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<p>This paper presents the peridynamic (PD) form of the products of derivatives in functionals by employing the peridynamic differential operator (PDDO). This operator can convert the local differentiation of the products of derivatives into nonlocal integral form. Based on the variational principles, a new peridynamic model is developed without the point-wise evaluation of dilatation term in Ordinary State-Based (OSB) PD theory. For the special case of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mu = \lambda\)</EquationSource> </InlineEquation>, the new model recovers the bond-based (BB) PD theory. The capability and accuracy of this approach are demonstrated by considering the product derivatives of two functions and simulating deformation and crack propagation in a plate under different loading conditions.</p>

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Peridynamic differential operator for products of derivatives in functionals: a new peridynamic model

  • 期刊论文

  • 发表日期：

    2026年2月17日

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  • Yanan Zhang,
  • Sundaram Vinod K. Anicode,
  • Erdogan Madenci

摘要

This paper presents the peridynamic (PD) form of the products of derivatives in functionals by employing the peridynamic differential operator (PDDO). This operator can convert the local differentiation of the products of derivatives into nonlocal integral form. Based on the variational principles, a new peridynamic model is developed without the point-wise evaluation of dilatation term in Ordinary State-Based (OSB) PD theory. For the special case of \(\mu = \lambda\) , the new model recovers the bond-based (BB) PD theory. The capability and accuracy of this approach are demonstrated by considering the product derivatives of two functions and simulating deformation and crack propagation in a plate under different loading conditions.