There is a wide range of industrially-relevant problems where mechanical stresses directly affect kinetics of chemical reactions. For example, this includes formation of oxide layers on parts of micro-electro-mechanical systems (MEMS) and lithiation of Si in Li-ion batteries. Detailed understanding of these processes requires thermodynamically-consistent theories describing the coupled thermo-chemo-mechanical behaviour of those systems. Furthermore, as the majority of materials used in those systems have complex microstructures, multiscale modelling techniques are required for efficient simulation of their behaviour. Hence, the purpose of the present paper is two-fold: (1) to derive a thermodynamically-consistent thermo-chemo-mechanical theory; and (2) to propose a two-scale modelling approach based on the concept of computational homogenisation for the considered theory. The theory and the two-scale computational approach are implemented and tested using a number of computational examples, including the case of the reaction locking due to mechanical stresses.

Negative stiffness (NS) metamaterials have been widely studied in the fields of shock isolation and energy absorption due to their special properties. For various application scenarios, many types of NS metamaterials have been proposed, such as 2D honeycomb, 3D cube, hollow cylinder. However, when installation space is limited, the hollow cylindrical NS metamaterials may not achieve buffering effect due to its weak stiffness. In this paper, a cylindrical negative stiffness structure with inner hollow parts filled by inclined beam elements is proposed, which can obtain enhanced stiffness and energy absorption by improving space utilization. Theoretical analysis, numerical simulation and experimental validation were carried out to study the quasi-static and dynamic mechanical properties of the structure. Finally, the structure was applied as a cushion in a non-pyrotechnic separator, which could achieve good cushion performance. This work is expected to provide more potential for the applications of cylindrical negative stiffness structures.

Nonspherical granular materials are widely used in various industrial fields. Because the simulation of mixed granular flows consisting of arbitrarily shaped particles with smooth surfaces modeled by multiple discrete element models remains difficult for practical applications, a novel Minkowski sum contact algorithm in the CUDA-GPU architecture was proposed. In this algorithm, super-ellipsoidal equations, spherical harmonic functions, and polyhedrons were used to model differently shaped particles with smooth surfaces using the Fibonacci and Minkowski sum algorithms. Subsequently, single or multiple contact points between arbitrarily shaped particles were determined using the Minkowski sum contact algorithm. The automatic mesh simplification and GPU parallel computing methods were employed to improve the calculation efficiency of the discrete element method. The conservation, accuracy, and robustness of the proposed algorithm were verified by four sets of numerical examples: elastic collisions between particles, inelastic collisions between particles, accumulation of multiple particles, and dynamic granular flows. The relative DEM results show good agreement with the analytical solution, which indicates that the proposed Minkowski sum contact algorithm can accurately reflect the dynamic properties of arbitrarily shaped granular materials containing differently dilated DEM models.

We present a data-driven modeling approach to quantify morphology effects on transport properties in nanostructured materials. Our approach is based on the combination of stochastic modeling of the 3D nanostructure and numerical modeling of effective transport properties, which is used to investigate process-structure–property relationships of hierarchically structured cathode materials for lithium-ion batteries. We focus on nanostructured LiNi1/3Mn1/3Co1/3O2 (NMC) particles, the nanoporous morphology of which has a crucial impact on their effective transport properties (i.e, effective ionic and electric conductivity) and thus on the performance of the cell. First, we develop a parametric stochastic model for the 3D morphology of the nanostructured NMC particles based on excursion sets of so-called χ2-fields. This model, which has only two parameters, is then fitted to FIB-SEM image data of the NMC particles manufactured with different calcination temperatures and different particle sizes. This way it is possible to generate digital twins of the NMC particles. In a second step, measured 3D image data and corresponding digital twins are used as input for the numerical simulation of effective transport properties. Based on the results obtained by these simulations, we can quantify process-structure–property relationships. Overall, we present a methodological framework that allows for an efficient optimization of the fabrication process of nanostructured NMC particles.

