Micromechanical analysis of hyperelastic composites with localized damage using a new low-memory Broyden-step-based algorithm
| Autor: | Nathan Perchikov, Jacob Aboudi |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Condensed Matter - Materials Science
Materials science Discretization 74-10 74Sxx Mechanical Engineering Materials Science (cond-mat.mtrl-sci) FOS: Physical sciences 02 engineering and technology Solver 01 natural sciences Homogenization (chemistry) symbols.namesake Nonlinear system 020303 mechanical engineering & transports Fourier transform 0203 mechanical engineering Finite strain theory Hyperelastic material 0103 physical sciences symbols Boundary value problem Composite material 010301 acoustics Algorithm |
| Zdroj: | Archive of Applied Mechanics. 90:47-85 |
| ISSN: | 1432-0681 0939-1533 |
| DOI: | 10.1007/s00419-019-01598-x |
| Popis: | A multiscale (micro-to-macro) analysis is proposed for the prediction of the finite strain behavior of composites with hyperelastic constituents and embedded localized damage. The composites are assumed to possess periodic microstructure and be subjected to a remote field. At the microscale, finite-strain micromechanical analysis based on the homogenization technique for the (intact) composite is employed for the prediction of the effective deformation. At the macroscale, a procedure, based on the representative cell method and the associated higher-order theory, is developed for the determination of the elastic field in the damaged composite. The periodic composite is discretized into identical cells and then reduced to the problem of a single cell by application of the discrete Fourier transform. The resulting governing equations, interfacial and boundary conditions in the Fourier transform domain, are solved by employing the higher-order theory in conjunction with an iterative procedure to treat the effects of damage and material nonlinearity. The initial conditions for the iterative solution are obtained using the weakly-nonlinear material limit and a natural fixed-point iteration. A locally-convergent low-memory Quasi-Newton solver is then employed. A new algorithm for the implementation of the solver is proposed, which allows storing in the memory directly the vector-function history-sequence, which may be advantageous for convergence-control based on specific components of the objective vector-function. The strong-form Fourier transform-based approach employed here, in conjunction with the new solver, enables to extend the application of the method to nonlinear materials and may have computational efficiency comparable or possibly advantageous to that of standard approaches. Comment: 38 pages, 28 figures |
| Databáze: | OpenAIRE |
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