Macroscopic Properties of Open-Cell Foams Based on Micromechanical Modelling

This paper presents a micromechanical analysis for the assessment of macroscopic behaviour of threedimensional open-cell solid foams. The analysis is based on material properties of a solid phase and topological arrangement of cell structure. A foam structure consists of idealized tetrahedral unit cells, which are built of four identical half-struts forming a diamond-like structure and identified as Plateau borders. Such a unit cell represents the essential microstructural features of foam. An analytical formulation of force-displacement relations for struts can be found by considering the affinity of node displacements in tensile, bending, and shear deformation. The elements of the stiffness matrix for a single cell are expressed as functions of the compliance coefficients for stretching and bending of struts. The effective elastic constants for metallic foam considered as isotropic material are determined as functions of foam relative density and compared with available results. In this paper we define an energy-based limit condition of linear elasticity for open-cell foams and calculate the critical energy density pertinent to a particular orthogonal energy state accounting for elementary interactions in a microstructure. The study based on the assumption of linear elasticity leads to simple analytical formulas. Nevertheless, it should be stressed that the proposed theoretical basis of micromechanical modelling could be also applied for the analysis of nonlinear elastic behaviour, plasticity, and failure of foams. Such problems require, however, a more complex numerical approach

Model mikromechaniczny materiałów komórkowych o ujemnym współczynniku Poissona

An effective anisotropic continuum formulation for auxetic cellular materials is the objective of this paper. A skeleton is modelled as a plane beam elastic structure with stiff joints. The skeleton topology, forming concave polygons, is responsible for negative Poisson’s ratio effect. The essential macroscopic features of mechanical behaviour are inferred from the deformation response of a representative volume element using the framework of micromechanical analysis. The strain energy of a unit cell is calculated by adding the tensile, shearing and bending strain energy of individual members. The equivalent continuum is based on averaging this energy, thus formulating the basis for computing the anisotropic stiffness matrix. The structural mechanics methodology and ANSYS finite element code are applied to solve the beam model of the skeleton. Graphical representation of certain material constants such as Young’s modulus, Poisson’s ratio, shear modulus and generalized bulk modulus is given. The results of included parametric study may be used for proper choice of geometric and material data of the skeleton for a given structural application of the anisotropic continuum.Celem pracy jest sformułowanie efektywnego anizotropowego continuum sprężystego dla materiałów komórkowych o ujemnym współczynniku Poissona. Szkielet materiału jest modelowany przez płaską strukturę belkową połączoną w sztywnych węzłach tworzącą układ wielokątów wklęsłych. Kąty wklęsłe w strukturze materiału odpowiadają za efekt ujemnego współczynnika Poissona. Poprzez zastosowanie modelu mikromechanicznego istotne cechy mechaniczne materiału komórkowego są wyprowadzone z wyników analizy komórki reprezentatywnej. Potencjał sprężysty szkieletu komórki jest wyznaczony jako suma energii w belkach tworzących szkielet od ich rozciągania, ścinania i zginania. Efektywne continuum jest oparte na uśrednianiu potencjału sprężystego, co jest podstawą konstruowania macierzy sztywności. Metoda analizy strukturalnej przeprowadzona za pomocą programu MES-ANSYS jest stosowana dla modelu belkowego szkieletu. Jako wynik tej analizy przedstawiono graficznie rozkłady modułu Younga, współczynnika Poissona, modułu na ścinanie i uogólnionego współczynnika ściśliwości objętościowej. Studium parametryczne umożliwia prześledzenie wpływu parametrów geometrycznych struktury i charakterystyk materiału szkieletu na własności kontinuum zastępczego jako materiału o zastosowaniu strukturalnym

Numeryczne oszacowanie własności sprężystych kompozytowych pian węglowo-poliuretanowych

This paper presents micromechanical approach to assessment of elastic properties of composite polyurethane-carbon foams. Analysis is based on specific choice of RVE combined with micro-macro transition. It leads to evaluation of strength and elastic constants of a composite. Foam behaviour is investigated numerically. Solid skeleton part shape is based on the tetrahedron cut out with spheres. 3D unit cell model is FE discetized. Calculations are performed for foams of selected densities using ABAQUS system. The comparison shows good agreement between the theoretical approach and experimental data. The presented method may be applied to design novel materials such as graphitized foam and nano composites and tailoring these materials for desired elastic properties.Artykuł przedstawia zastosowanie podejścia mikromechanicznego do oszacowania własności sprężystych kompozytowych pian poliuretanowo-węglowych. Analiza ośrodka sprężystego jest oparta na podejściu mikromechanicznym, które prowadzi do określenia własności sprężystych kontinuum, jakim jest materiał kompozytowy na podstawie reprezentatywnej komórki. Kształt szkieletu komórki jest oparty na czworościanie z wyciętymi sferami wypełnionymi innym materiałem. Obliczenia są przeprowadzone programem ABAQUS metodą elementów skończonych. Porównanie wyników numerycznych i eksperymentalnych dla wybranych gęstości pian wskazuje na dużą zgodność przewidywań teoretycznych z eksperymentem. Przedstawiona metoda może być użyta do projektowania pian kompozytowych o z góry zadanych własnościach sprężystych

