The filling characterization of dual-scale fibrous reinforcements is challenging due to the presence of subdomains with dissimilar permeabilities, existence of wicking effects, and combination of air compressibility and dissolution phenomena. These factors cause flow imbalances inside the representative unitary cell (RUC), which lead to void formation and influence the behavior of macroscopic field variables, affecting the parts manufacturing by liquid composite molding (LCM). Here, the filling characterization of woven fabrics used in LCM is done using one-way coupled simulations. Once RUC geometry is characterized by scanning-electron microscopy (SEM), and stereomicroscopy, standard thickness test, and resin viscosity are measured, the multiphase finite volume method-volume of fluid (FVM-VOF) model of ANSYS Fluent is used for the three-dimensional filling of the RUC, incorporating an experimentally calibrated air entrapment parameter (λ) to consider air compressibility and dissolution; then, a lumped function for the coupling term with macroscopic equations is obtained in terms of volume-averaged variables. This function is used in the equivalent Darcy macroscopic model, which is solved using a dual-reciprocity boundary element method (DR-BEM) algorithm. By considering a single value of λ during the simulation, neglecting wicking effects, and normalizing physical variables, unified injection pressure-independent results for the local tows saturation and normalized pressure fields at mesoscopic scale were obtained, as well as for global tows saturation and normalized pressure and fluid front profiles at macroscopic scale, thus simplifying the filling characterization of reinforcements. Numerical results are coherent with unidirectional injection experiments at both scales.

The micro-structure of rock essentially affects its macroscopic mechanical behaviors. Based on the grain-based discretized virtual internal bond (GB-DVIB) model, an improved version of the model is developed to investigate the gain-scale, micro-cracking process. Compared with the original GB-DVIB model, a more realistic micro-structure of granular rock is generated by the improved model. A micro-structure generation method is developed to generate different types of mineral grains, grain boundaries, and voids. Based on the relationship between macro- and micro-parameters in the DVIB model, the mechanical parameters of micro-structure obtained by experiments can be employed to calibrate the micro-bond parameters directly. The ability of the improved GB-DVIB model in modeling tensile and compression-shear failure is verified by the simulation of a three-point-bending test and an asymmetric compressive test, respectively. The detailed micro-cracking process of a granite sample is investigated by the simulation of uniaxial compression and tension tests, and the intra-granular and inter-granular cracks both can be reproduced. The simulated results show that the micro-cracks generated in the uniaxial compression test are much larger than the uniaxial tension test. The intra-granular and inter-granular cracks both play important roles in rock compression failure, while the inter-granular cracks play a dominant role in rock tensile failure. For the convenience of the application of the improved GB-DVIB model, the effect of mechanical parameters of micro-structure, grain size, geometric heterogeneity, and porosity on the rock macroscopic mechanical behavior is systematically investigated. Due to the different mechanisms of tension and shear failure, the influence of micro-structure on rock compression and tension failure also varies. The improved GB-DVIB model can effectively generate the micro-structure of granular rock and provides a convenient and effective tool for researching the gain-scale, micro-cracking process of granular rock.

Implant osseointegration is an important factor dictating its long-term efficacy in situ. Along with various biological factors, it is greatly influenced by the mechanical stimulus at the peri-implant bone. The present study aims to understand the biomechanical response of progressive thread dental implants using multi-scale-based finite element analysis employing macro and micro models of bone. μ-CT images of a cadaveric human mandible of its premolar region were obtained, along with CT scan of the same region to generate computational models. Total of six dental implants were designed having regular and progressive thread depths. Three different stages of healing of the bone-implant assembly were simulated parametrically. The biomechanical environment at the peri-implant bone was analyzed considering the 'Mechanostat' hypothesis. The obtained results revealed that bone strain is significantly higher during the initial healing phase when the bone is weakest. During this phase, implant stress and its displacement in both buccolingual and coronoapical directions are also noticeably higher. Also, displacements of progressive thread implants were lower in all the healing phases as compared to the implants with constant thread depth. The observations of this μ FEA study highlights the clinical applicability of a progressive thread dental implant as it generates larger functional surface area, thus engages higher trabeculae and therefore is suitable for weaker bone conditions. Furthermore, by comparing the stress values at bone and implant between the two bone models, the CT-based model having inhomogeneous material was deemed suitable as an alternative to computationally expensive μ FEA.

