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There has been a huge interest in recent years in using phase -field theories for numerical analyses of fracture phenomena. However, in phase -field fracture theories, a critical aspect often involves a decomposition of the strain energy density to select physically trustworthy crack paths and to prevent interpenetration of crack surfaces. This aspect becomes even more critical in the case of mixed -mode loading under compression. To overcome these challenges, a hydrostatic-spectral-deviatoric decomposition, enhanced by separate critical energy release rates for different fracture modes, is employed in this study. In order to evaluate the enhanced decomposition strategy, a set of biaxially loaded crack experiments in global compression is designed. Samples of different geometries contain multiple flaws and holes. The experiments are numerically simulated using a unified set of material parameters and three different strain energy decomposition methods (i.e., hydrostaticspectral-deviatoric, spectral and hydrostatic-deviatoric). Simulations using the hydrostatic-spectral-deviatoric decomposition scheme capture both intricate crack paths and critical loads in the experiments. The enhanced decomposition strategy seems capable of simulating the experiments with reasonable precision, in sharp contrast to the two commonly used decomposition strategies (spectral and hydrostatic-deviatoric).

This research endeavors to investigate the geometrically nonlinear dynamic characteristics of Carbon Nanotubes (CNTs) while incorporating size effects based on the Second Strain Gradient (SSG) elasticity theory. To this end, the nonlinear governing equations and its corresponding boundary conditions are deduced in alignment with the Green-Lagrange strain tensor and Hamilton's principle. Concurrently, the weak form is expounded through the utilization of the C3 continuum Hermite interpolation functions, which ensure the continuity and smoothness of higher -order strain and displacement fields. Subsequently, a perturbation methodology is introduced, incorporating nonlinear phenomena into the context of linear wave propagation within the framework of periodic structures theory. The wave propagation characteristics manifest a pronounced disparity between the models based on linear SSG theory and those through nonlinear SSG theory with stiffness hardening phenomenon. In contrast to the zigzag CNTs, armchair CNTs evince an elevated aptitude for wave control. The application of nonlinear SSG theory in combination with the wave finite element method is significant for comprehending the wave propagation characteristics of complex CNTs.

The exploration of graphene has attracted extensive interest owing to its significant structural and mechanical properties. In this research, we numerically investigate wave propagation in defect -free single -layer graphene, considering its geometrically nonlinear behavior through second -strain gradient elasticity. To capture the geometric nonlinearity, firstly, the nonlinear strain-displacement relations are introduced. The governing equation and associated boundary conditions are derived using Hamilton's principle. Then, the weak form, including the element matrices, is established. The eigenvalue problem is solved for 2D wave propagation through periodic structures theory. Finally, the dynamical properties such as band structures, mode shapes, energy flow, and wave beaming effects are analyzed. The numerical results reveal that the geometric nonlinearity through the second strain gradient influences the wave propagation characteristics in graphene. The findings are significant and contribute to the understanding of graphene's dynamic response, with implications for the engineering applications of graphene-based nanostructures.

Hydrogen-induced fracture of X65 pipeline steel under in -situ electrochemical charging is investigated by using slow strain-rate tensile (SSRT) test, hydrogen diffusion test, fractography analysis, and finite element simulation. Smooth and notched tensile specimens with varying notch radii are utilized to ascertain the impact of stress triaxiality on hydrogen embrittlement (HE) susceptibility. A fully coupled model, H-CGM+, capable of simulating the synergy between hydrogen-enhanced plasticity and decohesion, is employed. The simulation proficiently replicates both the global stress-strain trajectories and the local failure initiation sites of the in -situ SSRT tests. The findings indicate a predominance of dislocation trapping hydrogen mechanism in HE, with crack inception at the notch surface where local plastic strain peaks, subsequently advancing towards the center of the specimen. Notably, an inverse relationship is observed between HE susceptibility and stress triaxiality. A hydrogen-induced failure criterion, defined as a critical combination of local hydrogen concentration and plastic strain, is derived. The failure criterion is found to be independent of stress triaxiality, which serves as a good reference for safety assessment of hydrogen pipelines.

Exploring the wave propagation in nano-waveguides enables the development of on -chip nano -resonators, leading innovative capabilities that enhance acoustics and micro -mechanics. This paper conducts a numerical investigation into the dynamic properties of periodic nano-waveguides. The Second Strain Gradient (SSG) elasticity, which captures the size effects, is used in the determination of the constitutive relations. The weak form including the element matrices is deduced by the Hamilton's principle. Furthermore, a finite element method, based on the periodic structure theory, is introduced to explore the free wave propagation by solving the eigenvalue problems. The stiffness hardening phenomenon manifested in the dispersion curves, band structures, and energy flow vector fields is discussed. The sensitivity of higher order parameters existing in the SSG theory is analyzed. The numerical investigation for wave propagation in the periodic nano-waveguides through the SSG theory is an innovative work, highlighting the significance of the proposed methodology in explaining the special dynamic characteristics of complex nano-waveguides.

Physical systems are modeled by field equations; these are coupled, partial differential equations in space and time. Field equations are often given by balance equations and constitutive equations, where the former are axiomatically given and the latter are thermodynamically derived. This approach is useful in thermomechanics and electromagnetism, yet challenges arise once we apply it in damage mechanics for generalized continua. For deriving governing equations, an alternative method is based on a variational framework known as the extended Noether's formalism. Its formal introduction relies on mathematical concepts limiting its use in applied mechanics as a field theory. In this work, we demonstrate the power of extended Noether's formalism by using tensor algebra and usual continuum mechanics nomenclature. We demonstrate derivation of field equations in damage mechanics for generalized continua, specifically in the case of strain gradient elasticity.

