A Finite Element Formulation for No-Tension Materials in Finite Deformations

In the paper it is presented a non linear finite element formulation for unilateral materials in the field of finite deformations. This kind of materials are not able to sustain any compressive (resp. tensile) stress and represent a special case of anelastic materials, whose irreversible deformations is ruled by a potential. Particularly it has been developed a constitutive model for no tension materials on the basis of a multiplicative split of the gradient of deformation tensor in an elastic and anelastic part introducing an intermediate (stress free) configuration and assuming that no dissipations occurs in the anelastic process. It is proved that the symmetric part of the gradient of velocity tensor can be additively decomposed in an elastic and an anelastic component that yield the elastic and anelastic mechanical power provided that a properly defined covariant velocity of deformation tensor is used. The model is implemented in a standard isoparametric finite elements model using a linearisation of the time derivative of the right Cauchy-Green tensor, of the velocity of deformation tensors and of the Lie derivative of the Kirchhoff stress tensor. Explicit expressions for the components of the material and geometric tangent stiffness matrices and for the equivalent internal nodal forces are furnished.