An electromagnetic split Hopkinson tensile bar system was employed to determine the dynamic mechanical behaviors of riveted joints under different shear/tension combinations. Combining with results obtained from quasi-static tests, the effects of loading state and loading rate on both ultimate strength and yield strength of riveted joints are analyzed. An obvious elevation for the levels of yield force and ultimate force when increasing the loading speed is observed, meanwhile, such strengthening effects are sensitive to the loading state. On the basis of detailed load analysis, two analytical models considering both the loading rate effect and loading state effect were proposed to predict the ultimate strength and yield strength under different loading conditions. The theoretical calculations by applying such two analytical models agree well with the experimental results under five different loading states over a wide range of loading speeds (5 × 10-6 m/s ∼ 17 m/s), indicating the coupling effect of loading angle and loading speed on both ultimate strength and yield strength of riveted joint is reasonable defined.

Biomimetic fish scale structures on soft substrates can provide tailorable and tunable mechanical stiffness. When distributed over a reference 2D flat substrate, their simultaneous in-plane and out of plane sliding kinematics give rise to highly intricate geometrically dictated nonlinear and asymmetric behavior. Existing studies which focus on beam with filamentous structures, only partially reveal these complexities. Using finite element based numerical simulations, in this work we reveal the kinematics and bending mechanics of these structures. Scales are treated as stiff and rigid with flat plate-like geometry. We discover five distinct engagement patterns determined by the dihedral angles and overlap of the scales. These complexities are reflected in the multi-axial moment–curvature responses for bending revealing a rich landscape of tailorable and variable stiffness that can be exploited to create new types of flexible substrates which can significantly impact evolving frontiers of segmented armors, soft robotics, rehabilitation engineering and medium scale aerospace vehicles.

The ability of materials to adapt to changing environments is attractive for various applications, ranging from deployable structures to soft robots. In this work, we develop a multistable metamaterial that allows for autonomous recovery and programmable deformation in response to varying temperatures. The tunable multi-stability is achieved by incorporating a bi-material sinusoidal beam as the constituent element of the metamaterial. The mechanical response of the bi-material beam is explored theoretically. A phase diagram of its temperature induced bistability-to-monostability transition is obtained, validated by experiments and finite element simulations. With the phase diagram, the bi-material beam based building blocks of the metamaterial can be designed to transit from one stable state to another one via snap-through after compression, and return to its first stable configuration when the temperature rises above a critical temperature. Numerical and experimental results show clearly from the force–displacement-temperature path that the developed metamaterial possesses temperature-induced recoverability and programmable deformation. Construction of bi-material sinusoidal beams with more triggering temperatures for stability transition is also discussed.

The effect of confinement and Alkali-Silica Reaction (ASR) in concrete is of paramount importance when assessing damage in existing structures. It appears that this effect has been only seldom investigated with respect to the vast literature on free-expanding ASR, especially in its modeling aspect. This paper proposes to address this topical issue. For this purpose, an exhaustive review on the effect of confinement and ASR was first provided. Key features that must be taken into account were discussed and a discrete model equipped with the relevant multi-physics models was proposed. The computational framework which includes models for moisture diffusion, heat transfer, cement hydration and aging, thermal expansion, creep, and shrinkage was validated through a detailed comparison with a recent large experimental campaign for which all model parameters have already been calibrated. After accounting for possible alkali-leaching in the experiments and adjusting three model parameters, the numerical framework was used to simulate expansion curves, crack distribution, and damage evolution in unconfined samples, and drilled cores. Results show that overall, the model is able to well reproduce the transfer of expansion in the transversal unrestrained direction, cracks having a preferential direction in the restrained direction, expansion behaviors in the three spatial directions, and the evolution of mechanical properties in time for different confinement configurations. The important effect of creep and shrinkage was also emphasized. Crack distributions numerically generated were found consistent with Damage Rating Index analysis. One major finding of this study is that the true strength inside concrete subjected to multi-axial confining loads was found unaltered due to ASR in the direction of confinement. This striking result confirms many practitioners’ field experience with core testing and raises the fact that as sophisticated modeling tools become more and more reliable, existing methods of assessment must be improved by incorporating results from numerical modeling.