Highly anisotropic materials like wood and unidirectional polymer composite structures are sensitive to shear deformations, in particular close to fixed joints. Large wooden structures in buildings and, e.g. wind-turbine blades, are designed to last for decades, and hence are susceptible to unwanted creep deformations. For improved structural design, the shear-creep properties of the material are needed. These are rarely available in the literature, possibly because of technical difficulties to achieve a well-defined shear-stress state in test specimens. For cost-efficient testing, this goal of a pure stress state necessarily needs to be compromised. In the present study, we propose a simple test method based on uniaxial compression on wooden cubes, but is equally applicable for fibre composites. The viscoelastic shear properties of Norway spruce (Picea abies) under off-axis creep compression tests have been characterised in all three directions. The tests are performed in a controlled climate chamber and the creep strains are captured using digital-image correlation.

Background and objective Accurate numerical and physical models of trabecular bone, correctly representing its complexity and variability, could be highly advantageous in the development of e.g. new bone-anchored implants due to the limited availability of real bone. Several Voronoi tessellation-based porous models have been reported in the literature, attempting to mimic the trabecular bone. However, these models have been limited to lattice rod-like structures, which are only structurally representative of very high-porosity trabecular bone. The objective of this study was to provide an improved model, more representative of trabecular bone of different porosity. Methods Boolean operations were utilized to merge scaled Voronoi cells, thereby introducing different structural patterns, controlling porosity and to some extent anisotropy. The mechanical properties of the structures were evaluated using analytical estimations, numerical simulations, and experimental compression tests of 3D-printed versions of the structures. The capacity of the developed models to represent trabecular bone was assessed by comparing some key geometric features with trabecular bone characterized in previous studies. Results The models gave the possibility to provide pore interconnectivity at relatively low porosities as well as both plate- and rod-like structures. The mechanical properties of the generated models were predictable with numerical simulations as well as an analytical approach. The permeability was found to be better than Sawbones at the same porosity. The models also showed the capability of matching e.g. some vertebral structures for key geometric features. Conclusions An improved numerical model for mimicking trabecular bone structures was successfully developed using Voronoi tessellation and Boolean operations. This is expected to benefit both computational and experimental studies by providing a more diverse and representative structure of trabecular bone.

This thesis addresses the intricate mechanical behaviour of natural materials, with a particular focus on wood. Despite millennia of use, understanding the mechanical behaviour of wood materials remains challenging due to their complex microstructures. For instance, they exhibit variations in properties among samples, nonlinear behaviour under elevated loads, and are sensitive to alterations in moisture content. Wood and related natural biobased materials hold immense potential due to their renewability, cost-effectiveness, eco-friendliness, and ease of use in sustainable construction. Wood boasts remarkable stiffness and strength along its primary axis, surpassing many man-made materials in strength-to-weight ratios. However, its anisotropic and heterogeneous nature gives rise to challenges, necessitating the consideration of multiple parameters for accurate characterization to be used in design. Wood is intrinsically heterogeneous, leading to considerable variations in local stresses and deformations during loading. To address these microstructural effects on macroscopically measurable phenomena, mathematical homogenization methods, established since the 1970s, have found applications in material mechanics, including both fibre composites and wood. In recent years, there has been a growing focus on the viscoelastic behaviour of composites and timber structures, given their increased long-term use in load-carrying applications. While numerous investigations have explored the relationship between the microstructure of wood and its elastic properties, few studies have explored the connection between microstructure and viscoelastic properties. The thesis focuses on the static and, more notably, on the time-dependent mechanical properties of wood, bridging the gap from cell-wall creep to structures. It includes experiments and numerical work, culminating in the development of a material model suitable for orthotropic materials like wood. The multiscale model establishe

In the present study, a numerical multiscale model is made to show how the hierarchical structure of softwood affect its macroscopic viscoelastic properties. The performance of the model is demonstrated for two softwood species — Norway spruce and Japanese cypress, whose creep behavior has been characterized experimentally. The results show that by using the same transversely isotropic viscous properties of the cell wall for both species, it is possible to predict creep deformation relatively close to experimental creep measurements for both species. Assuming that the variability is larger on the microstructural level (density, cell-wall geometry, microfibril angle, composition of wood tissues) than on the cell-wall level, it is possible to predict the macroscopic creep behavior based on the microstructural parameters alone. Such predictions can potentially save cost and time, since creep characterization in all material directions is demanding.

A dynamic phase-field fracture finite element model is applied to discretized high-resolution three-dimensional computed tomography images of human trabecular bone to analyse rapid bone fracture. The model is contrasted to quasi-static experimental results and a quasi-static phase-field finite element model. The experiment revealed complex stepwise crack evolution with multiple crack fronts, and crack arrests, as the global tensile displacement load was incrementally increased. The quasi-static phase-field fracture model captures the fractures in the experiment reasonably well, and the dynamic model converges towards the quasi-static model when mechanically loaded at low rates. At higher load rates, i.e., at larger impulses, inertia effects significantly contribute to an increased initial global stiffness, higher peak forces and a larger number of cracks spread over a larger volume. Since the fracture process clearly is different at large impulses compared to small impulses, it is concluded that dynamic fracture models are necessary when simulating rapid bone fracture.

