A yield function in the stress resultant space of geometrically exact beams based on the elastoplastic cross-sectional warping problem has been proposed by Herrnböck et al. (Comput Mech, 67(3):723–742, 2021). This plasticity framework has been extended with a hardening tensor to model the kinematic hardening effects in Herrnböck et al. (Comput Mech, 71(1):1–24, 2022). While this framework provides scaling for the yield surface in ideal plasticity, scaling in hardening plasticity has not yet been explored. This paper focuses on the numeric modelling of hardening beams and beam assemblies at different geometric scales. Discretization effects from the introduction of plasticity into the geometrically exact beam model are demonstrated. Furthermore, the effects of scaling are explored, and a method to mitigate undesirable effects in order to achieve a size-agnostic formulation is proposed. Consistent geometric scaling is demonstrated for two alternative scaling approaches of the yield function.

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Lightweight materials used for impact mitigation must be able to resist impact and absorb the maximum amount of energy from the impactor. Auxetic materials have the potential to achieve high resistance by drawing material into the impact zone and providing higher indentation and shear resistance. However, these materials must be artificially designed, and the large deformation dynamic effects of the created structures must be taken into consideration when deciding on a protection concept. Despite their promise, little attention has been given to understanding the working mechanisms of high-rate and finite deformation effects of architected auxetic lattice structures. This study compares the static and dynamic elastic properties of different auxetic structures with a honeycomb structure, a typical non-auxetic lattice, at equivalent mass and stiffness levels. In this study, we limit the investigation to elastic material behavior and do not consider contact between the beams of the lattices. It is demonstrated that the equivalent static and dynamic properties of individual lattices at an undeformed state are insufficient to explain the variations observed in impact situations. In particular, the initial Poisson's ratio does not determine the ability of a structure to resist impact. To gain a thorough comprehension of the overall behavior of these structures during localized, high rate compression, the evolution of the elastic tangent properties under compression and shear deformation was monitored, leading to a more profound understanding. Observations made in one configuration of stiffness and mass are replicated and analyzed in related configurations.

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Adobe is a traditional masonry made of sundried earthen bricks and mud mortar. Despite a millennial history of buildings of architectural value, adobe still connotes a so called ‘not engineered’ construction type. Namely, the material and structural properties of adobe are still not entirely addressed, resulting in an equally uncertain normative framework for adobe buildings design. However, over the last ten years, a large research program has been conducted in the Netherlands to qualify the material and structural properties of this sustainable building technology. In this paper, a critical analysis of the current normative body for the material characterization of adobe is addressed. Guidelines, prescriptions and requirements related to test methods, materials selection and properties contained in the available building codes for adobe around the world are assessed. A critical normative review is performed using the most recent literature produced on adobe, with particular regards to the results of experimental tests and numerical simulations performed by the authors. On the basis of these findings, some issues have been identified in relation to the knowledge currently condensed in the norms for adobe. A series of programmatic guidelines is aimed at orienting future research on adobe as well as fostering the process of updating its current normative body.

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In this study, the impact of a steel spherical projectile on an alumina ceramic is considered. New experimental and numerical results are presented and analysed. Numerical results are obtained using the Finite Element Method and the upgraded viscosity regularized Johnson-Holmquist-2 constitutive model to describe the ceramic material behaviour. First, a short investigation is done using 2d Finite Element simulations to establish a proper numerical framework. Second, the numerical framework is extended to 3d and experimental results are used to validate the framework and the ceramic material model. This shows that all relevant ceramic failure mechanisms are captured correctly and the framework and model can be used to simulate sphere impact on ceramic material. Third, the simulations are used to analyse the failure processes in the ceramic material in more detail. Here the focus lies in obtaining information which can currently not be retrieved from experiments. Timing and interaction of propagating conical and radial cracks are investigated and corroborate with the typical failure mechanisms observed in sphere impact on ceramic material.

