A 3D PVP co-rotational formulation for large-displacement and small-strain analysis of bi-modulus materials

Zhang, Lunxiang; Dong, Kaijun; Zhang, H.T.; Yan, Bo

doi:10.1016/j.finel.2015.11.002

Cited by 17 publications

(4 citation statements)

References 28 publications

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“…Afterwards, the FBM is successfully applied to nonlinear elasticity problems, contact Commercial numerical software in engineering, including ABAQUS, are widely used in engineering and manufacturing. However, it is still a challenging task to solve bimodular problems efficiently [21][22][23][24][25][26]. Nevertheless, the development of new numerical methods is always attractive to solve difficult and complicated engineering problems.…”

Section: Introductionmentioning

confidence: 99%

Semi-Infinite Structure Analysis with Bimodular Materials with Infinite Element

et al. 2022

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The modulus of elasticity of some materials changes under tensile and compressive states is simulated by constructing a typical material nonlinearity in a numerical analysis in this paper. The meshless Finite Block Method (FBM) has been developed to deal with 3D semi-infinite structures in the bimodular materials in this paper. The Lagrange polynomial interpolation is utilized to construct the meshless shape function with the mapping technique to transform the irregular finite domain or semi-infinite physical solids into a normalized domain. A shear modulus strategy is developed to present the nonlinear characteristics of bimodular material. In order to verify the efficiency and accuracy of FBM, the numerical results are compared with both analytical and numerical solutions provided by Finite Element Method (FEM) in four examples.

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Section: Introductionmentioning

confidence: 99%

Semi-Infinite Structure Analysis with Bimodular Materials with Infinite Element

et al. 2022

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“…The basic hypothesis of the bimodulus theory and the basic frame of judging tension or compression by the signs of principal stresses were clarified (Ambartsumyan and Khachatryan, 1966). Subsequently, many scholars performed further research on the constitutive model, analytical solution and numerical calculation method of bimodulus theory (Khan et al, 2014;Rosakis et al, 2015;Zhang et al, 2016). Because of the inherent constitutive relation of bimodulus materials, this kind of problem presents strong nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

Creep damage model considering unilateral effect based on bimodulus theory

Guo

Liu

et al. 2021

International Journal of Damage Mechanics

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Based on the continuous damage mechanics (CDM) theory, Ambartsumyan bimodulus theory and creep damage theory, a bimodulus creep damage constitutive model is proposed in this paper. The model is able to describe the damage-induced unilateral behaviour related to the microdefect closure effect. The unilateral behaviour is considered a special bimodulus property. By judging the tension or compression state in bimodulus theory, different elasticity properties matrixes are selected according to signs of principal stresses. Then, an elasticity properties matrix is linearly converted to a general stress space. The model effectively solves the difficulty of determining tension or compression in complex stress states when the unilateral effect of damage is considered in the analysis of actual structures. The tangent elasticity matrix is used to improve the convergence of the proposed algorithm. In this study, a numerical simulation of the proposed model is achieved by writing subroutines in the FORTRAN language. A numerical example of a hole-in-plate structure under uniaxial stress is analysed. By comparing the results with those obtained by the traditional model, which does not consider the unilateral effect of damage, it is demonstrated that the proposed model is capable of describing the damage-induced unilateral behaviour related to microcracked closure effects. The numerical example validates the effectiveness and realizability of the proposed model.

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“…Examples of these materials are concrete and ceramics [1], specially under damage [2], rocks [3,4], graphite [5], nacre [6], polypropylene composites [7], asphalt-mixture materials [8], some cellular materials [9], Nitinol [10][11][12], etc. The resulting materials from 3D printing, may also show elastic tension-compression asymmetry [13].…”

Section: Introductionmentioning

confidence: 99%

“…They applied the Ambartsumyan model to these materials containing stress switches and introducing variations to improve consistency aspects in the theory; Jones by using a weighted compliance matrix and Bert by retaining a non-symmetric tangent. Indeed, an important issue in all these works is the symmetry of the constitutive matrix, so followers of the work of Ambartsumyan [26] frequently restrict the theory with the requirement (assumed implied from thermodynamic considerations) that ν − /E − = ν + /E + , where ν + and ν − are the Poisson ratios for tension and compression respectively; see for instance the recent works [1,31,35,36,39,40], among others. This leaves an "isotropic" theory restricted to only materials with three independent constants, a formulation criticised in [41] for arguably being incompatible with isotropy.…”

Section: Introductionmentioning

confidence: 99%