Handbook Of Peridynamic Modeling
Nancy Benigar
This handbook covers the peridynamic modeling of failure and damage. Peridynamics is a reformulation of continuum mechanics based on integration of interactions rather than spatial differentiation of displacements. The book extends the classical theory of continuum mechanics to allow unguided modeling of crack propagation/fracture in brittle, quasi-brittle, and ductile materials; autonomous transition from continuous damage/fragmentation to fracture; modeling of long-range forces within a continuous body; and multiscale coupling in a consistent mathematical framework.
N2 - This handbook covers the peridynamic modeling of failure and damage. Peridynamics is a reformulation of continuum mechanics based on integration of interactions rather than spatial differentiation of displacements. The book extends the classical theory of continuum mechanics to allow unguided modeling of crack propagation/fracture in brittle, quasi-brittle, and ductile materials; autonomous transition from continuous damage/fragmentation to fracture; modeling of long-range forces within a continuous body; and multiscale coupling in a consistent mathematical framework.
AB - This handbook covers the peridynamic modeling of failure and damage. Peridynamics is a reformulation of continuum mechanics based on integration of interactions rather than spatial differentiation of displacements. The book extends the classical theory of continuum mechanics to allow unguided modeling of crack propagation/fracture in brittle, quasi-brittle, and ductile materials; autonomous transition from continuous damage/fragmentation to fracture; modeling of long-range forces within a continuous body; and multiscale coupling in a consistent mathematical framework.
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Ever wondered why does glass break in such complex patterns, fragments and chips? Or how does corrosion of a few bolts and plates bring an entire bridge down? Our research group works on computational models that answer such questions and explain the behavior observed experimentally in some of the most challenging problems that have puzzled researchers for decades. We use these models for solving problems that deal with heat and mass diffusion, dynamic fracture, and fragmentation. Recent focus is on: peridynamics for impact fracture in glass, glassy-polymers, polycrystalline ceramics, and fiber-reinforced composites; fracture in concrete induced by corrosion; corrosion damage and Stress Corrosion Cracking; dynamics of granular materials and their interaction with elastic media, multidisciplinary optimization, inverse problems, and multiscale and multiphysics methods.
Damage, corrosion, and fracture with peridynamics
The peridynamic theory is a novel reformulation of the classical continuum mechanics which allows one to model fracture, damage, fragmentation in a natural way. In peridynamics, cracks are part of the solution, not part of the problem. We have used such models to explain the role Van der Waals forces play in the deformation and damage behavior of nanofiber networks, to explain the growth of cracks and fragmentation evolution in glass plates, to model trans- and intergranular fracture in polycrystalline ceramics, to discover strain-rate effects in the failure of fiber-reinforced composites, and to simulate the growth of subsurface damage in corrosion. This research is being funded by NSF, AFOSR through a MURI project, by ONR, by NAVAIR, by ARO and ARL. Recent past funding includes grants from Boeing Co, Sandia National Laboratories, Callahan Innovation (New Zealand), NASA.
Dynamics of Granular Materials interacting with vibrating plates
Granular materials are one of the most puzzling material systems. The models we proposed, simulate the dynamic interaction between a layer of granular material and an elastic vibrating plate to provide us with a deeper understanding of the fascinating dynamic behavior of granular materials. Think of a land- or rock-slide and imagine the possibility of predicting their behavior under their interaction with the elastic soil support.
Optimization of material composition
Is it possible to find the "best" composition of a multi-component material (such as a composite or a functionally graded material - FGM) that maximizes its strength or stiffness, and reduces its mass? Our results on optimal material design of FGMs show new possible architectures that minimize the chance of failure due to thermal and mechanical stresses.
Optimal shape design
What is the best shape of a cooling thermal fin? Our novel algorithms compute optimal shape of systems when there are large shape changes between the initial guess and the final optimal design. Our meshfree approach leads to interesting solutions that mimic naturally occurring systems like the plates on the back of a stegosaurus dinosaur, or the extended surfaces on the inner side of the intestine (intestinal villi).
Y. Liu, F. Yang, W. Zhou, Z. Chen, F. Bobaru, "Peridynamics modeling of early-age cracking behaviour in continuously reinforced concrete pavement", International Journal of Pavement Technology, (2022).
