An elastic, incompressible, infinite body is considered subject to biaxial, finite and homogeneous deformation. At a certain value of the loading, when the material is still in the elliptic range, a small concentrated line load is considered acting in a point of the body and extending orthogonally to the plane of deformation. This plane strain problem is solved and, using superposition of incremental solutions, two equal and opposite line loads are considered in a region of a continuum. The solution of this problem allows us to quantify the decay rate of self-equilibrated loads in finite elasticity. In particular, it is shown that the decay rate depends crucially, say, the distance of the current state from the boundary of the elliptic regime. When this boundary is approached, the solution blows up and, at the elliptic boundary, decay does not occur.
On decay effects in nonlinear elasticity
CAPUANI, Domenico
2000
Abstract
An elastic, incompressible, infinite body is considered subject to biaxial, finite and homogeneous deformation. At a certain value of the loading, when the material is still in the elliptic range, a small concentrated line load is considered acting in a point of the body and extending orthogonally to the plane of deformation. This plane strain problem is solved and, using superposition of incremental solutions, two equal and opposite line loads are considered in a region of a continuum. The solution of this problem allows us to quantify the decay rate of self-equilibrated loads in finite elasticity. In particular, it is shown that the decay rate depends crucially, say, the distance of the current state from the boundary of the elliptic regime. When this boundary is approached, the solution blows up and, at the elliptic boundary, decay does not occur.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