In addressing the construction of beam solutions for elastic guided waves in plates, we propose expressions of the amplitude function for the Lamb wave and the shear horizontal plate wave. The amplitude function is governed by an in-plane amplitude equation describing plate waves that has a same form as the two-dimensional Helmholtz equation. Therefore, beam solutions can be constructed within the same framework as this Helmholtz equation. The paraxial approximation is then applied to this in-plane amplitude equation. On the basis of this approximation, Gaussian beam solutions for both the Lamb and shear horizontal plate waves are derived. The effects of beam width, wavenumber, and guided-wave mode upon the wavefields are examined through several numerical examples.

The crystal plasticity finite element method (CPFEM) is used to investigate the coupling between the cylindrical void growth or collapse and grain refinement in face-centred cubic (FCC) single crystals. A 2D plane strain model with one void is used. The effect of the initial lattice orientation, similarities, and differences between stress- and strain-driven loading scenarios are explored. To this end, boundary conditions are enforced in two different ways. The first one is based on maintaining constant in-plane stress biaxiality via a dedicated truss element, while the second one is imposing a constant displacement biaxiality factor. Uniaxial and biaxial loading cases are studied. For the uniaxial loading case a special configuration, which enforces an equivalent pattern of plastic deformation in the pristine crystal, is selected in order to investigate the mutual interactions between the evolving void and the developed lattice rotation heterogeneity. Next, biaxial loading cases are considered for three crystal orientations, one of which is not symmetric with respect to loading directions. It is analysed how stress or strain biaxility factors and initial lattice orientation influence the void evolution in terms of its size and shape. Moreover, the consequences of variations in the resulting heterogeneity of lattice rotation are studied in the context of the grain refinement phenomenon accompanying the void evolution. Scenarios that may lead to more advanced grain fragmentation are identified.

A cohesive interface model based on a master curve is proposed for the analysis of delamination in paperboard under various loading, unloading, and reloading conditions. The model is thermodynamically consistent and considers the effects of elasticity, plasticity, and damage. The proposed model is verified by comparing its predictions with experimental data obtained from multiple loading–unloading–reloading cycle experiments using a split double cantilever beam specimen. The results show that the model can predict the cyclic behavior of shear loading and provide insight into the damage evolution associated with different loading paths by analyzing the shear stress distribution in the fracture process zone. The model’s calibration process requires monotonic normal and shear loading data but only cyclic normal loading data. Additionally, the model accounts for the paperboard’s fiber–fiber friction and normal dilatation due to shear loading. In total, nine parameters are needed to calibrate the model.

A 3D analytical approach is proposed to investigate the peeling mechanism of IC chip from substrate, which is important for reliable electronic packaging. Chip-adhesive-substrate system is considered as a composite structure composed of a rectangular plate of free edges and a clamped circular plate bonded with an interfacial layer. Peeling a chip from substrate is treated as the interfacial fracture of this structure. Based on the theory of elasticity, the problem of interfacial fracture is reduced to a set of coupled integral and differential equations. An analytical scheme is developed to solve these equations. With the approach, dynamic evolution process of peeling is analyzed due to various needle ejecting and vacuum absorption. Stress distributions of both chip and adhesive at different stages of peeling process are obtained. It is shown that stresses of both chip and adhesive are nonuniformly distributed in the whole region. As a result, peeling initiates from four corners, and propagates toward the center of interface with a very complex advancing front. For a definite displacement of needle point, peeling process is determined by both the magnitude and application time of vacuum absorption. When these two parameters locate in a specific region, a chip can be separated completely from substrate without damage. Furthermore, peeling process is sensitive to the position deviation of needle point. In case the position deviation is beyond a certain range, peeling process is incomplete.

