Description
The nonlocal peridynamic theory has been proven extremely robust for predicting damage initiation and its propagation in materials under complex conditions. Its equations of motion do not contain any spatial derivatives of the displacement components, and thus, valid everywhere in the material. The original peridynamic equations of motion were derived in terms of the stretch between the material points, and did not address the determination of strain and stress components. This study presents a new form of the peridynamic equations of motion in terms of the classical strain components. Thus, its solution leads to the determination of the strain and stress components directly. This study also provides the exact form of the deformation gradient tensor that enables the use of the existing constitutive models in the peridynamic theory.
Recommended Citation
Madenci, E., & Oterkus, S. (2014). Peridynamics for stress and strain fields. In A. Bajaj, P. Zavattieri, M. Koslowski, & T. Siegmund (Eds.). Proceedings of the Society of Engineering Science 51st Annual Technical Meeting, October 1-3, 2014 , West Lafayette: Purdue University Libraries Scholarly Publishing Services, 2014. https://docs.lib.purdue.edu/ses2014/mss/damage/8
Peridynamics for stress and strain fields
The nonlocal peridynamic theory has been proven extremely robust for predicting damage initiation and its propagation in materials under complex conditions. Its equations of motion do not contain any spatial derivatives of the displacement components, and thus, valid everywhere in the material. The original peridynamic equations of motion were derived in terms of the stretch between the material points, and did not address the determination of strain and stress components. This study presents a new form of the peridynamic equations of motion in terms of the classical strain components. Thus, its solution leads to the determination of the strain and stress components directly. This study also provides the exact form of the deformation gradient tensor that enables the use of the existing constitutive models in the peridynamic theory.