Study on the Size Effect of Auxetic Cellular Materials

The objective of this paper is to investigate the effects of scale of an auxetic cellular material sample on the evaluation of elastic properties. Size and boundary effects are studied in detail. This is achieved by conducting computer simulations of the auxetic structure under the typical loading exerted by the compression and simple shearing test performed by means of ABAQUS FEA. The material microstructure is discretized by the plane network of Timoshenko beam elements. The results of the studies give insight to the scale effects. Structures with designed properties can be potentially used for engineering applications

Studium porównawcze sztywności giętnej płyty sandwichowej z wypełnieniem materiałem komórkowym o strukturze honeycomb oraz z wypełnieniem auksetycznym

This paper presents numerical simulation of a sandwich plate bending. Two types of plates are considered: with a cellular honeycomb core and with the cellular auxetic core. Finite element method (FEM) calculations are performed by means of ABAQUS system for determination of plates bending stiffness. Three methods are presented. The first one, numerically expensive, is based on detailed modelling of cellular core structure, the second applies laminated plate theory with an equivalent core stiffness, the third applies theory of composite beams. The results show limitations of applicability of abovementioned models to stiffness modelling. The influence of core lattice geometry parameters on plate stiffness is studied.W artykule przedstawiono numeryczne symulacje testów zginania płyt sandwichowych wypełnionych materiałami komórkowymi o strukturze plastra miodu oraz strukturze auksetycznej. Celem wyznaczenia sztywności giętnej płyt wykonano obliczenia numeryczne w systemie ABAQUS metodą elementów skończonych. Prezentowane są dwie metody. Pierwsza kosztowna numerycznie polega na szczegółowym modelowaniu struktury komórkowej, druga stosuje teorię laminatów, trzecia teorię belek zespolonych. Wyniki wskazują na możliwość modelowania sztywności giętnej płyty. Przeanalizowano wpływ parametrów geometrycznych, a w szczególności auksetyczności struktury

Studium projektowe nad auksetyczną strukturą szkieletu siedziska

This paper presents numerical study of deformation and stresses in seat skeleton elements subject to static and dynamic pressure loads. Elastic skeleton made of polyamide or elastomer is taken as an example of a seat material. Auxetic type of seat structure ensures the reduction of real contact stresses between human body and seat, making it more comfortable than typical. FEM analysis is performed using ABAQUS system. Numerical calculations are carried out to determine the nonlinear stiffness characteristics of seat springs. The study makes possible the selection of material and structural topology fulfilling design constraints and additional recommendations concerning structural flexibility, stability and optimal reduction of contact stresses. This paper presents an application of the theoretical prediction to solve the practical problem.Artykuł przedstawia studium obliczeniowe elementów szkieletu siedziska wykonanych z elastomeru lub poliamidu poddanych typowym obciążeniom statycznym i dynamicznym od siedzenia. Auksetyczne własności struktury szkieletu siedziska powodują redukcją naprężeń kontaktowych między ciałem człowieka i siedziskiem, czyniąc je bardziej komfortowym w użytkowaniu. Obliczenia przeprowadzono programem ABAQUS metodą elementów skończonych. W wyniku otrzymano nieliniowe charakterystyki sprężyn siedziska. Studium obliczeniowe pozwala na wybór materiału i kształtu sprężyn spełniających warunki projektowe dotyczące wytrzymałości, podatności stabilności oraz optymalnej redukcji naprężeń kontaktowych. Praca prezentuje zastosowanie teoretycznych rezultatów do rozwiązań stosowanych w praktyc

Comparison of Contact Stress Distribution for Foam Seat and Seat of Auxetic Spring Skeleton

The objective of this paper is to present and compare the results of numerical solutions of contact problem for two types of seats subjected to typical sitting loadings. The first seat is made of a typical hyperelastic foam, the other is designed with an auxetic polyamid spring skeleton. Computer simulations of the seat structure under a typical static loading exerted by a human body are performed by means of ABAQUS FEA. The model provides an insight into deformation modes and stress field in relation to geometric and material parameters of the seat structure.The other type of seat, due to the fact of global auxecity and progressive springs characteristics reduces contact stress concentrations, giving an advantegous distribution of pressure and provides the sensation of physical comfort. The proper seat skeleton shape leads to an improvement of ergonomic quality

