Erratum to: On the Determination of a Peridynamic Constant in a Linear Constitutive Model

Abstract

This erratum concerns a correction in the expression (42) of the original article. As a consequence, the text between this expression and the expression (47) in that article was revised and is presented below.Substituting both (40.a) and (42) into (37), we find thatwhere α is the peridynamic constant that appears in (22) and is given by (34.a). Substituting (43) into (33) and using (32) together with (25) and (20), we getNext, recall from above that (25) holds and substitute α 33 , given by (43), and both α 11 and α 12 , given by (44), into the expressions (14), (15), and (16), to obtainThe online version of the original article can be found under

Determination of material properties of a linearly elastic peridynamic material

“…Both relations in equation (73), obtained from the peridynamic equation (24) together with the class of second-degree polynomial displacements given by equation (29), are the same relations reported in [9, 10], which were obtained using energy arguments together with homogeneous deformations. Thus, this class of polynomial displacements is not sufficient to determine all the four peridynamic constants.…”

“…For completeness, we present some definitions and results from [3, 9, 10] that are used throughout this work.…”

“…Aguiar [9, 10] has shown that, near the natural state, the free energy function proposed in [4] for a simple elastic peridynamic material can be approximated by…”

“…To determine the arbitrary constant mentioned before, Aguiar [9, 10] introduces a correspondence argument between the free energy function evaluated at a material point and a weighted average of the strain energy function of classical linear theory in a δ -neighborhood of this point. This approach yields a general expression for the arbitrary constant.…”

“…In Section 3, we use the peridynamic equilibrium equation without body force, together with the class of polynomial displacement fields, to obtain two relations between three peridynamic constants and the two material constants from classical linear elasticity. In Section 4, we use the correspondence argument introduced by Aguiar [9, 10] together with the pure bending experiment to find the remaining fourth peridynamic constant. We then verify that this argument is closely satisfied for the experiments of a beam bent by terminal load and a circular cylinder subject to anti-plane shear.…”