Modeling damage and fracture in additively manufactured polymeric triply periodic minimal surface lattices

Investigating Fracture Behavior of Lattice Structures Using the XFEM and Equivalent Solid Material Model Techniques

This study aims to numerically investigate the mode I, II, and III fracture behaviors of additively manufactured degradable, bioplastic polylactic acid (PLA) lattice specimens. Numerical simulations were performed using the eXtended Finite Element Method (XFEM) based on the extracted PLA's mechanical and fracture material properties. The maximum principal stress and fracture energy power‐law criteria were utilized to simulate damage initiation and evolution in three‐dimensional (3D) numerical analyses. To consider the effects of build orientation, the transversely isotropic elasticity model (TIEM) was implemented. To facilitate the XFEM analyses, the equivalent solid material model (ESMM) technique was also utilized. The experimental load‐displacement responses of single‐edge notched bending specimens under the symmetric and asymmetric four‐point bending and mode III transverse shear cracked plate tests were conducted for comparison with the XFEM analyses in mode I, II, and III fracture, respectively. A common calibration factor, as well as the simultaneous utilization of the TIEM model, as well as the XFEM and ESMM techniques, reflected numerical results of acceptable accuracy compared to the experimental results; 5.3% (3.4%), 4.4% (5.8%), and 9.6% (5.4%) differences for the stiffness (peak load) of mode I, II, and III specimens, respectively.

Experimental Evaluation of Strut-Based Mesostructures: Brittle Behavior and Energy Absorption

This study investigates the compressive energy absorption behavior of parametrically defined, strut-based mesostructures fabricated using stereolithography additive manufacturing. Lattice specimens with four distinct geometries—body-centered cubic, octet, re-entrant, and Kelvin cell—were designed using implicit modeling, maintaining constant relative density and unit cell dimensions to enable direct comparison of structural efficiency. Specimens were printed with Formlabs Clear resin, chosen for its superior energy absorption and elastic properties, and subjected to uniaxial compression testing using a Tinius Olsen universal testing machine. Experimental protocols ensured uniform loading and minimized size-dependent effects. Force–displacement data were processed to quantify energy absorption and benchmarked against prior literature and other mesostructure types using Ashby plots and bar chart visualizations. Results reveal that all strut-based lattices exhibited predominantly brittle behavior under compressive loading, characterized by abrupt failure and limited plastic deformation. Compared with serpentine and plate-based mesostructures, which show more ductile and progressive energy dissipation, the tested strut-based designs absorbed less energy and failed at higher densities. This study highlights the critical influence of lattice topology on mechanical response, demonstrating that slender strut-based architectures concentrate stress and are prone to catastrophic fracture, whereas alternative geometries, such as serpentine and plate-based lattices, facilitate distributed deformation and superior energy absorption. These findings underscore the importance of geometric innovation in the design of architected materials for impact mitigation and energy-absorbing applications. The research identifies current limitations associated with strut-based periodic lattices and points to future directions involving plate-based, hybrid, and multiscale lattice architectures. Integrating computational modeling with experimental validation is recommended for optimizing both geometry and material properties, ultimately advancing the functional performance of energy-absorbing mesostructures.

Dynamic fracture modeling in ductile materials using phase field approach

Understanding dynamic fracture in both brittle and ductile materials has attracted considerable attention from engineers and researchers due to its practical importance. In ductile materials, crack initiation and growth are strongly influenced by plastic deformation and the associated microstructural damage, which gradually reduces the material's resistance to crack propagation. Capturing this evolving fracture resistance remains a key challenge for predictive phase-field models. In this study, a phase-field framework is presented in which the effect of plastic deformation on fracture evolution is introduced through a history-dependent fracture resistance. The critical energy release rate is allowed to degrade as a function of accumulated plastic strain, providing a phenomenological description of plasticity-induced weakening without treating plastic dissipation as a direct crack driving force. The formulation is developed within a small-strain elasto-plastic setting based on classical von Mises plasticity with isotropic hardening and is extended to dynamic fracture by accounting for inertia effects in the phase-field evolution. The model is implemented in a commercial finite element environment and examined through a set of representative quasi-static and dynamic numerical examples. The results illustrate the ability of the framework to capture key trends in ductile crack initiation and propagation, as well as the influence of plastic deformation on fracture behavior. The capabilities and limitations of the proposed approach are discussed in the context of existing phase-field models for ductile fracture.

Constitutive structural response of Concrete Damaged Plasticity model under Willam’s test

The present work aims to analyze and calibrate the mechanical description of plastic strain-induced anisotropy and damage coupling by the so-called Concrete Damaged Plasticity (CDP) constitutive model, which is rather well known, also since it has become available within popular FEM platforms, such as ABAQUS, and shall reproduce typical features of failure processes in quasi-brittle materials, such as concrete. This is achieved by combining an effective stress-based non-associative hardening/softening plasticity model with an isotropic damage model based on plastic strains, at a smeared continuum scale. In the paper, focusing on the mere elastoplastic coupling for tensile-dominated responses, and introducing an enhanced tuning by setting tensile exponential softening and damage evolutions through a convenient plastic to inelastic strain ratio parameter, by means of an external user implementation, an exhaustive numerical parametrization analysis is performed, starting at a constitutive-driver level, to experiment with the outcomes of the constitutive description and to quantify the amount of material anisotropy induced by plastic deformation, under biaxial elongation/shearing Willam’s test, which prescribes/involves the rotation of the principal axes of strains/stresses. It is shown that the constitutive response is effectively regularized, allowing to fulfil the requirements of Willam’s test, independently of the amount of inherent plastic dilatancy, showing a rather mild presence of plastic-induced anisotropy, at the pure constitutive-driver scale. Furthermore, first extrapolating implications and outcomes at the small (specimen) structural scale are also investigated, with clear appearance of strain localization and related much pronounced plastic-induced anisotropy, in the (imperfection-triggered) macroscopic response, with features that are similar to those coming, for example, from more sophisticated anisotropic damage models, while significant practical applications may subsequently follow, within different structural engineering contexts, such as that of large-scale concrete structures under static and dynamic loading scenarios, toward informed safety assessment and evaluation.

Elastic and failure properties of 2D primitive TPMS lattices with varying shape factor

Architected materials based on Triply Periodic Minimal Surfaces (TPMS) have demonstrated outstanding mechanical performance; however, their two-dimensional (2D) counterparts remain insufficiently explored. This study presents a comprehensive numerical investigation of the elastic response and failure behavior of 2D Primitive TPMS lattice structures, with particular emphasis on the role of geometric parameters C1 and C2. A phase-field damage framework is employed to capture the full mechanical evolution, from initial elastic deformation to crack initiation and subsequent propagation leading to ultimate failure. The results reveal that mechanical performance is governed not only by relative density but also critically by geometric configuration. In particular, structures with nearly identical relative densities can exhibit strength variations of up to five times, underscoring the dominant influence of shape parameters. In addition, certain configurations display pronounced auxetic behavior, with a minimum Poisson’s ratio of −0.12 observed for C1 = 1.2 and C2 = 0.8. Failure consistently initiates at the specimen center, where stress concentration is most severe. Overall, this study provides both a high-quality numerical dataset and fundamental insights into the geometry–mechanical performance relationship of 2D TPMS lattices. The findings establish a foundation for the rational design and optimization of TPMS-based architected materials in advanced engineering applications.

A nonlinear constitutive model for fine sandstone considering freeze–thaw induced compaction and damage evolution