Evolocumab and clinical outcomes in patients with cardiovascular disease

peer reviewedBACKGROUND Evolocumab is a monoclonal antibody that inhibits proprotein convertase subtilisin-kexin type 9 (PCSK9) and lowers low-density lipoprotein (LDL) cholesterol levels by approximately 60%. Whether it prevents cardiovascular events is uncertain. METHODS We conducted a randomized, double-blind, placebo-controlled trial involving 27,564 patients with atherosclerotic cardiovascular disease and LDL cholesterol levels of 70 mg per deciliter (1.8 mmol per liter) or higher who were receiving statin therapy. Patients were randomly assigned to receive evolocumab (either 140 mg every 2 weeks or 420 mg monthly) or matching placebo as subcutaneous injections. The primary efficacy end point was the composite of cardiovascular death, myocardial infarction, stroke, hospitalization for unstable angina, or coronary revascularization. The key secondary efficacy end point was the composite of cardiovascular death, myocardial infarction, or stroke. The median duration of follow-up was 2.2 years. RESULTS At 48 weeks, the least-squares mean percentage reduction in LDL cholesterol levels with evolocumab, as compared with placebo, was 59%, from a median baseline value of 92 mg per deciliter (2.4 mmol per liter) to 30 mg per deciliter (0.78 mmol per liter) (P<0.001). Relative to placebo, evolocumab treatment significantly reduced the risk of the primary end point (1344 patients [9.8%] vs. 1563 patients [11.3%]; hazard ratio, 0.85; 95% confidence interval [CI], 0.79 to 0.92; P<0.001) and the key secondary end point (816 [5.9%] vs. 1013 [7.4%]; hazard ratio, 0.80; 95% CI, 0.73 to 0.88; P<0.001). The results were consistent across key subgroups, including the subgroup of patients in the lowest quartile for baseline LDL cholesterol levels (median, 74 mg per deciliter [1.9 mmol per liter]). There was no significant difference between the study groups with regard to adverse events (including new-onset diabetes and neurocognitive events), with the exception of injection-site reactions, which were more common with evolocumab (2.1% vs. 1.6%). CONCLUSIONS In our trial, inhibition of PCSK9 with evolocumab on a background of statin therapy lowered LDL cholesterol levels to a median of 30 mg per deciliter (0.78 mmol per liter) and reduced the risk of cardiovascular events. These findings show that patients with atherosclerotic cardiovascular disease benefit from lowering of LDL cholesterol levels below current targets. © 2017 Massachusetts Medical Society

Evolocumab and clinical outcomes in patients with cardiovascular disease

BACKGROUND Evolocumab is a monoclonal antibody that inhibits proprotein convertase subtilisin-kexin type 9 (PCSK9) and lowers low-density lipoprotein (LDL) cholesterol levels by approximately 60%. Whether it prevents cardiovascular events is uncertain. METHODS We conducted a randomized, double-blind, placebo-controlled trial involving 27,564 patients with atherosclerotic cardiovascular disease and LDL cholesterol levels of 70 mg per deciliter (1.8 mmol per liter) or higher who were receiving statin therapy. Patients were randomly assigned to receive evolocumab (either 140 mg every 2 weeks or 420 mg monthly) or matching placebo as subcutaneous injections. The primary efficacy end point was the composite of cardiovascular death, myocardial infarction, stroke, hospitalization for unstable angina, or coronary revascularization. The key secondary efficacy end point was the composite of cardiovascular death, myocardial infarction, or stroke. The median duration of follow-up was 2.2 years. RESULTS At 48 weeks, the least-squares mean percentage reduction in LDL cholesterol levels with evolocumab, as compared with placebo, was 59%, from a median baseline value of 92 mg per deciliter (2.4 mmol per liter) to 30 mg per deciliter (0.78 mmol per liter) (P<0.001). Relative to placebo, evolocumab treatment significantly reduced the risk of the primary end point (1344 patients [9.8%] vs. 1563 patients [11.3%]; hazard ratio, 0.85; 95% confidence interval [CI], 0.79 to 0.92; P<0.001) and the key secondary end point (816 [5.9%] vs. 1013 [7.4%]; hazard ratio, 0.80; 95% CI, 0.73 to 0.88; P<0.001). The results were consistent across key subgroups, including the subgroup of patients in the lowest quartile for baseline LDL cholesterol levels (median, 74 mg per deciliter [1.9 mmol per liter]). There was no significant difference between the study groups with regard to adverse events (including new-onset diabetes and neurocognitive events), with the exception of injection-site reactions, which were more common with evolocumab (2.1% vs. 1.6%). CONCLUSIONS In our trial, inhibition of PCSK9 with evolocumab on a background of statin therapy lowered LDL cholesterol levels to a median of 30 mg per deciliter (0.78 mmol per liter) and reduced the risk of cardiovascular events. These findings show that patients with atherosclerotic cardiovascular disease benefit from lowering of LDL cholesterol levels below current targets