In additive manufacturing, also called 3-D printing, one of widely used materials is polylactide thermoplastic polymer (PLA) by means of the fused deposition modeling. For weight reduction purposes, infill density is an often used feature in slicing for 3-D printing. We aim at investigating the effect of infill density on the mechanical properties of structures. Therefore, we demonstrate how to prepare tensile specimens and test them by a universal testing machine. Results are collected by a so-called digital image correlation method. As infill density increases, from 10% to 100%, the nominal strain at break decreases from about 2.1% to 1.2%, respectively. In other words, the material becomes more ductile by decreasing the infill density of PLA material, which is possible to justify with an effect of the microstructure created by the infill density. Furthermore, we discuss a possible material model fitting all the presented results and report that a hyperelastic material model is needed for the PLA. We utilize Neo-Hookean, Mooney–Rivlin, and Yeoh models, all for different infill densities. All three models show a fairly good agreement to the experimental data. Neo-Hookean model has an advantage of only one parameter, which increases monotonously with infill density.

In this work, parallel plate capacitors are numerically simulated by solving weak forms within the framework of the finite element method. Two different domains are studied. We study the infinite parallel plate capacitor problem and verify the implementation by deriving analytical solutions with a single layer and multiple layers between two plates. Furthermore, we study the finite parallel plate capacitor problem and verify it by Love’s potential equation and Xiang’s capacitance equation. Moreover, the fringing effect is considered and extended to problems with multiple dielectric layers, such a solution is not possible by means of the existing analytical solutions. Besides, we realize the possibility of choosing different boundary conditions (electric potential boundary conditions and charge density boundary conditions) by changing the weak form. Finally, a transient solution that includes dielectric loss and calculates the quality factor of a capacitor is presented, which may be used in capacitor design. Convergence and consistency of results are demonstrated by comparing the results between analytical and numerical solutions and also the results from different boundary conditions.

A fundamental understanding of the interaction between microstructure and underlying physical mechanisms is essential, especially for developing more accurate multi-physics models for heterogeneous materials. Effects of microstructure on the material response at the macroscale are modeled by using the generalized thermomechanics. In this study, strain gradient theory is employed as a higher-order theory on the macroscale with thermodynamics modeled as a first-order theory on the microscale. Hence, energy depends only on the temperature such that we circumvent an extension of Fourier’s law and analyze the “simplest” thermo-mechanical model in strain gradient elasticity. Developing multiphysics models for heterogeneous materials is indeed a challenge and even this “simplest” model in generalized thermomechanics creates dozens of parameters to be determined. We develop a thermo-mechanical framework, in which microstructure is modeled as a periodic structure and through asymptotic homogenization approach, higher-order parameters at macroscopic scale are calculated. To illustrate the importance of higher-order parameters in overall thermo-mechanical response of a heterogeneous materials, finite element method (FEM) is employed with the aid of open-source codes (FEniCS). Verification example of a bulk system and several case studies of porous structures demonstrate how such numerical framework can be beneficial in the design of materials with tailored microstructures.

This paper presents a large experimental campaign and the corresponding analysis quantifying mortar curing effects on the pull-out performance of bonded anchor systems. Standard confined pull-out tests were performed on two commonly used adhesive anchor systems. The two investigated bonded anchor systems were based on different materials, where the mortar of the first bonded anchor system (BAS-VE) was a vinyl-ester based product and the second bonded anchor system (BAS-EP) contained an epoxy-based mortar. In order to isolate the mortar curing effects on the anchor performance, a mature concrete was used as base material minimizing well-known aging and curing effects related to the substrate, concrete. In total, 93 pull-out tests were performed for various curing times in order to characterize influences on bond strength, stiffness, and peak displacement. Depending on the product specifications and corresponding approval documents, tests were carried out in a time-range of a few minutes up to three months after the anchor installations. Measured temperature (and humidity histories) of the environment have been utilized for predicting the mortars’ degree of cure for each structural anchor test. The results show a cure-dependent behavior in BAS-VE and BAS-EP. Although the bond strength fails to increase significantly after reaching the manufacturer approved minimum curing time, the stiffness shows an increase for longer cured anchors.

Dynamic failure in advanced ceramic materials is a complex mechanical phenomenon, which is challenging to study in experimental and computational works. This work models and investigates the crack initiation, growth, propagation, and branching in two-dimensional single crystalline boron carbide at the nanometer length-scale and picosecond time-scale. A phase-field approach is used by carefully selecting the interfacial energy allowing a monolithic numerical solution method capturing strong coupling between mechanics and damage. Specifically, the transient Ginzburg–Landau equation is coupled with the balance of momentum including geometric nonlinearities and solved by using the open-source computing platform FEniCS. The monolithic computation ensures necessary accuracy for dynamic fracture under pure mode I loading, and also demonstrates the capability of crack branching depending on the loading rate. The effect of crack regularization length and kinetic coefficient on the crack interface profile and crack tip velocity is also studied. Altogether, the results are important for modeling anisotropic fracture in advanced ceramics and designing materials with desired dynamic failure characteristics.