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This paper presents the results of an experimental research aimed at assessing the material performance of adobe bricks in compression for a wide range of induced strain rates, from statics to high velocity impact. Adobe connotes a traditional masonry whose bricks are made of sundried soil mixtures possibly reinforced with natural fibres and joined together using mud mortar. The inclusion of fibre and the presence of water in the mixture have a dominant effect on the mechanical performance of adobe bricks and masonry. Their influence on the dynamic behaviour of this material is quantified and interpreted in this study at high strain rates also with data produced through Hopkinson bar testing. Appropriate dynamic increase factors and constitutive equations for adobe materials in dynamics are also investigated. The paper presents the experimental campaign, shows the main results and offers qualitative and quantitative interpretations for the principal damage patterns observed.@en

A local damage model is proposed for the numerical assessment of the static performance of Adobe masonry components. The model was applied to simulate the experimental behaviour of sundried soil bricks and mud mortar tested in uniaxial compression and bending. Numerical simulations of the model are made mesh objective by means of a rate dependent regularization algorithm in statics. This is achieved using a generalization of the damage delay concept based on a decomposition of the Dirichlet boundary condition. It allows non-dimensionality of model parameters mathematically needed to prevent loss of ellipticity of the equilibrium equations of the model. The entire regularization algorithm is integrated within an implicit Newton-Raphson solver.

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This study presents the numerical analyses conducted to investigate the impact behavior of different porous concretes, which have also been cast and tested experimentally. For a realistic representation of the real porous concretes containing arbitrary shaped air pores, a mesh generation code was developed in which the aggregates in the mixtures were directly extracted through computed tomography. In the code, mineralogically different aggregates in porous concretes with gravel could also be individually defined. In the explicit finite element analyses conducted, porous concrete was considered as a four-phase material, consisting of aggregates, interfacial transition zones (ITZ), bulk cement paste and air. The pore size distribution and the fragmentation behavior of the concretes were also numerically analyzed. Among the parameters that have been investigated both numerically and experimentally, aggregate grading, which determines the porosity and pore size distribution of the material, was found to have a dominant effect on the strength as well as the fragmentation properties of porous concretes. Although the amount of ITZ is higher in mixtures containing finer aggregates, those mixtures had higher impact strengths compared to coarser aggregate ones again owing to their much finer pore structures.

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Alumina ceramic is often used in armour systems. This material is known to have a brittle response under tensile loading, while a ductile response is found when sufficiently high pressures are reached. During projectile impact a ceramic material experiences both tensile loading and high pressures, hence fails in both a brittle and ductile way. Properly capturing the ceramic failure in a single material model remains challenging. A viscosity regularized Johnson-Holmquist-2 model has been used to simulate dynamic loading on alumina ceramic. The simulations show that the brittle and ductile nature of the material can not be captured simultaneously in the current material model. A new failure strain formulation is proposed where the behaviour under tensile and compressive loading can be controlled independently. This allows to properly capture both the brittle and ductile response of the material in a single constitutive framework, with a single set of model parameters.@en

Adobe is one of the most ancient forms of masonry. Adobe bricks are sundried mixtures of clay, silt, sand and natural fibres locally available joined together using mud mortar. Adobe structures are largely spread in areas of the world prone to earthquakes or involved in military conflicts. Unfortunately, almost no literature concerns the dynamic assessment of soil-based masonry components. From earlier research, it was derived that the mechanical behaviour of adobe in statics fits in the class of quasi brittle materials. Its resemblance with cementitious materials concerns the main failure modes and the constitutive models in compression. This study deals with the experimental characterization of adobe components response in dynamics. It is aimed to study and quantify the rate sensitivity of adobe material from bricks at a wide range of strain rates, from statics up to impact conditions. In particular, the influence of fiber reinforcement in the mixture on the mechanical behaviour of the material has been addressed. Adobe bricks are commonly mixed using organic content locally available in the field, from straw to chopped wood. Fibres are added to prevent shrinkage cracks during the air drying process. In modern materials such as concrete, inclusion of artificial fibres is originally meant to enhance the mechanical performance of the material, benefiting from the selective properties of reinforcement and binder. An experimental campaign was carried out in a collaboration between Delft University of Technology, Dutch Ministry of Defence, TNO and the Joint Research Centre (JRC) of the European Commission. Two types of bricks were tested. They both had the same soil composition in terms of mineralogical family and soil elements proportions but only one was mixed using straw and wood. Cylindrical samples were subjected to compression tests at different rates of loadings in compression: low ( _ 1 = 3 104 s1), intermediate ( _ 2 = 3 s1) and high ( _ 3 = 120 s1). High strain rate tests were performed using the split Hopkinson bar of the Elsa-HopLab (JRC). For each test, high resolution videos registered the failure process and force-displacement plots were recorded. Elaboration of results revealed clear trends in the dynamic material behaviour. Adobe, as concrete, is sensitive to the loading rate. The rate effects on the main properties of the material in strength and deformation are also analytically and numerically quantified. Rate sensitivity and failure mode are significantly influenced by the inclusion of fibers in the mixture. These effects are quantified, interpreted and compared with modern SFRC. This paper presents the experimental campaign and the obtained results. Moreover, physical interpretations for the observed trends are discussed. Finally, new formulations for the assessment of the dynamic increase factor of the compressive strength of adobe are proposed.@en

