On the Determination of a Peridynamic Constant in a Linear Constitutive Model
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This work is an extension of previous investigation concerning a free energy function for an isotropic, linearly elastic peridynamic material that depends quadratically on infinitesimal normal and shear strain states. The free energy function contains four peridynamic material constants, from which three constants are related to the classical elasticity coefficients of an isotropic linear elastic material, with one of the three constants being arbitrary. To determine this arbitrary constant, the difference displacement quotient state at a point is decomposed in terms of radial and non-radial components. If the radial component is zero, the quadratic free energy function reduces to an integral expression that multiplies the arbitrary constant. This result together with a correspondence argument is used next to find a general expression for this constant. A simple experiment in mechanics is then used to evaluate this constant in terms of the classical shear modulus and the horizon \(\delta\). The correspondence argument can also be used to find a general expression for the fourth peridynamic constant that appears in the quadratic free energy function.
KeywordsPeridynamic model Nonlocal theory Classical linear elasticity Constitutive modeling Free energy function
Mathematics Subject Classification (2010)74A20 74B05
The author acknowledges the financial support provided by CNPq (The National Council for Scientific and Technological Development), grants # 444896/2014-7 and # 301806/2013-6, and the infrastructure provided by the University of Minnesota Supercomputing Institute.