As a non-destructive inspection method, micro-computed tomography has been employed for determining local properties of a cellulose-based product, specifically pressboard. Furthermore, by utilizing the determined properties in a detailed numerical model, by means of a finite element analysis, we demonstrate a continuum anisotropic viscoelastic-viscoplastic model. Through such a combination of non-invasive experiments with accurate computations in mechanics, we attain a better understanding of materials and its structural integrity at a pre-production stage increasing the success of the first prototype. In detail, this combination of micro-computed tomography and finite element analysis improves accuracy in predicting materials response by taking into account the local material variations. Specifically, we have performed indentation tests and scanned the internal structure of the specimen for analysing the densification patterns within the material. Subsequently, we have used a developed material model for predicting the response of material to indentation. We have computed the indentation test itself by simulating the mechanical response of high-density cellulose-based materials. In the end, we have observed that pressboard, having initially a heterogeneous density distribution through the thickness, shows a shift in the densification to the more porous part after indentation. The densification maps of the simulated results are presented by comparing with the experimental results. A reasonable agreement is observed between the experimental and the simulated densifications patterns, which suggests that the proposed methodology can be used to predict densification also for other fibre-based materials during manufacturing or in service loading.

In percussive drilling of rock, use is made of high-amplitude short-duration force pulses generated through impacts of a hammer on a drill bit or a drill rod assembly. The mass of the hammer is crucial for the impact velocity and the impact frequency, while its length and variation of characteristic impedance control the duration and shape of the force pulses. High efficiency of conversion of kinetic impact energy to work results if the force pulses have suitable shapes and durations. Commonly, hammers of hydraulic rock drills are nearly uniform and generate nearly rectangular force pulses admitting high efficiencies. When space is constrained, short hammers are advantageous as they allow short rock drills. Here, therefore, shorter substitutes for uniform original hammers are sought. They should have the same mass as the original hammer, be shorter than the original hammer, and generate approximately the same impact force history as the original hammer. A method based on 1D theory is developed for realization of substitute hammers with axially periodic characteristic impedance. Impact force histories generated by such hammers agree well with that generated by a uniform original hammer in a 1D context, and also in a 3D context if 3D effects are small enough. Also, for bit-rock interaction conditions from soft to hard, the efficiencies obtained by use of substitute hammers agree well with that obtained by use of the original hammer.

Lattice materials are artificial materials made of repeating unit-cells. The internal architecture of these materials can be engineered for a specific application such as energy absorption, heat transfer, or acoustic damping. The advancements in additive manufacturing have enabled the design and fabrication of lattice materials with complex geometries, but the lack of understanding about their mechanical performance has limited their application. This thesis investigates the mechanics of lattice materials via numerical simulations and mechanical tests. We start with development of a discrete homogenization scheme for the elastic analysis of lattice materials with arbitrary level of complexity. Next, the method is extended to a continuum elastoplastic homogenization and accompanied with the theory of critical distances to assess the low cycle fatigue behaviour of lattice materials. Following that, the model is coupled with continuum damage mechanics to mimic the fracture initiation of the material unit-cell under quasi-static loads. The proposed model is calibrated using tensile tests, leading to a defect-informed numerical model that accommodates the manufacturing imperfections. Following this, an environmentally assisted failure known as hydrogen embrittlement is studied by incorporating hydrogen failure mechanisms into elastoplastic homogenization model. In the next step, numerical simulations and compression tests are employed to analyze the mechanical coupling and elastic anisotropy in the so-called non-regular tetrahedron lattice. The results show a good correspondence but the periodicity assumption in computational homogenization –mimicking an infinite cell number–should be considered when comparing numerical results with the data obtained from real samples. To capture the size effect, as the final step, we develop a homogenization scheme based on strain-gradient elasticity. The model is verified using numerical and experimental three-point bending tests and h

Mechanical coupling in architectured materials has been traditionally investigated in the context of generalized continuum mechanics and is often assumed to be non-existent in the framework of classical continuum mechanics. In this paper, we challenge this misconception and study an anisotropic architectured material exhibiting shear-shear and shear-normal coupling from the standpoint of classical continuum mechanics. The material is non-regular tetrahedron lattice, a potential candidate for biomedical implants, but the lack of understanding about its anisotropic behavior and mechanical couplings has limited its application. We exploited the unit-cell definition with periodic boundary conditions and performed elastic and elastoplastic homogenizations. Non-zero coupling sub-matrices appeared in the homogenized elasticity matrix, which we further transformed into material’s natural coordinate system using elastic distance function. This allowed for anisotropy identification and determination of all the coupling parameters. Next, compression tests are conducted on laser powder bed fused Al-12Si (mass%) lattice samples with different relative densities and spatial orientations. Employing test data, mechanical anisotropy and shear-normal couplings are experimentally characterized. Both numerical and experimental results confirmed the presence of mechanical couplings and predicted a similar anisotropic tendency in the material. Finally, the role of manufacturing defects in deterioration of as-designed mechanical properties is discussed.

