A consistent finite element formulation for laminated composites with nonlinear interlaminar constitutive law

2020 ◽  
Vol 247 ◽  
pp. 112445
Author(s):  
Damjan Lolić ◽  
Dejan Zupan ◽  
Miha Brojan
Keyword(s):  
Finite Element ◽  
Laminated Composites ◽  
Constitutive Law ◽  
Finite Element Formulation ◽  
Element Formulation

Solutions of the Right Classes for Laminated Composites Satisfying Interlamina Physics

2001 ◽  
Author(s):  
K. S. Surana ◽  
H. Ngyun
Keyword(s):  
Finite Element ◽  
Material Properties ◽  
Laminated Composites ◽  
Dissimilar Materials ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Computational Framework ◽  
Mixed Formulations ◽  
The Right ◽  
Mesh Refinements

Abstract This paper presents a new theoretical and computational framework for computing solutions of right classes for laminated composites using 2D p-version least squares finite element formulation incorporating the correct physics of interlamina behavior. At the interface between two laminas of dissimilar materials we have continuity of displacements u, v, stresses σyy, τxy, and strain εxx, while the stress σxx and the strains εyy and γxy are discontinuous. Thus, a finite element formulation, incorporating the physics of laminate behavior, would require interpolation of u, v, εxx, σyy and τxy instead of u, v, σxx, σyy and τxy which is generally the case in most mixed formulations. In the p-version LSFEF presented here, we interpolate u, v and σyy, τxy (εxx = ∂u/∂x is used to eliminate εxx as a variable) using appropriate p-version interpolations which would ensure correct interlamina behavior of these components. When the mating lamina properties are different, interlamina discontinuity of σxx, εyy and γxy is automatically generated due to dissimilar material properties of the laminas. In this formulation interlamina jumps in σxx, εyy and γxy do not constitute singularities, hence mesh refinements and higher p-levels are not needed in the vicinity of inter-lamina boundaries. The major thrust of this paper is to construct interpolations for the dependant variables that are of right classes in appropriate spaces so that a sequence of converged solutions in these spaces may be computed which, when converged, would yield a numerical solution that has exactly the same characteristics (in terms of continuity and differentiability) as the analytical or theoretical (strong) solution.

Dynamics of Thick Viscoelastic Beams

1997 ◽  
Vol 119 (3) ◽  
pp. 273-278 ◽  
Author(s):  
A. R. Johnson ◽  
A. Tessler ◽  
M. Dambach
Keyword(s):  
Finite Element ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Constitutive Law ◽  
Finite Element Formulation ◽  
Internal Variables ◽  
Element Formulation ◽  
Modal Interactions ◽  
Cantilevered Beam ◽  
Thick Beam

A viscoelastic higher-order thick beam finite element formulation is extended to include elastodynamic deformations. The material constitutive law is a special differential form of the Maxwell solid, which employs viscous strains as internal variables to determine the viscous stresses. The total time-dependent stress is the superposition of its elastic and viscous components. In the constitutive model, the elastic strains and the conjugate viscous strains are coupled through a system of first-order ordinary differential equations. The use of the internal strain variables allows for a convenient finite element formulation. The elastodynamic equations of motion are derived from the virtual work principle. Computational examples are carried out for a thick orthotropic cantilevered beam. Relaxation, creep, relaxation followed by free damped vibrations, and damping related modal interactions are discussed.

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