Learning goal: to use the stress-strain relationships for triaxial stress to calculate unknown values. a material is homogenous and isotropic when it has a modulus of elasticity that does not vary with direction and it has uniform properties throughout. when a point in a material is subjected to only normal stresses in three dimensions, but they are not necessarily equal, the state is called triaxial stress. when the response of the material is linear elastic, the strains along the three axes can be calculated using a generalized form of hooke's law. each strain depends on all three stresses because of the poisson effect. ϵx=1e[σx−ν(σy+σz)] ϵy=1e[σy−ν(σx+σz)] ϵz=1e[σz−ν(σx+σy)] the change in volume per unit volume, or dilatation, is e=1−2νe(σx+σy+σz)