A known complication for mechanically loaded bone implants is the instability due to screw loosening, resulting in infection and the non-union of fractures. To investigate and eventually prevent such bone degradation, it is useful to know the stress state in the bone around the screw. Considering only in-plane loadings and simplifying the mandibular bone into an orthotropic laminated plate, the analysis was reduced to a two-dimensional pin-loaded plate problem. An analytic model, based on the complex stress analysis, was introduced to the bone biomechanics field to obtain the stress distributions around the screw hole in the bone. The dimensionless normalized stresses were found to be relatively insensitive to the locations of the screw hole over the mandible. Parametric analyses were carried out regarding the friction coefficient and load direction. It was found that the load direction had a negligible influence. On the contrary, the friction coefficient had a significant effect on the stress distributions. Whether the screw was well bonded or not thus played an important role. The proposed analytic model could potentially be used to study bone failure together with stress-based failure criteria.

The literature in the field of higher-order homogenization is mainly focused on 2-D models aimed at composite materials, while it lacks a comprehensive model targeting 3-D lattice materials (with void being the inclusion) with complex cell topologies. For that, acomputational homogenization scheme based on Mindlin (type II) strain gradient elasticity theory is developed here. The model is based on variational formulation with periodic boundary conditions, implemented in the open-source software FreeFEM to fully characterize the effective classical elastic, coupling, and gradient elastic matrices in lattice materials. Rigorous mathematical derivations based on equilibrium equations and Hill-Mandel lemma are provided, resulting in the introduction of macroscopic body forces and modifications in gradient elasticity tensors which eliminate the spurious gradient effects in the homogeneousmaterial. The obtained homogenized classical and strain gradient elasticity matrices are positive definite, leading to a positive macroscopic strain energy density value—an importantcriterion that sometimes is overlooked. The model is employed to study the size effects in 2-D square and 3-D cubic lattice materials. For the case of 3-D cubic material, the model is verified using full-field simulations, isogeometric analysis, and experimental three-point bending tests.The results of computational homogenization scheme implemented through isogeometric simulations show a good agreement with full-field simulations and mechanical tests. The developed model is generic and can be used to derive the effective second-grade continuum forany 3-D architectured material with arbitrary geometry. However, the identification of the proper type of generalized continua for the mechanical analysis of different cell architectures is yet an open question.

Additive manufacturing techniques, especially fused deposition modelling (FDM) based polymer 3-D printers are opening new possibilities in engineering design. Multiscale structures have a macroscale and miscroscale geometry. Composite materials are available as filaments allowing multiphysics applications. Microscale structure or even heterogeneous materials cause deviations from predictions of the materials response by using the classical first-order theory. Hence, we use the secondorder modeling in mechanics and study how to determine additional constitutive parameters that arise with the strain gradient theory. Different homogenization methods are demonstrated to result in differing material parameters based on assumptions used in modeling.

The quality of wirebond interconnects is characterized by shear and pull tests. For such a simulation we need an adequate damage model, since a purely elasto-plastic model fails to give the full picture [1]. For the description of damage, the Lemaitre damage model is selected, because this model is already used in comparable blanking simulations [2]. In addition, the main damage-driving factor of this damage model is the equivalent plastic strain, which is known to be the suitable failure criteria for ductile materials. The model, introduced by Lemaitre in 1985, is for isotropic ductile damage [3]. It has been used and extended in many other works. Still, more than three decades later, modelling free evolving multiaxial damage is often a more scientific topic and has not yet been proven a sufficient engineering tool to investigate destructive tests by numerical simulation. Reducing the amount of tests has been and still is a demand to save time in the design process. Therefore, it is needed to further investigate the capabilities of such damage models on complex applications. Indeed, the damage parameters first need and will be determined in this study for the material used in the application.

Especially at high frequencies, as they occur in 5G or relevant applications, electromagnetism in electronic components plays a significant role in system behavior. Moreover, dissipative effects are triggered by mechanical deformation. Indeed, dissipation is an energy loss and thus the industry tries to minimize this effect by optimizing the design. We examine this justification by using multiphysics simulations by means of the Finite Element Method (FEM) and solve deformation and dissipative dielectric material equations for a simple electronic component in a monolithic manner.

This work concerns the probabilistic analysis of particle-based materials. More precisely, this work is devoted to the stochastic modeling of the geometric and constitutive microscale parameters associated with particle-pair interactions of an existing model for particle-based materials. Such an issue is addressed with a probabilistic methodology that relies on the maximum entropy principle from information theory. After defining and improving the chosen second-gradient continuum model for particle-based materials, it is shown that for micro-homogeneous and micro-isotropic materials, the involved microscale parameters turn out to be statistically independent. More precisely, the particle-pair distance between two consecutive particles is a uniformly distributed random variable and the specific micro-scale stiffness parameters are Gamma-distributed random variables. A homogeneous and isotropic 2D concrete plate subjected to an axial load is considered for illustration purposes. A stochastic solver based on Monte Carlo numerical simulations and mixed finite element (FE) method are chosen. The FE discretization is applied to the weak formulation of the equivalent continuum model with random mechanical properties. On the contrary, the particle-pair distance and the micro-scale stiffness parameters, which are the parameters of the boundary value problem formulated for the equivalent continuum model, are modeled as random variables. Finally, uncertainties propagation is discussed and statistical fluctuations of the macro mechanical response are found to be significant.