Buildings and structures in many cities have recently been exposed to an increased number of highly dynamic hazards. These include not only floods and earthquakes but also man made threats such as ballistic impacts and blasts. Thus, the assessment of the dynamic performance of structures made of quasi-brittle materials must account also for high strain rate loadings. In engineering software, numerical simulations of dynamic failure processes are often carried out in a framework of damage mechanics, in which failure is interpreted as a degradation of the elastic material capacity. However, for many damage models, the link between the implemented numerical functions representing the corresponding physical mechanisms aimed is still a controversial issue. This is also the case because damage models suffer from a numerical pathology which prevents the objective evaluation of failure for different spatial discretization. To solve this issue, non local regularization algorithms are often used to solve mesh dependence, often at the expenses of complex identification procedures and non- trivial code implementation. Instead, a locally regularized rate dependent model has been developed by the authors for the static assessment of unbaked masonry materials made of clay sand and silt [1]. It adapts damage delay functions originally proposed in [2] in a local damage model developed for cementitious materials [3] based on the decomposition of the Dirichlet boundary conditions solved with an implicit solver. The regularization properties of the model were shown in [1] in statics. The regularization properties of the algorithm are analysed in this contribution for the dynamic problem of a bar uniaxially compressed at high velocity deformation rates. Furthermore, the physical background of the delay formulation is interpreted in light of the main failure processes commonly depicted for quasi-brittle materials in dynamic tests. In particular, the material parameters of the delay function in [1] are linked in this study to the bridging processes of micro-cracks starting from initial flaws inside the material and the resulting macro-crack development up to failure. Considering the physics shown in literature for quasi-brittle materials under multi-strain rate tests, the constant parameters in [1] are made functions of internal and environmental factors, namely material mineralogical properties and applied loading rates in this study. The resulting delay formulation produces an improvement in the capability of the model both to address the complete stress-strain curve of the response of traditional masonry materials subjected to a dynamic load and the rate of enhancement of the main mechanical parameters typical for these rate sensitive materials when subjected to multi-strain rates tests. This is shown in this paper by means of theoretical tests and practical applications with regards to the results of an experimental campaign performed by the authors on adobe specimens subjected to dynamic tests at three different strain rates, ranging from statics to Split Hopkinson bar tests.@en

In this work, findings of a numerical study performed to investigate the impact behavior of porous concrete, modeled as a four phase cementitious composite consisting of aggregates, cement paste, interfacial transition zones (ITZ) and air, are presented. The numerical analyses contributed to the process of designing a special type of concrete for safety purposes i.e. as a protective building material to be used in safety walls outside important buildings or munition magazines for storing explosives. In case of an explosion, large concrete fragments that are formed, cause a very important threat. Therefore, in the scope of a research project, designing a special type of concrete having sufficient strength, but fracturing into small fragments under impact loading was aimed. In the numerical analyses, model porous concretes, in which the amounts and properties of pores and aggregates could be varied individually, were used to see the sole effect of each parameter. According to the results, it was found that at constant total porosity, the impact strength increased with decreasing pore size while multiple fragmentation was observed. On the other hand, the impact strengths of porous concretes with different size aggregates (with constant total aggregate content and porosity) were approximately the same when no ITZ was defined. However, when ITZ was present, the impact strength was found to decrease as the aggregates were finer. This trend was also valid for the respective full concretes. Representative experimental results of porous concretes were also presented in order to support the numerical results.@en

