# Material Point Method (MPM)

## Top PDF Material Point Method (MPM):

### Material point method for crack propagation in anisotropic media: a phase field approach

Material Point Method (MPM) [37] has emerged as an extension of Particle- In-Cell methods, combining concepts pertinent to both the Eulerian and La- grangian description of classical mechanics [6]. To this point, MPM has been proven advantageous in the analysis of large scale problems involving material and geometric non-linearities, especially within the context of coupled field problems, e.g., poro-mechanics [19, 3]. In MPM, the deformable domain is dis- cretised into a set of material points that are moving within a fixed (Eulerian) computational grid. Solution of the governing equations is performed in the Eulerian grid utilizing appropriate interpolation functions.

### MODELING CPT PENETRATION UNDER UNDRAINED CONDITIONS BY THE MATERIAL POINT METHOD MODELLAZIONE DELLA PENETRAZIONE DEL PIEZOCONO IN CONDIZIONI NON

Large deformation problems are quite common in geotechnical engineering, e.g. pile driving, landslides, underground excavations. Because of mesh distorsions, Finite Element Method (FEM) which takes into account large deformation effects, such as Updated Lagrangian FEM, is not suitable to analyze these problems. Advanced techniques have recently been developed to overcome mesh distortion drawbacks. The Material Point Method is one of them. In the MPM the continuum is discretized by a cloud of material points (MP) which moves through a background mesh, thereby reproducing the large deformations of the solid. The MP carry all the properties of the continuum. This note shows the application of the MPM to the penetration of a piezocone in undrained clay.

### Phase field material point method for brittle fracture

The Material Point Method for the analysis of deformable bodies is revisited and originally upgraded to simulate crack propagation in brittle media. In this setting, phase field modelling is introduced to resolve the crack path geometry. Following a particle in cell approach, the coupled continuum/ phase-field governing equations are defined at a set of material points and interpolated at the nodal points of an Eulerian, i.e. non-evolving, mesh. The accuracy of the simulated crack path is thus de-coupled from the quality of the underlying finite element mesh and relieved from corresponding mesh-distortion errors. A staggered incremental procedure is implemented for the solution of the discrete coupled governing equations of the phase field brittle fracture problem. The proposed method is verified through a series of benchmark tests while comparisons are made between the proposed scheme, the corresponding finite element implementation as well as experimental results. Copyright c 2016 John Wiley & Sons, Ltd.

### Numerical Method of Simulation of Material Influences in Mr Tomography

double precision arithmetic and suﬃciently ﬁne mesh, because change of the magnetic ﬁeld in vicinity of slightly magnetic materials is weak in comparison to basic static magnetic ﬁeld. Second approach may use single precision arithmetic, because only reactional ﬁeld (induced own ﬁeld of magnetic material) is computed.

### Material Selection Method in Design of Automotive Brake Disc

Disc brake systems generate braking force by clamping brake pads onto a rotor that is mounted to the hub. A schematic view of the brake system is shown in Fig. 2. The high mechanical advantage of hydraulic and mechanical disc brakes allows a small lever input force at the handlebar to be converted into a large clamp force at the wheel. This large clamp force pinches the rotor with friction material pads and generates brake power. The higher the coefficient of friction for the pad, the more brake power will be generated. Coefficient of friction can vary depending on the type of material used for the brake rotor. Typically service brakes are concerned with dynamic coefficient of friction, or the coefficient of friction measured while the vehicle is moving.

### A Method for Improving the Electrochemical Properties of a Li1.2Ni0.15Co0.1Mn0.55O2 Cathode Material

discharging, the vacancy for embedding Li + ions is reduced, so the initial coulombic efficiency is lower [7]. In addition, the rate capability of these materials is relatively weak. At present, the primary methods of improving the cathode materials of the lithium-rich solid solution include phase mixtures [8, 9], surface modifications [10-12] and improved synthetic methods [13, 14]. In addition, the literature reports that the process of rapid cooling can acquire smaller grains and reduce migration resistances of Li + ions [15, 16], which improve the electrochemical performance of lithium-rich cathode materials. Thus, with a sol-gel method and rapid cooling with water quenching, a Li 1.2 Ni 0.15 Co 0.1 Mn 0.55 O 2 cathode material was synthesized. Moreover, the influences of different

### Effective Solutions to the Transport Distribution of Material by the Mayer Method

If the capacity is not filled, the process continues with finding another place with the minimum distance to the two places which were already added. The same procedure con- tinues until filling the vehicle capacity. Place selection for next circular route begins again by the furthermost place from the central point which have not been added to the pre- vious circuit (circular route). In the second step of the Mayer method, after separation of all places into distribution groups, aligning (adding) within each route places takes place. Places selected into individual circular routes are ordered by a minimum length of individual connections and routes in total. Routes can be modified based on intuitive decision-making and knowledge [1,2,6,18,19,25].