This study presents some results on the mechanical behavior of polylactide (PLA) material, produced using the fused deposition modeling (FDM) additive manufacturing technique. We investigate the effect of infill density on the mechanical properties of PLA specimens. We used tensile specimens, prepared according to ISO 527-2 standard, and tested them by a universal testing machine with analysis by means of digital image correlation (DIC) method. The results in terms of UTS and nominal strain at break of PLA material are presented. They demonstrate a significant impact of infill density on material behavior of PLA specimens, as expected. Yet the effect is nonlinear that is indeed valuable to understand. As infill density increases, from 10% to 100%, the nominal strain at break decreases from about 2.1% to 1.2%, respectively. In other words, the material becomes more ductile by decreasing the infill density of PLA material, which is possible to justify with an effect of the microstructure created by the infill density. There is a transition of this observed behavior, from being more ductile to more brittle, by increasing the infill density of the PLA specimens.

The elastic modulus at the single trabecular level is an important parameter for the understanding of the mechanical behavior of trabecular bone. Current methods are commonly limited by the irregular trabecular shape and the accuracy of displacement measurement. The aim of this study was to propose a method to estimate the trabecular modulus overcoming some of these limitations. For high-precision displacement measurements, insitu compression within a synchrotron radiation based X-ray tomograph was used. Trabecular displacements were subsequently estimated by a global digital volume correlation algorithm, followed by high-resolution finite element analyses to account for the irregular geometry. The trabecular elastic moduli were then estimated by comparing the loads from the finite element analyses with those of the experiments. With this strategy, the average elastic modulus was estimated to 3.83 +/- 0.54 GPa for three human trabeculae samples. Though limited by the sample size, the demonstrated method shows a potential to estimate the mechanical properties at the single trabecular level.

Mechanical behavior of additively manufactured lattice materials has been mainly investigated under uniaxial compression, while their performance under uniaxial and multiaxial tension are yet to be understood. To address this gap, a generic elastoplastic homogenization scheme with continuum damage model is developed, and three different lattice materials, namely cubic, modified face-center cubic and body-center cubic, are analyzed under uniaxial, biaxial and triaxial tension. The influence of micro-architecture on the material's failure behavior as well as its macroscopic mechanical performance is thoroughly discussed. For validation, a set of uniaxial tensile experiments are conducted on functionally graded cubic lattice samples that are additively manufactured using Electron Beam Melting (EBM) process. Digital image correlation technique is employed to obtain the macroscopic stress-strain curves, and manufacturing imperfections are inspected using light omitting microscopy. It turns out that the behavior of as-built samples could substantially differ from numerical predictions. Thus, a defect-informed numerical model is employed to accommodate the effect of imperfections. The outcome is in a very good agreement with experimental data, indicating that with proper input data, the developed scheme can accurately predict the mechanical and failure behavior of a given lattice material.

A general simulation framework for modelling ductile-to-brittle transition in metals is proposed. The method combines the complete Gurson model and cohesive zone model, which brings ductile and brittle fracture mechanisms into one play. We found that the transition of failure mode is the result of a competition between fracture due to micro-void growth and coalescence and fracture in the cohesive zone. It is found that the fracture mode is dependent on the ratio between the cohesive strength and the yield strength of the material; brittle fracture only occurs when the strength ratio is below a critical value. This generic rule can be used to rationalize various failure scenarios featured by ductile-to-brittle transition, such as low temperature embrittlement and hydrogen embrittlement. As an application of the general framework, hydrogen embrittlement is simulated. It is revealed that a critical hydrogen concentration has to be achieved in order to trigger brittle fracture, which is consistent with many experimental observations.

Microstructure related deviation from elastic response is known as "size-effect."Metamaterials - for example modeled by strain gradient elasticity - capture this effect adequately by means of additional parameters to be determined. We employ a methodology based on asymptotic homogenization in order to obtain metamaterials parameters and then present the influence of these additional parameters by using simulations. By means of the finite element method, we solve metamaterials deformation modeled by the strain gradient elasticity. The implementation is established by open-source packages (FEniCS) for a realistic, composite structure with round and oval inclusions.

Axial impact between two elastic rods with piecewise constant characteristic impedance is considered. The distribution of characteristic impedance of the impacted rod and the impact velocity are given. By use of a 1D recursive algorithm, the characteristic impedances of the impacting rod are determined as long as they are all positive so that a prescribed impact force is realized. A condition for positivity of the characteristic impedance is derived in terms of transmission coefficients for wave energy. At the time from which positivity of all characteristic impedances cannot be maintained, or earlier, the characteristic impedance of the impacting body is continued, e.g., at the level of the last positive characteristic impedance or at level zero corresponding to cutting off the impacting rod. Examples of prescribed exponentially decreasing and linearly increasing impact forces are presented for a uniform impacted rod with constant characteristic impedance. In these examples, there is good agreement between the prescribed impact force and the impact force obtained from 3D FE simulation with a piecewise linear diameter of the impacting body that approximates the piecewise constant diameter obtained by use of the 1D recursive algorithm.

Strain gradient theory is an accurate model for capturing the size effect and localization phenomena. However, the challenge in identification of corresponding constitutive parameters limits the practical application of the theory. We present and utilize asymptotic homogenization herein. All parameters in rank four, five, and six tensors are determined with the demonstrated computational approach. Examples for epoxy carbon fiber composite, metal matrix composite, and aluminum foam illustrate the effectiveness and versatility of the proposed method. The influences of volume fraction of matrix, the stack of RVEs, and the varying unit cell lengths on the identified parameters are investigated. The homogenization computational tool is applicable to a wide class materials and makes use of open-source codes in FEniCS. We make all of the codes publicly available in order to encourage a transparent scientific exchange.