We have great pleasure in presenting this special issue of the International Journal for Multiscale Computational Engineering (IJMCE) on multiscale micromechanical modeling of damage in polycrystalline materials. The modeling of damage in polycrystalline materials is an enduring challenge in computational simulation, due largely to the disparate length scales associated with the physical mechanisms of damage, material heterogeneities, rare-event statistics, and engineering geometries. Complications arise in the resolution of lattice-scale heterogeneities, modeling nonlinear inelastic material response, and treatment of localization phenomena associated with the onset of damage that causes physical softening and ill-posedness. This complexity necessitates novel approaches in geometric modeling, meshing, constitutive modeling, damage modeling, computational mechanics, mathematics, and multiscale methods. The articles in this special issue include a coupled chemomechanical framework applied to modeling the effect of hydrogen on deformation and damage; a wavelet-enriched adaptive coupling of crystal plasticity and phase-field models; advancements in plasticity-damage formulations for crystalline materials; an investigation of the effect of preexisting defects on damage mechanisms in dual-phase steels; a peridynamic model and associated upscaling approach for capturing the effects of microstructure on tensile failure in additively manufactured steel; and, lastly, the extension of a Gurson-Tvergaard-Needleman ductile damage model to include a Hill's yield criterion. By highlighting these recent developments, we hope that this IJMCE special issue provides groundwork and inspiration for future advancements in multiscale computational modeling of polycrystalline materials.

In this work, a thermoviscoplastic GTN ductile damage model is extended to account for anisotropic plastic behavior. The novel feature of the proposed model is the enrichment of a GTN model, with the Hill's yield criterion accounting for hardening, softening, strain-rate effect, plastic work heating, thermal diffusion, and void shearing mechanism. The anisotropy is introduced by changing the equivalent stress definition, which provides greater flexibility to the model. The resultant modifications in the yield criterion and in the damage evolution equations are described. Two numerical problems involving plates subjected to tension loading that leads to ductile damage and eventual fracture are presented and discussed in order to validate the present approach. A mixed finite element formulation is adopted together with the fully damaged zone technique to represent the ductile fracture. Results obtained through computational simulations highlight the effect of the anisotropic parameters on mechanical behavior in terms of the global stress-strain curve and the local evolution of plastic strains, porosity and temperature. We conclude that the proposed anisotropic model is simple to implement yet provides more flexibility in capturing complex ductile fracture processes.

Mechanics has been a fundamental tool and principal motivation for the development of basic sciences and engineering. Its use has recently been extended from macroscopic to microscopic and nanoscopic scales and phenomena. A particular methodology in this direction is the generalization of classical theories of elasticity, plasticity, and failure through the introduction of higher order gradients of the pertinent variables and corresponding internal lengths. This article, writ-ten in honor of a charismatic contributor in the field of generalized continuum mechanics, Professor Patrizia Trovalusci, begins with a simple paradigm of how to extend standard thermoelasticity theory to its gradient counterpart. It then provides a number of other examples ranging from strength of materials and stress concentrations to plastic flow and failure.

By investigating the benefits and shortcomings of the existing form of continuous defect theory (CDT) and using recent advancements in size-dependent continuum mechanics, we develop a fully coherent theoretical framework, denoted as Consistent Continuous Defect Theory (C-CDT). Among several important potential applications, C-CDT may provide a proper foundation to study the continuum theory of crystal plasticity. The development presented here includes an examination of the character of the bend-twist tensor, Weingarten's theorem, Burgers and Frank vectors, continuous dislocation and disclination density tensors, and the dualism between geometry and statics of CDT based on couple stress theory (CST). Then, by using Consistent Couple Stress Theory (C-CST), the new C-CDT is derived in a totally systematic manner. In this development, the geometry of C-CDT is dual to the statics formulation in C-CST. Previously, the fundamental step in the creation of C-CST was recognizing the skew-symmetric character of the couple-stress tensor, which requires the skew-symmetrical part of the bend-twist tensor to be the additional measure of deformation in size-dependent continuum mechanics. Via Weingarten's theorem and arguments from C-CST, we establish that in defect theory the dislocation density tensor must be skew-symmetric and thus can be represented by an equivalent dislocation density vector. In addition, we investigate the character of a classical version of C-CDT with unexpected consequences. For full consistency, there can be no continuous dislocation density tensor within classical continuum mechanics, and the continuous disclination density tensor becomes symmetric. This clearly is analogous to the absence of couple-stresses and the symmetry of force-stresses in classical continuum mechanics.