This paper presents a cyclic joint constitutive model within a Distinct Element Method framework to simulate the in-plane response of unreinforced masonry structures. The model combines multi-surface failure criteria, including tensile cut-off, Coulomb friction, and an elliptical compression cap. It incorporates exponential softening, a unified damage scalar for stiffness degradation, and a hardening–softening law for compression. Shear-induced dilatancy is captured via an uplift-correction mechanism with an exponential dilatancy-decay law, while stiffness degradation governs energy dissipation. The model is validated at both material and structural scales. Material-level simulations of cyclic compression and shear tests show close agreement with experimental data. Structural-scale validation on full-height calcium-silicate walls under combined compression and cyclic lateral loading demonstrates the ability to reproduce rocking-dominated, shear-dominated, and hybrid failure mechanisms. The model successfully replicated global hysteretic force–drift loops, capturing stiffness decay and energy dissipation, as well as local failures like cracking, sliding, and toe crushing. The model also reproduced the drift-dependent transition from rocking to friction-controlled sliding, a key mechanism for earthquake assessment. By integrating these features into a single, efficient framework, the proposed constitutive model provides a robust tool for evaluating seismic performance and conserving heritage.

Simulating the seismic behaviour of unreinforced masonry (URM) is challenging due to large deformations and severe damage. Capturing this highly nonlinear response requires advanced numerical modelling strategies that represent block separation, debonding, friction, and impact. Discontinuum-based modelling strategies, such as the Distinct Element Method (DEM), are well suited, as they explicitly represent bond failure and damage progression from cracking to collapse. DEM relies on the explicit time integration scheme of motion equations; hence, the choice of the damping scheme becomes critical. Typically, mass-proportional damping is used in dynamic analysis, often without complementing it with stiffness-proportional damping which requires unpractical reduction of the time steps to ensure numerical stability. Yet relying solely on mass-proportional damping can overdamp low frequencies and underdamp high frequencies. This study implements and validates an alternative damping approach, Maxwell damping, where multiple spring-dashpot elements are introduced at unit-mortar interfaces within a simplified micro-model. This work introduces an optimization algorithm to tune the Maxwell elements without heuristics, targeting near-uniform damping over a broad frequency range. Effectiveness is assessed against shake-table tests on a full-scale cross-vault URM specimen. Predicted displacements, accelerations, damage evolution, and computational efficiency is compared with mass-proportional and zero-viscous damping models. This study investigates Maxwell damping as a practical relaxation scheme for the seismic analysis of complex masonry systems using DEM, building on prior formulations in the literature and extending them to the present modelling and validation context.

Masonry structures, integral components of architectural heritage, are diffuse worldwide and continue to be interwoven within modern infrastructures. The complex nature of their constituents has driven active research toward understanding their mechanical behavior. Accurately and robustly representing the nature of masonry constituents is essential for structural analysis, design, and preservation tasks. This study adopts an adjustable contact constitutive model recently proposed to simulate bond behavior in masonry assemblages subjected to in-plane shear-compression loading. The adopted contact constitutive model, recently proposed by the authors within the Distinct Element Method (DEM) framework, addresses the intricate behavior of unit-mortar interfaces by employing a piecewise linear softening function controlled by the user to capture the softening regime in tension and shear. Meanwhile, the compressive region of the masonry interfaces is controlled by a compressive cap with a radial return algorithm under the explicit time-marching integration scheme of DEM to implicitly couple the shear and compressive behavior. The performance of the constitutive model was assessed on a set of calcium silicate wall experiments tested under in-plane shear and compression loading and presented a comprehensive variety of failure modes. The experimental and numerical results are compared on each system’s global and local behaviors. The findings underscore the robustness of the proposed contact constitutive model in accurately capturing the complex mechanical response of masonry and highlight its potential for structural analysis and damage prediction of a diverse spectrum of masonry structures.

This study presents a robust contact constitutive model in the distinct element method (DEM) framework for simulating the mechanical behavior of masonry structures. The model is developed within the block-based modeling strategy, where the masonry unit is modeled as deformable blocks with potential crack surfaces in the middle of the bricks, while the mortar joints are defined as zero-thickness interfaces. The modeling strategy implements multi-surface plasticity with damage mechanics, including a tension cut-off, Coulomb failure criterion, and an elliptical compressive cap for the damage in tension, shear, and compression, respectively. Two new features are introduced in this contact model: a piecewise linear softening function for strength degradation in tension and shear and a hardening/softening function to phenomenologically define the compressive damage of masonry composite into the unit-mortar interface. The constitutive model is implemented in commercial DEM software using the small displacement configuration and validated against material and experimental tests on masonry walls subjected to constant pre-compression and monotonically increasing in-plane load. The experimental and numerical results regarding the force-displacement relationship and damage pattern produced by the proposed constitutive model are compared and critically discussed, demonstrating the capability of DEM coupled with the suitable constitutive law in simulating the behavior of masonry structures.