A novel numerical framework for low cycle fatigue analysis of lattice materials is presented. The framework is based on computational elastoplastic homogenization equipped with the theory of critical distance to address the fatigue phenomenon. Explicit description of representative volume element and periodic boundary conditions are combined for computational efficiency and elimination of the boundary effects. The proposed method is generic and applicable to periodic micro-architectured materials. The method has been applied to 2-D auxetic and 3-D kelvin lattices. The classical Coffin-Manson and Morrow models are used to provide fatigue life predictions (strain-life curves). Predicted fatigue lives for the auxetic lattice are shown to provide good correspondence to experimentally found fatigue lives from the literature.

Spinal fusion is the gold standard for treating patients with degenerative disc disease. Titanium alloys and PEEK are the two most common materials used to manufacture cages for spinal fusion, used to maintain disc height while the vertebrae fuse. Other materials, such as morselised bone, may be added to the cage to enhance the bioactivity. A monetite-based calcium phosphate has (as a composite implant in combination with titanium) shown potentially osteoinductive properties and may be a synthetic alternative to bone graft. Maximizing the ratio of calcium phosphate to titanium could be desirable to maximize bone ingrowth and fusion. Further, the calcium phosphate can be incorporated into the cage and stored ahead of surgery. The aim of this study was to topologically optimize cervical spine implants to incorporate a bioactive but mechanically weak material such as calcium phosphate.

Hydrogen embrittlement is a well-known source of cracking in metallic mechanical elements. This work studies the influence of hydrogen and carbides on the crack formation in a castnickel-alloy-component in a selective catalytic reduction system. It was found in literature that the alloy is prone to hydrogen embrittlement, and could therefore be a key factor in the crack formation. Cracks were found in the component, which is subjected to urea vapor (which contains a lot of hydrogen) at high temperatures. The propagation path of the crack seems to follow the carbide network in the material. From these observations two objectives for this project was formulated. The first objective of the work is to determine if hydrogen embrittlementis a plausible theory as a cause of the cracking. The second objective of this work is to investigate whether local stress levels in the vicinity of carbides is further raised by hydrogen. A modified boundary formulation of a crack tip is coupled with hydrogen diffusion, in order to realize the first objective. The coupled mechanical and diffusion problem is solved with a finite element model. The finite element model approximates the concentration of hydrogen that is diffused into the body during the working time, by the process of hydrogen diffusion for various parameters: hydrogen concentration in the crack, carbide trap density, carbide trap energy and more. A literature study is carried out and relevant intervals of such parameters is determined. It is found from the FE model that the concentration of hydrogen, 0.5mm ahead of the crack tip, can be approximately 1000 appm for smaller carbide trap energies (weak traps). For largercarbide trap energies (strong traps), the hydrogen concentration 0.5mm ahead of the crack tipcan be as high as 10000 appm and above. As a range of feasible hydrogen concentrations has been established, the second objective can be considered. The second objective is determined by considering dislocations and hy

Percutaneous Cement Discoplasty (PCD) is a surgical technique developed to relieve pain in patients with advanced degenerative disc disease characterized by a vacuum phenomenon. It has been hypothesized that injecting bone cement into the disc improves the overall stability of the spinal segment. However, there is limited knowledge on the biomechanics of the spine postoperatively and a lack of models to assess the effect of PCD ex-vivo. This study aimed to develop a biomechanical model to study PCD in a repeatable and clinically relevant manner. Eleven ovine functional spinal units were dissected and tested under compression in three conditions: healthy, injured and treated. Injury was induced by a papain buffer and the treatment was conducted using PMMA cement. Each sample was scanned with micro-computed tomography (CT) and segmented for the three conditions. Similar cement volumes (in %) were injected in the ovine samples compared to volumes measured on clinical PCD CT images. Anterior and posterior disc heights decreased on average by 22.5% and 23.9% after injury. After treatment, the anterior and posterior disc height was restored on average to 98.5% and 83.6%, respectively, of their original healthy height. Compression testing showed a similar stiffness behavior between samples in the same group. A decrease of 51.5% in segment stiffness was found after injury, as expected. The following PCD treatment was found to result in a restoration of stiffness—showing only a difference of 5% in comparison to the uninjured state. The developed ex-vivo model gave an adequate representation of the clinical vacuum phenomena in terms of volume, and a repeatable mechanical response between samples. Discoplasty treatment was found to give a restoration in stiffness after injury. The data presented confirm the effectiveness of the PCD procedure in terms of restoration of axial stiffness in the spinal segment. The model can be used in the future to test more complex loading scenar, This research has received funding from EIT Health(SOFTBONE, project nr 20519), supported by EIT, a body of the European Union, and from the European Union’s Horizon2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 812765.

