In that case, the number of non-zero stiffnesses (or compliances) is reduced to 12, all are a function of only 2 elastic constants.A material is said to be isotropic if its properties are independent of direction.The following formalism is convenient for problems in which the strains components are known and the stress components are the dependent variables: In cases where the strain components are the dependent parameters, it is more convenient to use the following formalism: Where Sijkl is a matrix whose entries are the compliance coefficients. Thanks to the symmetry of the strain tensor, the number of independent elastic constants is further reduced to 36. Thanks to the symmetry of the stress tensor, the number of independent elastic constants is reduced to 54. It thus seems that one needs 81(!) constants in order to describe the stress strain relations. Hooke’s law: In three dimensions, Hooke’s law is written as: where Cijkl is a matrix whose entries are the stiffness coefficients. The material is said to be linear elastic if n=1. Here the strain is the infinitesimal strain.For example: A visco-elastic (or Maxwell) solid: An elasto-plastic (Prandtl) material:Ī visco-plastic (or Bingham) material: A firmo-viscous (Kelvin or Voight) material: It turns out that rocks subjected to small strains (seismic waves, slip on faults, etc.) behave as linear elastic materials.Įlasticity: The one-dimensional stress-strain relationship may be written as: where C is an elastic constant.
#Define viscosity and elasticity series#
The behavior of real materials is better described by combining simple models in series or parallel. Real materials exhibit a variety of behaviors: from ic./~casey/eart150/Lectures/Rheology/13rheology.htm While elastic deformation is recoverable, viscous and plastic deformations are not. The eformation is recoverable if the material returns to its initial shape when the stress is removed. Recoverable versus permanent: Deformation is permanent if the material remains deformed when the stress is removed. Mechanical analogues Stress-Strain relations Elastic Viscous Plastic Ideal materials fall into one of the following categories: The material response to a stress is known asrheology.
Rheology Different materials deform differently under the same state of stress.
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