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مکانیک::
تانسور تنش، تانسور تنش
The peridynamic theory does not concern the concept of stress and strain; however, it is possible to define a stress tensor within the PD framework.
Lehoucq and Silling (2008) derived a PD stress tensor from nonlocal PD interactions.
The stress tensor is obtained from the PD forces that pass through a material point volume.
For sufficiently smooth motion, a constitutive model, and any existing nonhomogeneities, Silling and Lehoucq (2008) showed that the PD stress tensor converges to a Piola-Kirchhoff stress tensor in the limiting case where the horizon size converges to zero.
It is apparent that this requirement is automatically satisfied if the force vectors t(u' - u, x' - x, t) = T(x, t)(x' - x) and t'(u - u', x - x', t) = T(x', t)(x - x') are aligned with the relative position vector of the material points in the deformed state, (y7 - y)- However, their general form that satisfies the requirement of Eq. 2.42b can also be derived in terms of the deformation gradient and stress tensors of classical continuum mechanics.،The peridynamic theory does not concern the concept of stress and strain; however, it is possible to define a stress tensor within the PD framework.
Lehoucq and Silling (2008) derived a PD stress tensor from nonlocal PD interactions.
The stress tensor is obtained from the PD forces that pass through a material point volume.
For sufficiently smooth motion, a constitutive model, and any existing nonhomogeneities, Silling and Lehoucq (2008) showed that the PD stress tensor converges to a Piola-Kirchhoff stress tensor in the limiting case where the horizon size converges to zero.
It is apparent that this requirement is automatically satisfied if the force vectors t(u' - u, x' - x, t) = T(x, t)(x' - x) and t'(u - u', x - x', t) = T(x', t)(x - x') are aligned with the relative position vector of the material points in the deformed state, (y7 - y)- However, their general form that satisfies the requirement of Eq. 2.42b can also be derived in terms of the deformation gradient and stress tensors of classical continuum mechanics.
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