Application to elasticity
The historical application of the Virtual Fields Method was elasticity. In this case, it can be shown that what is usually considered as an inverse problem
can be solved directly.
The method relies on the principle of virtual work. The following slideshow illustrates how this principle can be used to derive specific
equilibrium equations.
The principle of virtual work
Principle of the method in the case of linear elasticity
The following slideshow describes the application of the VFM in the case of elasticity.
The VFM in linear elasticity
Principle of the method in the case of non-linear elasticity
Another very simple situation concerns non-linear elasticity, particularly when the stress can be expressed as a polynomial function of the strain. It is the
case for a composite non-linear in-plane shear behaviour with a softening terms expressed as a cubic function of the shear strain, as illustrated in the
following slideshow.
The VFM in non-linear elasticity: an example
References
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Direct identification of the damage behaviour of composite materials using the virtual fields method,
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Identification of the through-thickness rigidities of a thick laminated composite tube,
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Experimental identification of a nonlinear model for composites using the grid technique coupled to the virtual fields method,
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Strain: an International Journal for Experimental Mechanics, vol. 43, n° 3, pp. 250-259, 2007.
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plates by modal analysis: experiments and results, Journal of Sound and Vibration, vol. 210, pp. 645–659, 1998.
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Direct measurement of invariant parameters of composite plates,
Journal of Composite Materials, vol. 33, pp. 1939–1965, 1999.
- Xavier J., Avril S., Pierron F., Morais J.L.
Novel experimental approach for the characterisation of the LR stiffness parameters of clear wood using a single specimen
Holzforschung, vol. 61, pp. 573-581, 2007.