Hooke's Law for Plane Strain
 Hooke's Law for Plane Strain
 Formula Home Mechanics of Matl. Stress Strain Hooke's Law Orthotropic Material Transverse Isotropic Isotropic Material Plane Stress Plane Strain Finding E and n Finding G and K Applications Pressure Vessels Rosette Strain Gages Failure Criteria Calculators Stress Transform Strain Transform Principal Stress Principal Strain Elastic Constants Resources Bibliography
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 Hooke's Law for Plane Strain For the case of plane strain, where the strains in the z direction are considered to be negligible, , the stress-strain stiffness relationship for an isotropic material becomes, The three zero'd strain entries in the strain vector indicate that we can ignore their associated columns in the stiffness matrix (i.e. columns 3, 4, and 5). If we also ignore the rows associated with the stress components with z-subscripts, the stiffness matrix reduces to a simple 3x3 matrix, The compliance matrix for plane strain is found by inverting the plane strain stiffness matrix, and is given by, Note that the compliance matrix for plane strain is NOT found by removing columns and rows from the general isotropic compliance matrix.
 Plane Strain Hooke's Law via Engineering Strain The stress-strain stiffness matrix expressed using the shear modulus G and the engineering shear strain is, The compliance matrix is, The shear modulus G is related to E and n via,