Dry joint unreinforced masonry (URM) structures are particularly vulnerable to earthquakes, despite being widespread in many seismically prone areas. While Discrete Element Methods (DEM) are typically used for simulating the seismic fracturing of dry joint URM, such refined computational solutions often require prohibitive analysis times. A still marginally explored, yet promising, alternative to DEM for the structural analysis of dry joint URM is the use of physics engines, which feature an unmatched computational speed when simulating separation, re-contact, and collisions between rigid body elements. However, these methods, presently used in primarily digital animation and robotic industries and therefore seek visually plausible rather than rigorous outcomes, tend to sacrifice accuracy when evaluating equations of motion to reduce the computational burden. This study explores the capabilities of PyBullet, a Python-based module operating the well-known, open-source Bullet Physics engine, in replicating the experimental in-plane (IP) fracturing behavior of dry joint URM walls under varying axial compression rates. Preliminary results indicate that PyBullet models can accurately predict the diagonal shear failures observed during IP testing and that the implicit Coulomb friction cone model utilized is suitable for simulating joint slip under shear-compression. Despite satisfactorily capturing the maximum displacement capacities and lateral strength for all the wall specimens, the adopted stick-slip interface model yields excessive IP stiffness in the linear elastic range, and improvements to this model are currently in progress. Quantitative comparisons with previous traditional DEM results show that response predictions obtained using PyBullet have analogous accuracy, but require significantly less time to complete, making them a promising alternative for full-scale URM seismic simulations.

The heterogeneous and biological nature of wood has historically led to difficulties in modeling fracture behavior. Finite element models often fail to relate the inherent material properties to model parameters, and the resulting complexity of parameter identification makes such models unsuited to infrastructure applications. Moreover, high-strain rate effects are not easily captured and generally require significant experimental data. To address both concerns, a connector-beam lattice model was developed. This 3D lattice model uses a novel method to represent the cellular structure of wood at the mesoscale via Voronoi tessellation and Lloyd relaxation. The resulting model geometry can capture the unique fracture behavior of wood arising from the orthotropic biostructure of wood cells and their annual growth ring patterns. Following this, a generalized Timoshenko beam formulation was derived which better captures the effects of curved beam deformations. The formulation was implemented via isogeometric analysis with zero-length beam connector elements capturing both in-plane and longitudinal fracture patterns of wood fibers. Model parameters can be largely identified via existing species data. This CBL model is shown to capture the orthotropic elastic behavior, the effects of growth ring orientation on fracture patterns, size effect the transverse plane, and strain-rate effects.

This contribution offers a comprehensive derivation of equations for the macroscopic stress tensor, couple stress tensor, and flux vector in both continuous and discrete heterogeneous systems, where displacements and rotations are treated independently. In the first step, the macroscopic quantities are obtained for a heterogeneous Cosserat continuum. In the second step, these continuum equations are discretized, allowing to identify macroscopic quantities within discrete heterogeneous systems. Finally, the expressions for discrete systems are re-derived without the use of continuous formulation. The resulting formulas are presented in two variations, accounting for either internal or external forces, couples, and fluxes. The differences between these formulations are discussed.

The derivation relies on the principle of virtual work equivalence and sheds light on the essential role of the couple stress tensor concerning balance equations and permissible virtual deformation modes. Specifically, a crucial assumption regarding the selection of virtual kinematic modes was previously overlooked. We demonstrate that these modes can be arbitrarily chosen, resulting in different formulations of macroscale statics. One particular choice yields the formulation previously derived, but without acknowledging the hidden assumption. Particularly noteworthy is also the emergence of an additional term in the formula for the couple stress tensor, elucidating its dependence on location of the macroscopic point. To validate the resulting equations, comparisons are made with established analytical solutions and outcomes from other numerical models, considering both steady-state and transient conditions.