Determination of material constants for a linearly elastic peridynamic material
Adair Roberto Aguiar1; Alan Bourscheidt Seitenfuss1
1 University of São Paulo
doi:10.20906/CPS/CILAMCE2017-0884
Resumo
Peridynamics is a nonlocal theory that extends the classical continuum theory by considering collective motion of all the material within a $\delta$-neighborhood of any point of a peridynamic body. It considers the interaction of material points due to forces acting at a finite distance smaller than $\delta$, called the peridynamic horizon. A relation between interaction force and relative displacement between particles is proposed in Aguiar and Fosdick (2014) for an isotropic linear elastic peridynamic material. The relation is derived from a free energy function that depends quadratically on measures of strain that are analogous to the measures of strain of the classical linear theory. The energy function contains four peridynamic material constants; three of which were determined in previous work by using convergence results of the peridynamic theory to the classical linear elasticity theory and a correspondence argument between the proposed free energy function and the strain energy density function from the classical linear elasticity theory. In previous presentation we have also shown the expression for the fourth material constant, which was obtained from the correspondence argument by evaluating both the peridynamic free energy and the strain energy at a point of a peridynamic beam bent by terminal couples. In this work we show that this expression is valid regardless of the point chosen inside the beam. Also, we have considered two additional experiments to verify the validity of the expressions obtained for all the peridynamic constants. This work is of interest in all areas of continuum mechanics, such as in fracture mechanics, where surfaces of discontinuities exist, or, may appear as a result of deformation.
Palavras-chave: Nonlocal Theory; Peridynamics; Free Energy Function; Elasticity; Fracture Mechanics