Green's function for incremental nonlinear elasticity: shear bands and boundary integral formulation

• Published in: Journal of the mechanics and physics of solids Vol. 50; no. 3; pp. 471 - 500
• Main Authors: Bigoni, Davide, Capuani, Domenico
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.03.2002; Elsevier
• Subjects: Boundary element method; Boundary-integral methods; Computational techniques; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Green's function; Mathematical methods in physics; Nonlinear elasticity; Physics; Shear bands; Solid mechanics; Static elasticity; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Green's function; Nonlinear elasticity; Shear bands; Boundary element method; Deformation band; Constitutive equation; High strain; Numerical method; Incompressible material; Green function; Concentrated load; Perturbation method; Non linear elasticity; Non linear effect; Localization; Shear band
• ISSN: 0022-5096
• DOI: 10.1016/S0022-5096(01)00090-4

An elastic, incompressible, infinite body is considered subject to plane and homogeneous deformation. At a certain value of the loading, when the material is still in the elliptic range, an incremental concentrated line load is considered acting at an arbitrary location in the body and extending orthogonally to the plane of deformation. This plane strain problem is solved, so that a Green's function for incremental, nonlinear elastic deformation is obtained. This is used in two different ways: to quantify the decay rate of self-equilibrated loads in a homogeneously stretched elastic solid; and to give a boundary element formulation for incremental deformations superimposed upon a given homogeneous strain. The former result provides a perturbative approach to shear bands, which are shown to develop in the elliptic range, induced by self-equilibrated perturbations. The latter result lays the foundations for a rigorous approach to boundary element techniques in finite strain elasticity.