Publisher Summary The classical theory of solid mechanics is based on the assumption of a continuous distribution of mass within a body and all internal forces are contact forces that act across zero distance. The mathematical description of a solid that follows from these assumptions relies on PDEs that additionally assume sufficient smoothness of the deformation for the PDEs to make sense in their either strong or weak forms. The classical theory has been demonstrated to provide a good approximation to the response of real materials down to small length scales, particularly in single crystals, provided these assumptions are met. Nevertheless, technology increasingly involves the design and fabrication of devices at smaller and smaller length scales, even interatomic dimensions.

Peridynamic Theory of Solid Mechanics

One of the fundamental aspects in cohesive zone modeling is the definition of the traction-separation relationship across fracture surfaces, which approximates the nonlinear fracture process. Cohesive traction-separation relationships may be classified as either nonpotential-based models or potential-based models. Potential-based models are of special interest in the present review article. Several potential-based models display limitations, especially for mixed-mode problems, because of the boundary conditions associated with cohesive fracture. In addition, this paper shows that most effective displacement-based models can be formulated under a single framework. These models lead to positive stiffness under certain separation paths, contrary to general cohesive fracture phenomena wherein the increase of separation generally results in the decrease of failure resistance across the fracture surface (i.e., negative stiffness). To this end, the constitutive relationship of mixed-mode cohesive fracture should be selected with great caution.

Cohesive Zone Models: A Critical Review of Traction-Separation Relationships Across Fracture Surfaces

The peridynamic formulation for transient heat conduction

A non-ordinary state-based peridynamic method to model solid material deformation and fracture

The paper presents an overview of peridynamics, a continuum theory that employs a nonlocal model of force interaction Specifically, the stress/strain relationship of classical elasticity is replaced by an integral operator that sums internal forces separated by a finite distance This integral operator is not a function of the deformation gradient, allowing for a more general notion of deformation than in classical elasticity that is well aligned with the kinematic assumptions of molecular dynamics Peridynamics effectiveness has been demonstrated in several applications, including fracture and failure of composites, nanofiber networks, and polycrystal fracture These suggest that peridynamics is a viable multiscale material model for length scales ranging from molecular dynamics to those of classical elasticity

https://iopscience.iop.org/article/10.1088/1742-6596/125/1/012078/pdf

Peridynamics for multiscale materials modeling

Peridynamics via finite element analysis

The applicability of explicit time integration in structural dynamics is often limited by a restrictively small solution time increment. This paper presents a mass penalty technique whereby the highest natural frequencies of a dynamic system can be preferentially lowered with only a minimal effect on the structural modes. Because the critical time increment is inversely proportional to the highest natural frequency, a dramatic increase in the solution time increment may be achieved. An expression is developed for the frequency shift and a number of useful properties of this technique are derived analytically for linear systems. Its utility in non-linear analyses is demonstrated with several examples.

A mass penalty technique to control the critical time increment in explicit dynamic finite element analyses

Finite cavity expansion method for near-surface effects and layering during Earth penetration

A methodology for the viscoelastic analysis of filament-wound polymer matrix composites is developed and demonstrated. The procedure uses the elastic- viscoelastic correspondence principle with standard micromechanics models to obtain the viscoelastic properties of the composite. For global analysis, an efficient time-stepping algorithm is developed and implemented in a general purpose finite element code via a user-supplied material subroutine. The algorithm is verified by comparison to the exact analysis of a rigid inclusion in an infinite viscoelastic plate and the utility of the entire methodology is shown by analysis and testing of a composite spring.

Viscoelastic analysis of filament-wound composite material systems

A finite spherical cavity expansion technique is developed to simulate the loading on projectiles penetrating geologic media. Damaged Mohr-Coulomb plasticity models and general pressure-dependent damaged plasticity models are used with incompressible kinematics to approximate a wide range of targets. The finite cavity expansion approximation together with directional sampling reasonably captures near surface and layering effects without resort to ad hoc or empirical correction factors. The Mohr-Coulomb models are integrated exactly to provide a very efficient loading algorithm for use with conventional implicit or explicit finite element structural analysis. The more general constitutive model requires numerical integration and leads to a more computationally intensive procedure. However, subcycling is easily implemented with the numerical integration and thus an efficient loading method is readily achieved even for large complex simulations using explicit finite element analysis. The utility of the finite cavity expansion approach is demonstrated by comparison of simulations to measured test data from projectiles penetrating rock and soil targets.

https://digital.library.unt.edu/ark:/67531/metadc710622/m2/1/high_res_d/674573.pdf

Richard W. Macek

Papers

Peridynamics via finite element analysis

A mass penalty technique to control the critical time increment in explicit dynamic finite element analyses

Finite cavity expansion method for near-surface effects and layering during Earth penetration

Viscoelastic analysis of filament-wound composite material systems

Finite cavity expansion method for near-surface effects and layering during earth penetration