A theoretical-computational framework is proposed for predicting the failure behavior of two anisotropic brittle materials, namely, single crystal magnesium and boron carbide. Constitutive equations are derived, in both small and large deformations, by using thermodynamics in order to establish a fully coupled and transient twin and crack system. To study the common deformation mechanisms (e.g., twinning and fracture), which can be caused by extreme mechanical loading, a monolithically-solved Ginzburg–Landau-based phase-field theory coupled with the mechanical equilibrium equation is implemented in a finite element simulation framework for the following problems: (i) twin evolution in two-dimensional single crystal magnesium and boron carbide under simple shear deformation; (ii) crack-induced twinning for magnesium under pure mode I and mode II loading; and (iii) study of fracture in homogeneous single crystal boron carbide under biaxial compressive loading. The results are verified by a steady-state phase-field approach and validated by available experimental data in the literature. The success of this computational method relies on using two distinct phase-field (order) parameters related to fracture and twinning. A finite element method-based code is developed within the Python-based open-source platform FEniCS. We make the code publicly available and the developed algorithm may be extended for the study of phase transformations under dynamic loading or thermally-activated mechanisms, where the competition between various deformation mechanisms is accounted for within the current comprehensive modeling approach.

In this work, the dynamical behavior of a pantographic structure undergoing large deformations is analyzed. A harmonic force is applied on the structure, while its motion in time is recorded by means of a high-speed camera system. The resulting displacement field is obtained via the digital image correlation (DIC) method for the whole domain. A parametric study with respect to the amplitude of the imposed force exhibits the appearance of non-linear effects in the system response as well as the presence of a so-called boundary layer region. Such geometric nonlinearities are of paramount interest for studying the accuracy of a potential computational model. Boundary layers are known to be effected by the microstructure, but their roles in the system response are yet to be comprehended. The experimental results obtained in this work may be used as a benchmark case in modeling metamaterials.

Infill density used in additive manufacturing incorporates a structural response change in the structure. Infill pattern creates a microstructure that affects the mechanical performance as well. Whenever the length ratio of microstructure to geometry converges to one, metamaterials emerge and the strain-gradient theory is an adequate model to predict metamaterials response. All metamaterial parameters are determined by an asymptotic homogenization, and we investigate the effects of infill density and pattern on these parameters. In order to illuminate the role of infill characteristics on the strain-gradient parameters, an in-depth numerical investigation is presented for one, widely used case in three-dimensional (3D) printers, rectangular grid.

Crack initiation and propagation as well as abrupt occurrence of twinning are challenging fracture problems where the transient phase-field approach is proven to be useful. Early-stage twinning growth and interactions are in focus herein for a magnesium single crystal at the nanometer length-scale. We demonstrate a basic methodology in order to determine the mobility parameter that steers the kinetics of phase-field propagation. The concept is to use already existing molecular dynamics simulations and analytical solutions in order to set the mobility parameter correctly. In this way, we exercise the model for gaining new insights into growth of twin morphologies, temporally-evolving spatial distribution of the shear stress field in the vicinity of the nanotwin, multi-twin, and twin-defect interactions. Overall, this research addresses gaps in our fundamental understanding of twin growth, while providing motivation for future discoveries in twin evolution and their effect on next-generation material performance and design.

Porous materials are widely used in engineering applications because of their high stiffness, strength, and low density. Those advantages are mainly due to their open microstructures, which also makes it challenging to obtain a thorough understanding of their fracture mechanisms and to predict trustworthy crack paths. In this study, we analyse numerically fracture trajectories in brittle porous solids with varying porosity (or relative density) subject to different mixed-mode loading conditions using a phase-field theory for brittle fracture. The results reveal that the crack paths in porous solids with high porosity (low relative density) are very different from those in porous solids with low porosity (high relative density). The latter resemble stable crack paths in homogeneous solids, whereas the former seems somewhat arbitrary, more stochastic. In high porosity materials, the crack paths are governed by the local microstructure rather than by the global remote loading. A key observation is that there is a transition of the fracture behaviour in porous materials at relative densities of around 50%. At relative densities above 50%, the ma-terial behaves nearly as a classical continuum, and the crack paths are reasonably well captured by traditional fracture mechanics theories. The stochastic nature of the porous microstructure is also examined.

In elasticity, microstructure-related deviations may be modeled by strain gradient elasticity. For so-called metamaterials, different implementations are possible for solving strain gradient elasticity problems numerically. Analytical solutions of simple problems are used to verify the numerical approach. We demonstrate such a case in a two-dimensional continuum as a benchmark case for computations. As strain gradient enforces higher regularity conditions in displacements, in the finite element method (FEM), the use of standard elements is often seen as inadequate. For such piecewise or elementwise continuous elements, we examine a possible remedy to correctly simulate strain gradient elasticity problems by implementing two techniques. First, we enforce continuity of displacement gradient across elements; second, we employ a mixed finite element method where displacement and its gradient are solved both as unknowns. The results show the pros and cons of each numerical technique. All methods converge monotonically, but the mixed method is more reliable than the other one.

Materials may demonstrate electromagnetism and thermomechanics coupling. Although we benefit from this coupling in our modern lives, comprehending this coupling is challenging. We intuitively understand that temperature increase causes an expansion in polymers and alloys. Typical example is a plastic water bottle left in the sun, the expansion is visible by naked eyes. Yet it is more abstract to consider that an electric field may create a deformation or even a temperature change. Electromagnetic fields are more abstract since our senses fail to be sensitive to these physical quantities. There are indeed materials with so-called piezoelectric and pyroelectric properties and we use them for sensors and actuators. More confusingly, there is a thermoelectric effect relating electric current and heat flux. In order to set the ideas correctly, we explain these phenomena and introduce to the abstract world of electromagnetism and thermomechanics coupling. Furthermore, we provide an inside look to realize how different types of thermal and electric coupling phenomena work and how to model such materials adequately.