Time-harmonic Green's function and boundary integral formulation for incremental nonlinear elasticity: dynamics of wave patterns and shear bands |
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Authors: | Davide Bigoni Domenico Capuani |
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Institution: | a Dipartimento di Ingegneria Meccanica e Strutturale, Università di Trento, Via Mesiano 77, 38050 Povo, Trento, Italy b Dipartimento di Architettura, Università di Ferrara, Via Quartieri 8, 44100 Ferrara, Italy |
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Abstract: | Superimposed dynamic, time-harmonic incremental deformations are considered in an elastic, orthotropic and incompressible, infinite body, subject to plane, homogeneous—but otherwise arbitrary—deformation. The dynamic, infinite body Green's function is found and, in addition, new boundary integral equations are obtained for incremental in-plane hydrostatic stress and displacements. These findings open the way to integral methods in incremental, dynamic elasticity. Moreover, the Green's function is employed as a dynamic perturbation to analyze interaction between wave propagation and shear band formation. Depending on anisotropy and pre-stress level, peculiar wave patterns emerge with focussing and shadowing effects of signals, which may remain undetected by the usual criteria based on analysis of weak discontinuity surfaces. |
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Keywords: | Dynamic Green's function Boundary integral equations Nonlinear elasticity Shear bands Boundary element method Wave propagation Pre-stressed media Anisotropy |
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