Journal
APPLIED MATHEMATICAL MODELLING
Volume 66, Issue -, Pages 41-58Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2018.09.004
Keywords
Non-linear constitution equation; Bimodular material; Composites; Meshless finite block method; Mapping technique; Differential matrix
Funding
- National Natural Science Foundation of China [51704040, 51608055]
- Construction Project of Science and Technology of Ministry of Transport of the People's Republic of China [2015318825120]
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One of the difficulties in dealing with bimodular materials including composites, rock and asphalt-mixture material is the discontinuity of Youngs modulus when the principal stress changes sign, i.e. from a tensile stress state to a compressive stress state. According to the general elastic theory proposed by Ambartsumyan, there are two kinds of domains in which the coefficients of elasticity are constant. The discontinuity of Young's modulus causes divergence in the computational procedure. In order to overcome this difficulty, two continuous modes for bimodular materials are proposed in this paper. The non-linear equilibrium equations have been formulated with a continuous constitute equation of stress and strain. The meshless finite block method is successful in solving the nonlinear problems for bimodular materials. The numerical solutions of the meshless finite block method in a strong form are obtained using an iterative technique. The degree of accuracy and convergence of the proposed technique is demonstrated by directly comparing the achieved results with the finite element method and analytical solutions. (C) 2018 Elsevier Inc. All rights reserved.
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