Joss final draft

docs/joss/paper.md

@@ -23,13 +23,13 @@ bibliography: paper.bib
 
 # Summary
 
-Accurate simulation of granular materials under extreme mechanical conditions, such as crushing, fracture, and large deformation, remains a significant challenge in geotechnical, manufacturing, and mining applications. Classical discrete element method (DEM) models typically treat particles as rigid or nearly rigid bodies, limiting their ability to capture internal deformation and fracture. The PeriDEM library, first introduced in [@jha2021peridynamics], addresses this limitation by modeling particles as deformable solids using peridynamics, a nonlocal continuum theory that naturally accommodates fracture and significant deformation. Inter-particle contact is handled using DEM-inspired local laws, enabling realistic interaction between complex-shaped particles.
+Accurate simulation of granular materials under extreme mechanical conditions, such as crushing, fracture, and large deformation, remains a significant challenge in geotechnical, manufacturing, and mining applications. Classical discrete element method (DEM) models typically treat particles as rigid or nearly rigid bodies, limiting their ability to capture internal deformation and fracture. The PeriDEM library, first introduced by @jha2021peridynamics, addresses this limitation by modeling particles as deformable solids using peridynamics, a nonlocal continuum theory that naturally accommodates fracture and significant deformation. Inter-particle contact is handled using DEM-inspired local laws, enabling realistic interaction between complex-shaped particles.
 
 Implemented in \texttt{C++}, PeriDEM is designed for extensibility and ease of deployment. It relies on a minimal set of external libraries, supports multithreaded execution, and includes demonstration examples involving compaction, fracture, and rotational dynamics. The framework facilitates granular-scale simulations, supports the development of constitutive models, and serves as a foundation for multi-fidelity coupling in real-world applications.
 
 # Statement of Need
 
-Granular materials play a central role in many engineered systems, but modeling their behavior under high loading, deformation, and fragmentation remains an open problem. Popular open-source DEM codes such as YADE [@yade2021], BlazeDEM [@govender2016blaze], Chrono DEM-Engine [@zhang_2024_deme], and LAMMPS [@THOMPSON2022108171] are widely used but typically treat particles as rigid, limiting their accuracy in scenarios involving internal deformation and breakage. A recent review by Dosta et al. [@dosta2024comparing] compares several DEM libraries. Meanwhile, peridynamics-based codes such as Peridigm [@littlewood2024peridigm] and NLMech [@Jha2021NLMech] are designed to simulate deformation and fracture within a single structure, with limited support for multi-structure simulations. 
+Granular materials play a central role in many engineered systems, but modeling their behavior under high loading, deformation, and fragmentation remains an open problem. Popular open-source DEM codes such as YADE [@yade2021], BlazeDEM [@govender2016blaze], Chrono DEM-Engine [@zhang_2024_deme], and LAMMPS [@THOMPSON2022108171] are widely used but typically treat particles as rigid, limiting their accuracy in scenarios involving internal deformation and breakage. A recent review by @dosta2024comparing compares several DEM libraries. Meanwhile, peridynamics-based codes such as Peridigm [@littlewood2024peridigm] and NLMech [@Jha2021NLMech] are designed to simulate deformation and fracture within a single structure, with limited support for multi-structure simulations. 
 
 PeriDEM fills this gap by integrating state-based peridynamics for intra-particle deformation with DEM-style contact laws for particle interactions. This hybrid approach enables direct simulation of particle fragmentation, stress redistribution, and dynamic failure propagation—capabilities essential for modeling granular compaction, attrition, and crushing.
 
@@ -55,17 +55,17 @@ where ${\rho}^{(p)}$, ${\boldsymbol{f}}^{(p)}_{int}$, and ${\boldsymbol{f}}^{(p)
 
 ### Internal force – State-based peridynamics
 
-The internal force term ${\boldsymbol{f}}^{(p)}_{int}(\boldsymbol{X}, t)$ in the momentum balance governs intra-particle deformation and fracture. In PeriDEM, this term is modeled using a simplified state-based peridynamics formulation that accounts for nonlocal interactions over a finite horizon. The underlying model and its numerical implementation are discussed in detail in [[@jha2021peridynamics], Sections 2.1 and 2.3].
+The internal force term ${\boldsymbol{f}}^{(p)}_{int}(\boldsymbol{X}, t)$ in the momentum balance governs intra-particle deformation and fracture. In PeriDEM, this term is modeled using a simplified state-based peridynamics formulation that accounts for nonlocal interactions over a finite horizon. The underlying model and its numerical implementation are discussed in detail by @jha2021peridynamics.
 