A local damage model has been recently developed for the numerical simulation of the static behaviour of adobe bricks. Mesh insensitivity of the local model was obtained by generalizing the damage delay concept based on a Dirichlet boundary condition decomposition integrated in an implicit solver. The regularization properties of the model were proven before only in statics. In this study, mesh independence is demonstrated in dynamics analysing the problem of a cantilever bar uniaxially loaded at high deformation rates. Furthermore, the physical background of the delay formulation is interpreted regarding the main failure processes in compression exhibited by quasi brittle materials used in masonry. Two limitations of the model in correctly simulating the dynamic behaviour of masonry bricks have been observed. Corrections to the original damage delay formulation are proposed in this study. These enhance the capability of the model to address also distributed failure of traditional geo-materials and the inherent rate dependence also at high strain rate regimes. The improvements are demonstrated in this paper by means of numerical simulations of both theoretical tests and practical applications. These consist of experimental tests in compression recently performed by the authors at different strain rates, from statics to high velocity impact tests.

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The deformation-to-fracture evolution of a flexible polymer material under high-strain-rate compressive loading conducted by a split Hopkinson pressure bar (SHPB) setup was investigated. Representative tests were carried out at different strain rate levels, followed by the characterization of dynamic damage after each test. Craze and crack patterns on the end surface of the specimen were carefully analyzed. The failure patterns appear along the radial and circumferential directions. The sequence of their formation with increasing strain/stress level was revealed. The mechanisms resulting in the craze and crack patterns were analyzed. The heterogeneous stress distribution in the specimen and the resultant damage morphologies were demonstrated. This research not only shows the deformation-to-fracture evolution of a flexible polymer material under SHPB loading, but also provides a better clarification of the localized stress distribution in the tested material via SHPB technique.

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This paper presents a constitutive relationship to describe the uniaxial response in statics of brick and mortar samples of Adobe. This defines a traditional masonry whose components are made of soil mixture reinforced with fibres. Only recently Adobe has started attracting scientific attention, primarily as a consequence of the dramatic failures these structures have suffered in regions prone to earthquakes due to dynamic loadings. Furthermore, it possesses eco-friendly material properties which are attractive features for western countries forced to reduce the environmental impact of modern building industry. Nevertheless, the mechanical properties of Adobe are still largely neglected, especially with regards to the influence of soil mixture components. The study of the structural performance of masonry starts from the assessment of the material performance of its components. Thus, an extensive characterization campaign was organized and performed by Delft University of Technology and the Military Engineering Laboratory of the Netherlands, in order to characterize the material properties of Adobe components. Three types of bricks and one type of mortar, made with different mixture components proportions, were subjected to granulometry, moisture content, density tests and uniaxial compressive and three point bending tests. Predictive formulations for compressive and tensile strength and deformation values have been proposed by the authors [1]. These relations include the dependency of mixture components and moisture contents. In this paper, constitutive laws are developed for Adobe in pure compression and tension according to the experimental results. In compression, the force-displacement curves were interpolated according to several existing constitutive laws and the model originally developed by Priestley for concrete masonry elements was finally selected as best fitting. Despite the differences in terms of mechanical parameters, the analytical assessment revealed that the experimental force-displacement graphs of all the different types of bricks could be interpolated using the same model with the same calibrating values. Furthermore, the uniaxial response in tension was derived according to an inverse approach. A numerical model recently developed and calibrated with respect to the compressive and bending tests was used to simulate uniaxial tensile tests [2]. Also in this case, a common trend among types was observed. The results of the constitutive modelling frames components of Adobe within the class of quasi brittle (geo)materials, with particular reference to concrete-like materials. This paper presents the experimental results of the tested samples and the related analytical and numerical modelling. @en