The crack-tip in-plane (Q and A2) and out-of-plane constraint (Tz) parameters have been extensively studied for ductile fracture problems on the basis of the pioneering HRR and J-Tz solutions. However, these analytic solutions rarely focus on the steady growing cracks, which play a vital role in J-R curve and integrity assessments of complicated structures. In this work, three-dimensional finite element method and GTN damage model are adopted to simulate quasi-static ductile crack growth under different plastic exponents, geometries and load levels. With the follow-up coordinate system, the J-Tz solution is extended to describe the crack-tip stress distributions of the quasi-static elastic–plastic growing cracks. It is found that in front of steady growth cracks, Tz strongly depends on specimen geometry. In the range of small-scale yielding, tensile stress and Tz gradually increase with increasing load J/JC. When the large-scale yielding stage is approaching, tensile stress and Tz tend towards a stable state. The maximum relative errors between the J-Tz solution and three-dimensional finite element results are 4.16% and 9.28% with J/JC smaller than 1 and 2, respectively. Such dominance and geometry independence of the leading order J-Tz solution make it more simply and effectively to assess the ductile fracture problems.

We investigate the indentation of thin adhesive beams by a rigid frictionless circular punch in two-dimensions through computations and experiments. A non-linear geometrically exact (GE) beam formulation that allows for arbitrarily large displacements and rotations is employed for the thin beam. The Karush-Kuhn–Tucker condition for unilateral contact is adapted to model adhesive interaction in a nonlinear finite element (FE) framework. In this contact is enforced through a penalty method and adhesion is incorporated through two different cohesive zone models (CZMs), viz. exponential and bilinear. The indentation of the adhesive GE beam is then studied in terms of the variations of the applied force, the pressure distribution, the cross-sectional rotation and the sizes of the contact area and the adhesive zone for different indentation extents, adhesive strengths, punch radii, beam thicknesses and end supports. We find that the system is largely agnostic to the CZM utilized, as well as the type of end supports unless the contact area spans the beam. At the same time, thinner beams tend to initiate contact with a punch more easily, and are harder to detach. We then demonstrate that thin beams may undergo large rotations even if the indentation is small, which necessitates a nonlinear beam theory. Under such conditions approximating a circular punch by a parabolic one introduces errors. Finally, we conduct experiments on clamped adhesive beams made of two different types of PDMS (polydimethyl-siloxane) and various thicknesses, and find a good match with our computations.

The identification accuracy of material model parameters is essential for accurately predicting the deformation behavior of metallic materials (e.g., metal forming) using a finite element (FE) simulation. Numerous researchers have studied inverse material model characterization, where parameters are determined by minimizing a cost function that quantifies the difference between experimental data and mechanical test simulation results. However, sensitivity analysis in the optimization process hinders the extensibility of inverse methods due to issues like computational cost and complex numerical implementation. In this study, we developed a novel inverse methodology for material model characterization that improves extensibility by applying an ensemble-based four-dimensional variational method (En4DVar), which has the potential to address the challenges associated with conventional FE-based inverse material model characterization. The developed method was verified through numerical experiments in which En4DVar was applied to an elastoplastic FE simulation of the deformation of an aluminum alloy during a uniaxial tensile test, including diffuse necking. We investigated the estimation accuracy of the strain-hardening parameters in Swift’s hardening law and evaluated the simulation results under various conditions through numerical experiments. We focused on the effect of time and location to incorporate synthetic experimental data into the simulation to examine the quantities of synthetic experimental data required for parameter estimation. The results of the numerical experiments showed that En4DVar is a powerful approach for estimating the parameters and characterizing the deformation behavior of a material. Moreover, it was shown that accurate estimation results can be obtained even using synthetic experimental data with a relatively low temporal resolution or a small field of view. The proposed method's ease of extensibility using En4DVar expands the range of problems solvable in the field of material model characterization.

Computationally efficient and numerically accurate modelling of heterogeneous materials with complex internal architectures at the macroscale is a current problem. For instance, in engineering materials such as 3D woven composites, retaining the description of material architectures is important to obtain an accurate prediction of stiffness. However, computational cost increases in proportion to the level of mesoscale details modelled. To enable efficient and accurate calculations on the structural scale, a multiscale method that can identify repeatable patterns in the mesoscale and represent them efficiently at the macroscale is proposed. This method has two important novelties, (i) a method to identify and store repeatable patterns during offline stage in the form of 3D Voronoi cells using a data compression algorithm, k-means clustering. This improves the identification with a minimum number of data clusters and minimises the effects of mesh sizes, and (ii) a method to select most similar Voronoi cells from the mesoscale database during online stage using image registration and k-d tree data structure. This enables computations being performed without explicitly modelling mesoscale details and reduces the computational cost that are otherwise required. The proposed method is validated against 3D woven unit-cell and three-point bending examples. Furthermore, the ability to find repeatable patterns is tested by analysing a woven architecture previously not stored in the database.