Peridynamics is a nonlocal extension of classical continuum mechanics that was introduced by Stewart Silling in 2000 [1]. The key characteristic of peridynamics is that the governing equations do not include spatial derivatives of the displacement field, and are therefore well suited for modeling material discontinuities such as cracks. As with classical continuum mechanics, peridynamic simulations are constructed in the form of initial value problems or boundary value problems, for example, solution of the balance of linear momentum subject to prescribed initial and boundary conditions. The solution of the initial or boundary value problem for any nontrivial case requires software tools that implement the relevant numerical methods.
The Peridigm code was developed for high-fidelity peridynamic simulations over three-dimensional domains using the meshfree discretization approach of Silling and Askari [2]. Peridigm is an open-source C++ code that utilizes software libraries from the Trilinos [3] project to enable large-scale parallel simulations. It was designed to facilitate engineering simulations of solid mechanics problems that include material failure, and also to provide a software framework for use by peridynamic methods developers. Key features include a range of constitutive models, bond failure laws, contact models, and support for both explicit and implicit time integration. A MPI-based design supports simulations on hardware ranging from laptop computers to massively parallel supercomputing platforms.
Peridigm has been utilized by researchers for a wide range of methods development and engineering applications. Examples of engineering applications include a blind prediction of ductile fracture in additively manufactured metal in [23, 24]. Peridigm was applied by the authors of [25, 26] to model shock compaction of granular materials. The authors of [27] modeled damage due to indentation and scratching in 3C-SiC. Peridigm was used to model impact of a Al\(_2\)O\(_3\)/ZrO\(_2\) composite in [28], impact of a Al-Si12/SiC composite in [29], and compression of SiC foam in [30]. The authors of [31] simulated fracture and shock wave propagation in a harmonic structured material. In [32], Peridigm was utilized to model impact response of cellular materials. Peridigm was used in [33] for comparison between peridynamics and smoothed-particle hydrodynamics for modeling fragmentation of ceramic tile. The authors of [34,35,36] used Peridigm to model damage and fragmentation of objects during atmospheric re-entry. The authors of [37] utilized Peridigm in their work on modeling mode I fracture of phase-separated glasses. Damage in nanoparticle-implanted glass was modeled using Peridigm in [38, 39]. The influence of probabilistic material property distributions was investigated using Peridigm in [40]. Peridigm was used to model mixed-mode fracture in PMMA in [41]. The authors of [42] utilized Peridigm in to model particle impact and interfacial bonding in cold spray processes. A study comparing experimental results against peridynamic simulations of ring bending tests on float glass plates is described in [43].
Peridigm has proven to be a valuable tool for researchers focusing on methods development and algorithms research for peridynamic models. The authors of [13], for example, used Peridigm in their development of a peridynamic Kirchhoff-Love shell formulation. The authors of [44] reviewed and extended peridynamic models for frictional contact. Peridigm was used in the development of an energetically consistent surface correction method for bond-based peridynamics in [45]. In [46,47,48], Peridigm was used to develop a formulation for mean stress and incubation time fracture models. The authors of [49, 50] developed a peridynamic plasticity model for the dynamic flow and fracture of concrete. Concrete was also studied in [51], in which the authors implemented a microplane (M7) constitutive model. Peridigm was employed in [52, 53] for development of a fatigue model for capturing damage in railway applications. Energy-based failure criteria for peridynamic models were explored in [54,55,56,57]. The authors of [58] investigated the stability of generalized peridynamic correspondence models. In [59], the authors used Peridigm in their comparison of different methods for calculating tangent stiffness matrices for peridynamic models. Mesh sensitivity for quasi-static simulations was investigated in [60]. The use of so-called partial volumes for improved fidelity and convergence of meshfree peridynamics was explored in [61, 62]. In [63], a touch-aware model of frictional contact for granular materials with arbitrary particle shapes was introduced. A correspondence energy-based damage model and adaptive Verlet time integration scheme were developed in [64] for modeling PMMA. The authors of [65] also employed Peridigm to model PMMA, in their case for development of a rate-dependent visco-elastic constitutive model to capture the rate-sensitivity of damage evolution.
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