### Polymer mortar composite pipe material and manufacturing method

Composite material and plunger-cast pipe manufacturing method and system wherein the composite material includes waste, chemically unmodified PET material, one or more waste filler materials (e.g. rock crusher fines, lime sludge or waste coal combustion by-products), and fiber reinforcement (e.g. glass, metal, ceramic, carbon, organic, and polymer fibers) and wherein the PET material is melted and mixed in a container to disperse filler material and fiber reinforcement in the PET material. The resulting mixture can be formed into a tubular pipe shape using the plunger-cast manufacturing method and system wherein a plunger piston and inner collapsible mold are pushed into the melted composite material contained in an outer mold. When cooled and solidified in the mold, a composite material having a matrix comprising PET with filler material and fiber reinforcement distributed in the matrix is formed in the shape of a tubular body.

### Confidence bands for regression: the independence point method

It has been shown that the independence point method extends to higher dimen- sions but that in general the existence of a complete set of k independence points may require conditions on the design. It is clear that a construction is intimately related to multivariate Gaussian quadrature with respect to the “design measure”. The constructions given here are not unique and in fact there is typically a family of solutions. For example in the linear regression case of Section 2 any Z with the property given in (6) provides a solution. It may be that different choices can be compared using extra criteria such as minimum average width.

### A fault detection method for railway point systems

Variation in movements of fault-free RPS. The last feature of the in- field RPS data, which usually is not observed in the data obtained in the laboratory environment, is the variation in current trends of movements of fault-free RPS. Figure 4 illustrates a number of movements for one RPS when no faults have been recorded. Such variability might be explained by the deterioration of the point system, i.e. when a failure is due to occur in the future, influence of weather conditions or preventive maintenance actions, i.e. before a failure occurs.

### Stochastic Approximation Method for Fixed Point Problems

So, we consider iterative processes of stochastic approximation in the form (1.5) for finding fixed points of weakly contractive (Definition 1.1) and nonexpansive (Definition 1.3) mappings in Hilbert spaces under the conditions (1.8). We prove mean square convergence and convergence almost sure of iterative approximations and establish both asymptotic and nonasymptotic estimates of the convergence rate. Perhaps, we present here the first results of this sort for fixed point problems. Formerly the stochastic approximation methods were studied mainly to find minimal and maximal points in optimization problems (see, for example, [1-6] and references within).

### Polymer mortar composite pipe material and manufacturing method

Composite material and plunger-cast pipe manufacturing method and system wherein the composite material includes waste, chemically unmodified PET material, one or more waste filler materials (e.g. rock crusher fines, lime sludge or waste coal combustion by-products), and fiber reinforcement (e.g. glass, metal, ceramic, carbon, organic, and polymer fibers) and wherein the PET material is melted and mixed in a container to disperse filler material and fiber reinforcement in the PET material. The resulting mixture can be formed into a tubular pipe shape using the plunger-cast manufacturing method and system wherein a plunger piston and inner collapsible mold are pushed into the melted composite material contained in an outer mold. When cooled and solidified in the mold, a composite material having a matrix comprising PET with filler material and fiber reinforcement distributed in the matrix is formed in the shape of a tubular body.

### Polymer mortar composite pipe material and manufacturing method

Composite material and plunger-cast pipe manufacturing method and system wherein the composite material includes waste, chemically unmodified PET material, one or more waste filler materials (e.g. rock crusher fines, lime sludge or waste coal combustion by-products), and fiber reinforcement (e.g. glass, metal, ceramic, carbon, organic, and polymer fibers) and wherein the PET material is melted and mixed in a container to disperse filler material and fiber reinforcement in the PET material. The resulting mixture can be formed into a tubular pipe shape using the plunger-cast manufacturing method and system wherein a plunger piston and inner collapsible mold are pushed into the melted composite material contained in an outer mold. When cooled and solidified in the mold, a composite material having a matrix comprising PET with filler material and fiber reinforcement distributed in the matrix is formed in the shape of a tubular body.

