Artur V. Dmitrenko^1,2,*, Vladislav M. Ovsyannikov²

FDMP-Fluid Dynamics & Materials Processing, Vol.20, No.9, pp. 1925-1939, 2024, DOI:10.32604/fdmp.2024.048389 - 23 August 2024

Abstract The differential equations of continuum mechanics are the basis of an uncountable variety of phenomena and technological processes in fluid-dynamics and related fields. These equations contain derivatives of the first order with respect to time. The derivation of the equations of continuum mechanics uses the limit transitions of the tendency of the volume increment and the time increment to zero. Derivatives are used to derive the wave equation. The differential wave equation is second order in time. Therefore, increments of volume and increments of time in continuum mechanics should be considered as small but finite More >

Runze Song¹, Fei Han^1,*, Yong Mei^2,*, Yunhou Sun², Ao Zhang²

CMES-Computer Modeling in Engineering & Sciences, Vol.133, No.2, pp. 389-412, 2022, DOI:10.32604/cmes.2022.021127 - 21 July 2022

Abstract This paper proposes a hybrid peridynamic and classical continuum mechanical model for the high-temperature damage and fracture analysis of concrete structures. In this model, we introduce the thermal expansion into peridynamics and then couple it with the thermoelasticity based on the Morphing method. In addition, a thermomechanical constitutive model of peridynamic bond is presented inspired by the classic Mazars model for the quasi-brittle damage evolution of concrete structures under high-temperature conditions. The validity and effectiveness of the proposed model are verified through two-dimensional numerical examples, in which the influence of temperature on the damage behavior More >

Tao Zhang, Jinglan Deng^*, Jihui Wang

CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.2, pp. 545-559, 2020, DOI:10.32604/cmes.2020.09536 - 20 July 2020

Abstract The out-of-plane fold is a common defect of composite materials during the manufacturing process and will greatly affect the compressive strength as well as the service life. Making it of great importance to investigate the influence of out-of-plane defects to the compressive strength of laminate plates of composite materials, and to understand the patterns of defect evolution. Therefore, the strip method is applied in this article to create out-of-plane defects with different aspect ratios in laminated plates of composite materials, and a compressive performance test is conducted to quantify the influence of out-of-plane defects. The… More >

Yongwei Wang¹, Fei Han^2,*, Gilles Lubineau^1,*

CMES-Computer Modeling in Engineering & Sciences, Vol.121, No.2, pp. 399-423, 2019, DOI:10.32604/cmes.2019.07192

Abstract Classical continuum mechanics which leads to a local continuum model, encounters challenges when the discontinuity appears, while peridynamics that falls into the category of nonlocal continuum mechanics suffers from a high computational cost. A hybrid model coupling classical continuum mechanics with peridynamics can avoid both disadvantages. This paper describes the hybrid model and its adaptive coupling approach which dynamically updates the coupling domains according to crack propagations for brittle materials. Then this hybrid local/nonlocal continuum model is applied to fracture simulation. Some numerical examples like a plate with a hole, Brazilian disk, notched plate and More >

R. Allena^*,†

Molecular & Cellular Biomechanics, Vol.11, No.3, pp. 185-208, 2014, DOI:10.3970/mcb.2014.011.185

Abstract Confined migration is a crucial phenomenon during embryogenesis, immune response and cancer. Here, a two-dimensional finite element model of a HeLa cell migrating across constricted–curved micro-channels is proposed. The cell is modelled as a continuum with embedded cytoplasm and nucleus, which are described by standard Maxwell viscoelastic models. The decomposition of the deformation gradient is employed to define the cyclic active strains of protrusion and contraction, which are synchronized with the adhesion forces between the cell and the substrate. The micro-channels are represented by two rigid walls and exert an additional viscous force on the… More >

Anna Y. Matveeva¹, Helmut J. Böhm², Grygoriy Kravchenko², Ferrie W. J. van Hattum¹

CMC-Computers, Materials & Continua, Vol.42, No.1, pp. 1-23, 2014, DOI:10.3970/cmc.2014.042.001

Abstract This paper presents a comparison of different finite element approaches to modelling polymers reinforced with wavy, hollow fibres with the aim of predicting the effective elastic stiffness tensors of the composites. The waviness of the tubes is described by sinusoidal models with different amplitude-to-wavelength parameters. These volume elements are discretized by structured volume meshes onto which fibres in the form of independently meshed beam, shell or volume elements are superimposed. An embedded element technique is used to link the two sets of meshes. Reference solutions are obtained from conventional three-dimensional volume models of the same More >

C.J. Huang¹, T.Y. Hung¹, K.N. Chiang²

CMC-Computers, Materials & Continua, Vol.36, No.2, pp. 99-133, 2013, DOI:10.3970/cmc.2013.036.099

Abstract The development in the field of nanotechnology has prompted numerous researchers to develop various simulation methods for determining the material properties of nanoscale structures. However, these methods are restricted by the speed limitation of the central processing unit (CPU), which cannot estimate larger-scale nanoscale models within an acceptable time. Thus, decreasing the CPU processing time and retaining the estimation accuracy of physical properties of nanoscale structures have become critical issues. Accordingly, this study aims to decrease the CPU processing time and complexity of large nanoscale models by utilizing, atomistic-continuum mechanics (ACM) to build an equivalent… More >

Lutz Nasdala¹ , Andreas Kempe¹ and Raimund Rolfes¹

CMC-Computers, Materials & Continua, Vol.19, No.1, pp. 57-104, 2010, DOI:10.3970/cmc.2010.019.057

Abstract In order to understand the underlying mechanisms of inelastic material behavior and nonlinear surface interactions, which can be observed on macroscale as damping, softening, fracture, delamination, frictional contact etc., it is necessary to examine the molecular scale. Force fields can be applied to simulate the rearrangement of chemical and physical bonds. However, a simulation of the atomic interactions is very costly so that classical molecular dynamics (MD) is restricted to structures containing a low number of atoms such as carbon nanotubes. The objective of this paper is to show how MD simulations can be integrated… More >

K. Y. Volokh ^{1, 2} , Y. Lev³

Molecular & Cellular Biomechanics, Vol.2, No.1, pp. 27-40, 2005, DOI:10.3970/mcb.2005.002.027

Abstract A simple phenomenological theory of tissue growth is used in order to demonstrate that volumetric growth combined with material anisotropy can lead to accumulation of residual stresses in arteries. The theory is applied to growth of a cylindrical blood vessel with the anisotropy moduli derived from experiments. It is shown that bending resultants are developed in the ring cross-section of the artery. These resultants may cause the ring opening or closing after cutting the artery \textit {in vitro} as it is observed in experiments. It is emphasized that the mode of the arterial ring opening More >

Shengping Shen¹, S. N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.1, pp. 49-68, 2005, DOI:10.3970/cmes.2005.007.049

Abstract The main objective of this paper is to develop a multiscale method for the static analysis of a nano-system, based on a combination of molecular mechanics and MLPG methods. The tangent-stiffness formulations are given for this multiscale method, as well as a pure molecular mechanics method. This method is also shown to naturally link the continuum local balance equation with molecular mechanics, directly, based on the stress or force. Numerical results show that this multiscale method quite accurate. The tangent-stiffness MLPG method is very effective and stable in multiscale simulations. This multiscale method dramatically reduces More >