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<p>We present an ordinary state-based formulation of the equation of motion of an elastic peridynamic solid, where the response function state is derived from a free energy functional that depends nonlinearly on measures of both stretch and volume changes and contains two peridynamic coefficients. To determine these coefficients, we assume that the quadratic form of this functional near the undistorted natural state of the peridynamic material corresponds to the quadratic strain energy of the classical linear elasticity at an interior point of the peridynamic solid. Next, we consider a particular class of homogeneous peridynamic cylindrical solids and expand the displacement field asymptotically in terms of the thickness coordinate, following classical arguments of thin plate theory. We then reduce the equation of motion to a system of equations for the determination of the expansion coefficients.</p>

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An Asymptotic Thin-Plate Theory Derived from State-Based Peridynamics

  • 期刊论文

  • 发表日期：

    2025年1月30日

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  • Adair Aguiar,
  • Luc Rehm,
  • David Steigmann,
  • Michael Taylor

摘要

We present an ordinary state-based formulation of the equation of motion of an elastic peridynamic solid, where the response function state is derived from a free energy functional that depends nonlinearly on measures of both stretch and volume changes and contains two peridynamic coefficients. To determine these coefficients, we assume that the quadratic form of this functional near the undistorted natural state of the peridynamic material corresponds to the quadratic strain energy of the classical linear elasticity at an interior point of the peridynamic solid. Next, we consider a particular class of homogeneous peridynamic cylindrical solids and expand the displacement field asymptotically in terms of the thickness coordinate, following classical arguments of thin plate theory. We then reduce the equation of motion to a system of equations for the determination of the expansion coefficients.