Adobe is an ancient building technology made of sun dried bricks joined together by mud mortar. This paper deals with the physical and mechanical characterization of three different typologies of adobe bricks and one typology of mud mortar produced in Europe. They differed in terms of internal soil element proportions and amount of organic content. Physical tests consisted of granulometry, moisture content and density tests. The mechanical characterization consisted of uniaxial compressive tests and three point bending tests. Tests were performed according to modern material standards. The main mechanical properties both in tension and compression were determined at different curing conditions. The outcome provided in this study offers a general overview on the assessment of the mechanical performance of adobe in relation to the properties and interactions of its soil constituents. In fact, the comparison between components with the same soil mineralogical family and production process made it possible to assess both at a qualitative and quantitative level the effect of the physical properties of the mixture (such as fiber and clay percentages or moisture content) on the mechanical parameters of the resulting bricks and mortar. This paper proposes new predictive formulations of the most relevant material parameters in strength and deformation, such as compressive strength, deformation at peak stress and ultimate displacement for both adobe bricks and mortar. They quantify the influence that water content, clay percentage and fiber reinforcement produce on the mechanical performance of the tested adobe components. This was made possible by means of multivariate statistical analyses on the mechanical parameters derived from all the tested samples.

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A local damage model has been developed for interpreting the dynamic performance of Adobe, a traditional form of masonry whose components are made of sun-dried and unpressed soil possibly reinforced with fibres. This paper presents a numerical model to assess the static performance of bricks and mortar of Adobe. It has been validated with reference to the results of a characterization campaign performed in 2016 on Adobe bricks and mortar produced in Germany. Although Adobe buildings are among the oldest examples of masonry constructions, spread in all continents of the world, the properties of the material and the overall mechanical performance are still poorly understood, especially with respect to the influence of the adopted mixture on the mechanical properties. As a consequence, very few numerical models are developed for Adobe. The assessment of Adobe structures is becoming a priority task because they are often spread in areas of the world prone to a wide range of dynamic hazards, whose disastrous consequences must be prevented. As for masonry, the overall performance of Adobe structures depends on the properties of bricks and mortar. Three

types of bricks and one type of mortar with different element mixture compositions were tested in compression and bending tests and their behaviour was analysed. The interpretation of experimental results classifies Adobe as a quasi brittle material, with special reference to concrete. Moreover, it was found out that for the same mineralogical family, the amount of fibres in the mixture of Adobe controls the deformation capacity of Adobe. Overall, a numerical model for Adobe was cast within a damage concept originally defined for concrete. A modified version of the last damage model by Mazars was developed. In order to avoid the typical mesh dependency that characterizes simulations of softening materials, a local regularization algorithm was implemented, starting from the damage delay model developed by Allix. Overall, only two mechanical parameters in compression and

tension are required to calibrate the loading evolution laws of the model. In fact, the initial damage strains and elastic moduli in tension and compression were derived directly from the mean values experimentally associated
to each mixture. For each type of mixture, numerical simulations on resulting bricks were performed in statics for uniaxial compression and three point bending tests using the strength and strain values experimentally derived. The mechanical parameters of the model were calibrated in order to match the experimental force displacement curves. The Adobe delta damage model proves to constitute a suitable tool to predict the material performance of Adobe. This paper resumes the experimental campaign, presents the algorithmic details of the model and the comparisons with respect to experimental data and mesh dependence.
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Plasticity models are frequently used to describe ceramic materials. Well established and often used ceramic models are those by Johnson and Holmquist. These are softening plasticity models for which mesh dependency is a well known problem. A viscosity or rate dependency can be added to the material model to provide regularization and solve the mesh dependency problems. For the Johnson-Holmquist models a viscosity is proposed to work on the hydrostatic tensile strength. A consistency visco-plastic formulation is used. For the Johnson-Holmquist-2 model it is demonstrated that the proposed viscosity indeed removes the mesh dependency problems. This is shown for both quasi-static and dynamic loading. In addition it is shown that the proposed viscosity can predict an experimentally measured rate dependent spall strength of alumina ceramic, while the original model fails to do so.

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In this study, an impact strength measurement method based on high speed photography, that has been developed for testing porous concrete, was introduced. In the experiments, a drop weight impact test set-up instrumented with a high speed camera was used. The impact strength analyses were conducted using impedance mismatch method, where the wave reverberations were investigated in detail. The measurement configuration carries the advantage of being a fast, non-contact and accurate experimental method where only the known material properties and particle velocity data of the drop weight are required. The target cementitious material itself is not actually involved in the measurements or the subsequent analyses. The method also facilitates the observation of the crack patterns throughout the experiment. The measurement method was verified to be accurate and consistent by testing different types of porous concretes and by comparing the results with those from other dynamic monitoring techniques, such as laser Doppler velocimetry and direct stress gauge measurements.

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