The mechanical properties of biodegradable polymers are strongly linked to molecular weight and crystallinity. In this study, our modelling approach is used to relate changes in physical properties (molecular weight, crystalline volume fraction and porosity) of a semi-crystalline PLLA during degradation to macroscopic mechanical properties (modulus). We create a database of mechanical behaviour based on possible values of these properties, which is then queried to quickly predict the modulus without the need for multiscale approaches. Initially, the semi-crystalline polymer is considered as an ensemble of crystalline amorphous regions with no preferential direction. In subsequent simulations, the effect of anisotropy is investigated by considering various orientations and dispersions of the crystalline phase. Theoretical bounds were calculated and compared to simulations and published data. The database of mechanical behaviour was modified to capture the emergence of porosity during degradation. These predictions are compared against previously published experimental values of Young’s modulus for PLLA (Poly (L-lactide)) during degradation with good agreement. These simulations also provide insight into the transition to brittle behaviour during degradation.

Scattering experiments can be leveraged to extract the effective properties of a heterogeneous metamaterial slab based on multi-point measurements in surrounding media. In this technique, two measurements are made in the ambient media on each side of a finite thickness micro-structured slab to decompose incoming and outgoing waves. The method is applied to an example with locally resonant micro-structured inclusions while paying close attention to parameters that influence the extracted material parameters. It is observed that the extracted overall parameters converge to limiting values when the number of unit cells across the slab thickness or ambient media modulus are increased. Dependence of extracted material parameters on the number of cells through thickness or ambient media properties are attributed to the different response of boundary (skin) and interior cells. A method is presented which represents a finite array with different effective properties for the skin regions vs. the interior regions with great success in reproducing the scattering for different slab thicknesses, and through which the interior regions properties become independent of ambient media properties. In stop bands with lower material loss, challenges arise that are associated with extremely small transmission. The assumption of continuity in transmission phase is enforceable to remove phase ambiguity, although in certain cases (associated with nearly lossless specimens) this assumption appears to fail. In such cases, interference from coupled shear modes may lead to apparent higher longitudinal transmission within the stop band. This work provides a proof of concept for the development of an experimental methodology capable of extracting the effective properties and dispersion behavior of heterogeneous mechanical metamaterials without any knowledge of the internal fields.

The single edge loading problem of a double thin film deposited on a finite thickness substrate is considered. The films and the substrate are assumed to be homogeneous and isotropic. The membrane analogy is adopted for the films and two dimensional elasticity is applied to the substrate. The compatibility of the tangential strain between the film and the substrate yields the governing singular integral equation in terms of the interfacial shear stress. The numerical solution is provided using the Gauss–Chebyshev discretization method. The sensitivity of the interfacial shear and the normal stresses to several effective parameters are examined. The results of current study are compatible with the finite element simulations. The lowest interfacial shear stress pertains to a substrate with a free edge boundary condition. The results of current study are applicable to the debonding failure assessment of the multi-layer joints and semiconductors which are susceptible to the interfacial shear stresses near the film edges.

The aim of this paper is to investigate the thermodynamics consistency of Gurson’s model and notably its relation to the class of standard generalized materials. First, we briefly recall Gurson’s model in its original format and reanalyzed it in the thermodynamic framework of poroplasticity of saturated media. This allows to properly define the coupling between elasticity and plasticity and to demonstrate that Gurson’s model fits into the framework of generalized standard materials model, provided that the internal variables being the plastic strain and the Lagrangian plastic porosity (and not the Eulerian porosity as in the original Gurson model). In particular, by construction, the porosity evolution law is proved to be a full part of the thermodynamic formulation of the model with a generalized normality rule. The implications in terms of numerical implementation of Gurson’s model are then investigated; a new numerical scheme based on the time-implicit discretization of the Lagrangian porosity is notably proposed and discussed with respect to available algorithms.