### Enumeration of salmonella in compost material by a nonculture based method

Composting is an aerobic, biological process that uses naturally occurring microorganisms to convert organic waste into a humus-like product. This process is designed to both sanitise and stabilize the organic material (Imbeah, 1998). It is an environmentally sound process which is gaining worldwide popularity and is of considerable economic importance (Franke-Whittle et al., 2005). The pathogen content in compost is important because, if not properly treated the compost could be a potential source for pathogen dispersal into the environment. Research work with municipal wastes (Déportes et al., 1998, Hassen et al., 2001), sewage sludges (Dudley et al., 1980), and other organic sludges (Bustamante et al., 2008) has shown that they can contain a wide range of pathogens. Salmonella spp. and E. coli are widely used as pathogen indicators, and are included in many compost standards. Typical levels required of Salmonella spp. and E. coli in many European standards are absence in 25g and less than 10 3 colony forming units (cfu).g -1 , respectively (Commission Decision 2001/688/EC; Commission Decision 2005/384/EC; and Briancesco, 2008). The UK composting “standard” PAS 100 (BSI, 2005) requires composts that are sold to be free of Salmonella spp. and to contain fewer than 1000 cfu of E. coli per gram of material.

### Analysis the i beam subjected to three point loading or bending for different material

There are many benefit of this project. The report can help the engineer to estimate the suitable material for the construction. This is because the dimension of I beam specimen is made according the ratio of the real I beam in the structural field. Then, this report will guide the engineer in investigating the two major of beam characteristics which are strength and stiffness. Strength describes how much load the beam can carry where stiffness describes how much beam deflects when loaded. So, by this researched, engineer can know how much force any structural member can take before it will deform or break.

### Optimization method of complex electronic device test point

In terms of complex electronic systems, in order to enhance the test efficiency and reduce the test cost, an optimization method of analog circuit test point combining with fault dictionary and branch and bound is proposed. It adopts fuzzy set and fault dictionary as tools, and takes fault detection and fault isolation as constraint condition, thus to build a 0-1 programming mathematical model for test point optimization, which is solved with branch and bound. Finally, it simulates and verifies the method with classical test optimization circuit. The simulation result indicates that the above method can realize rapid optimization of test point on the premise of guaranteeing the demand of fault diagnosis, providing guidance for test implementation.

### Method of registration for 3D face point cloud data

One of the applications that use the color image as an input to produce a 3D face model is Basel Face Model known as MorphFace [9]. MorphFace is based on the research of Paysan et al. [10]. They use a large database of 3D face models and compare it with the image taken. The closest comparison is decided as the result. Although this method produced very impressive results, but their designated process is not for real-time situation.

### Analysis of landscape pattern based on the point pattern method

Point Patterns Analysis: Point patterns can be studied by the order analysis [13]. One of the most commonly used order methods is Ripley’s K function, which is a tool for analyzing completely mapped spatial point process data, i.e. data on the locations of events and comparing a given point distribution with a random distribution; i.e., the point distribution under investigation is tested against the null hypothesis that the points are distributed randomly and independently [12]. Ripley’s K method is based on the number of points tallied within a given distance or distance class. As every point in the sample is taken once as the center of a plot circle, Ripley’s K function provides an inference at the global level of the studied element [15].

### A linear time method for the detection of point and collective anomalies

The resulting ROC curves, as well as examples of realisations of the data for the scenario of weak and strong changes in mean can be found in Figures 2 and 3 respectively. The results for joint changes in mean and variance, as well as changes in variance can be found in the supplementary material. We see that CAPA generally outperforms PELT, even in the absence of point anomalies. This is due to it having more statistical power, by exploiting the epidemic nature of the change. This becomes particularly apparent when the changes are weak. CAPA also outperform BreakoutDetection and luminol for epidemic changes in mean, the scenario for which these methods were developed. Moreover, the performance of CAPA is barely affected by the presence of point anomalies, unlike that of the non-robust methods. This observation remained true when we repeated our analysis with N (0, 1000 2 ) distributed point anomalies. The ROC curves for these additional simulations can be

### Convergence of the Proximal Point Method for Metrically Regular Mappings

In the last three decades a number of authors have considered generalizations and modifications of the proximal point algorithm, and have also found applications of this method to specific variational problems. Most of the rapidly growing body of the literature on this subject has been concentrated on various versions of the algorithm for solving inclusions involving monotone mappings, and specifically, on monotone variational inequalities. We mention here the more recent papers by Solodov and Svaiter [20], Auslender and Teboulle [2], a series of papers by Kaplan and Tichatschke [13], Ahn et al. [1], Yang and He [22] and Bauschke et al. [3]; see also the references therein. Weaker form of monotonicity have been considered first in Spingarn [21], for details see Iusem et al. [12]. A convergence result of a different type was recently derived by Pennanen [17] who replaced the global condition of monotonicity by the local condition of strong regularity and observed that under this condition the Yosida regularization of the mapping T can be locally monotone even when T is not, and this local monotonicity is sufficient to show local convergence. In all papers mentioned above X is assumed to be a Hilbert space and T acts from X to itself.