 ### DEM-inspired contact forces
 
-The external force term ${\boldsymbol{f}}^{(p)}_{ext}(\boldsymbol{X}, t)$ includes body forces, wall-particle interactions, and contact forces from other particles. Contact is modeled using a spring-dashpot-slider formulation applied locally when particles come within a critical distance; see \autoref{fig:peridemContact}. This approach introduces nonlinear normal forces, damping, and friction without relying on particle convexity or geometric simplifications. The full formulation of contact detection, force assembly, and implementation is detailed in [[@jha2021peridynamics], Section 2.2].
+The external force term ${\boldsymbol{f}}^{(p)}_{ext}(\boldsymbol{X}, t)$ includes body forces, wall-particle interactions, and contact forces from other particles. Contact is modeled using a spring-dashpot-slider formulation applied locally when particles come within a critical distance; see \autoref{fig:peridemContact}. This approach introduces nonlinear normal forces, damping, and friction without relying on particle convexity or geometric simplifications. The full formulation of contact detection, force assembly, and implementation is detailed by @jha2021peridynamics.
 
-![High-resolution contact approach in PeriDEM model for granular materials between arbitrarily-shaped particles. The spring-dashpot-slider system shows the normal contact (spring), normal damping (dashpot), and tangential friction (slider) forces between points $\boldsymbol{x}$ and $\boldsymbol{y}$.\label{fig:peridemContact}](./files/peridem-contact.png){width=40%}
+![High-resolution contact approach in the PeriDEM model for granular materials between arbitrarily shaped particles. The spring dashpot slider system represents normal contact elasticity, normal damping, and tangential friction between material points $\boldsymbol{x}$ and $\boldsymbol{y}$. Adapted from @jha2021peridynamics.](./files/peridem-contact.png){#fig:peridemContact width=40%}
 
 # Implementation
 
-[PeriDEM](https://github.com/prashjha/PeriDEM) is implemented in \texttt{C++} and hosted on GitHub. It depends on a minimal set of external libraries, most of which are bundled in the `external` directory. Key dependencies include Taskflow [@huang2021taskflow] for multithreaded parallelism, nanoflann [@blanco2014nanoflann] for efficient neighborhood search, and VTK for output. The numerical strategies for neighbor search, peridynamic integration, damage evaluation, and time stepping follow those introduced in [[@jha2021peridynamics], Section 3]. The core simulation model is implemented in [`src/model/dem`](https://github.com/prashjha/PeriDEM/blob/v0.2.1/src/model/dem), with the class [`DEMModel`](https://github.com/prashjha/PeriDEM/blob/v0.2.1/src/model/dem/demModel.cpp) managing particle states, force calculations, and time integration. This work builds on earlier research in the analysis and numerical methods for peridynamics; see [@jha2018numerical; @jha2019numerical; @jha2018numerical2; @Jha2020peri; @jha2025nodal].
+[PeriDEM](https://github.com/prashjha/PeriDEM) is implemented in \texttt{C++} and hosted on GitHub. It depends on a minimal set of external libraries, most of which are bundled in the `external` directory. Key dependencies include Taskflow [@huang2021taskflow] for multithreaded parallelism, nanoflann [@blanco2014nanoflann] for efficient neighborhood search, and VTK for output. The numerical strategies for neighbor search, peridynamic integration, damage evaluation, and time stepping follow those introduced by @jha2021peridynamics. The core simulation model is implemented in [`src/model/dem`](https://github.com/prashjha/PeriDEM/blob/v0.2.1/src/model/dem), with the class [`DEMModel`](https://github.com/prashjha/PeriDEM/blob/v0.2.1/src/model/dem/demModel.cpp) managing particle states, force calculations, and time integration. This work builds on earlier research in the analysis and numerical methods for peridynamics [@jha2018numerical; @jha2019numerical; @jha2018numerical2; @Jha2020peri; @jha2025nodal].
 
 ## Features
 
@@ -80,7 +80,7 @@ Example cases are described in [examples/README.md](https://github.com/prashjha/
 
 Preliminary performance tests show that compute time increases exponentially with particle count due to the nonlocal nature of both peridynamic and contact interactions—highlighting a computational bottleneck. This motivates future integration of MPI-based parallelism and a multi-fidelity modeling framework. Additional examples include attrition of non-circular particles in a rotating cylinder (\autoref{fig:peridemSummary}c).
 
-![(a) Nonlinear response under compression, (b) exponential growth of compute time due to nonlocality of internal and contact forces, and (c) rotating cylinder with nonspherical particles.\label{fig:peridemSummary}](./files/peridem-summary.png){width=70%}
+![(a) Nonlinear response under compression, (b) exponential growth of compute time due to nonlocality of internal and contact forces, and (c) rotating cylinder with nonspherical particles. Adapted from @jha2021peridynamics.](./files/peridem-summary.png){#fig:peridemSummary width=70%}
 
 # Acknowledgements