may occur due to flaws, while applying the local model to the rest of the structural domain. Both the local and nonlocal continuum domains are overlapped in the coupled subdomain. We study the speeds and angular frequencies of the plane waves, with small and large wavenumbers obtained by the hybrid model and compare them to purely local and purely nonlocal solutions. The error of the hybrid model is discussed by analyzing the ghost forces, and the work done by the ghost forces is considered equivalent to the energy of spurious reflections. One- and two-dimensional numerical examples illustrate the validity and accuracy of the proposed approach. We show that this dynamic hybrid local/nonlocal continuum model can be successfully applied to simulate wave propagations and crack nucleations induced by waves.

Dynamics of Stress-Driven Two-Phase Elastic Beams.

Abstract: The dynamic behaviour of micro- and nano-beams is investigated by the nonlocal continuum mechanics, a computationally convenient approach with respect to atomistic strategies. Specifically, size effects are modelled by expressing elastic curvatures in terms of the integral mixture of stress-driven local and nonlocal phases, which leads to well-posed structural problems. Relevant nonlocal equations of the motion of slender beams are formulated and integrated by an analytical approach. The presented strategy is applied to simple case-problems of nanotechnological interest. Validation of the proposed nonlocal methodology is provided by comparing natural frequencies with the ones obtained by the classical strain gradient model of elasticity. The obtained outcomes can be useful for the design and optimisation of micro- and nano-electro-mechanical systems (M/NEMS).

Multiscale thermodynamics of charged mixtures

Abstract: A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization, and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely geometric way by means of semidirect products. This leads to a complex Hamiltonian system with a new Poisson bracket, which can be used in principle with any energy functional. The thermodynamic (irreversible) part is added as gradient dynamics, generated by derivatives of a dissipation potential, which makes the theory part of the GENERIC framework. Subsequently, Dynamic MaxEnt reductions are carried out, which lead to reduced GENERIC models for smaller sets of state variables. Eventually, standard engineering models are recovered as the low-level limits of the detailed theory. The theory is then compared to recent literature.

Continuum Mechanics Modeling of Complex Fluid Systems Following Oldroyd's Seminal 1950 Work

Abstract: We present a review of some key developments in the continuum mechanics – based macroscopic modeling of complex fluid flows, following the pioneering work of Oldroyd in the 1950s. We start by reviewing the major developments achieved by Oldroyd, namely how his work established rules for consistency in developing continuum stress constitutive models extending the material into objective time derivatives for tensor quantities, with first application the stress tensor in viscoelastic constitutive relationships. We then show how the impact of his work to viscoelastic fluid flows has been amplified from the kinetic theory work of Bird and others who established a firm macromolecular structural connection. The use of objective time derivatives was then extended to include second order conformation tensors and through them the connection was made to internal deformation energy by Marrucci. We then further demonstrate the impact of this work by analyzing the models through the microstructural descriptions offered within the non-equilibrium thermodynamics formalism. We then conclude with a brief mentioning of direct applications of the original Oldroyd-B model (through stability analyses, etc.) towards bettering our understanding of the rheological behavior of complex fluid systems.