Material point method simulation of hydro-mechanical behaviour in twophase porous geomaterials: A state-of-the-art review

The material point method(MPM)has been gaining increasing popularity as an appropriate approach to the solution of coupled hydro-mechanical problems involving large deformation.In this paper,we survey the current state-of-the-art in the MPM simulation of hydro-mechanical behaviour in two-phase porous geomaterials.The review covers the recent advances and developments in the MPM and their extensions to capture the coupled hydro-mechanical problems involving large deformations.The focus of this review is aiming at providing a clear picture of what has or has not been developed or implemented for simulating two-phase coupled large deformation problems,which will provide some direct reference for both practitioners and researchers.

“Three Methods and Three Points” regulates p38 mitogen-activated protein kinase in the dorsal horn of the spinal cord in a rat model of sciatic nerve injury

Tuina is a traditional Chinese treatment for sensory disturbances caused by peripheral nerve injury and related diseases. Our previous studies showed that tuina regulates relevant regions and indices of the spinal dorsal horn using the Dian, Bo, and Rou method in Yinmen（BL37）, Yanglingquan（GB34）, and Weizhong（BL40）. Treatment prevents muscle atrophy, protects spinal cord neurons, and promotes sciatic nerve repair. The mechanisms of action of tuina for treating peripheral nerve injury remain poorly understood. This study established rat models of sciatic nerve injury using the crushing method. Rats received Chinese tuina in accordance with the principle of ＂Three Methods and Three Points,＂ once daily for 20 days. Tuina intervention reduced paw withdrawal latency and improved wet weight of the gastrocnemius muscle, as well as promoting morphological recovery of sciatic nerve fibers, Schwann cells, and axons. The protein expression levels of phospho-p38 mitogen-activated protein kinase, tumor necrosis factor-α, and interleukin-1β also decreased. These findings indicate that ＂Three Methods and Three Points＂ promoted morphological recovery and improved behavior of rats with peripheral nerve injury.

Mobility and dynamic erosion process of granular flow:insights from numerical investigation using material point method

In order to understand the dynamics of granular flow on an erodible base soil,in this paper,a series of material point method-based granular column collapse tests were conducted to investigate numerically the mobility and dynamic erosion process of granular flow subjected to the complex settings,i.e.,the aspect ratio,granular mass,friction and dilatancy resistance,gravity and presence of water.A set of power scaling laws were proposed to describe the final deposit characteristics of granular flow by the relations of the normalized run-out distance and the normalized final height of granular flow against the aspect ratio,being greatly affected by the complex geological settings,e.g.,granular mass,the friction and dilatancy resistance of granular soil,and presence of water in granular flow.An index of the coefficient of friction of granular soil was defined as a ratio of the target coefficient of friction over the initial coefficient of friction to quantify the scaling extent of friction change(i.e.,friction strengthening or weakening).There is a characteristic aspect ratio of granular column corresponding to the maximum mobility of granular flow with the minimum index of the apparent coefficient of friction.The index of the repose coefficient of friction of granular flow decreased gradually with the increase in aspect ratio because higher potential energy of granular column at a larger aspect ratio causes a larger kinetic energy of granular soil to weaken the friction of granular soil as a kind of velocity-related friction weakening.An increase in granular mass reduces gradually the indexes of the apparent and repose coefficients of friction of granular soil to enhance the mobility of granular flow.The mobility of granular flow increases gradually with the decrease in friction angle or increase in dilatancy angle of granular soil.However,the increase of gravity accelerates granular flow but showing the same final deposit profile without any dependence on gravity.The mobility of granular flow increases gradually by lowering the indexes of the apparent and repose coefficients of friction of granular flow while changing the surroundings,in turn,the dry soil,submerged soil and saturated soil,implying a gradually increased excessive mobility of granular flow with the friction weakening of granular soil.Presence of water in granular flow may be a potential catalyzer to yield a long run-out granular flow,as revealed in comparison of water-absent and water-present granular flows.In addition,the dynamic erosion and entrainment of based soil induced by granular flow subjected to the complex geological settings,i.e.,the aspect ratio,granular mass,gravity,friction and dilatancy resistance,and presence of water,were comprehensively investigated as well.

Impact dynamics of granular flow on rigid barriers:insights from numerical investigation using material point method

In order to advance the understanding of the impact dynamics of granular flow in complex geological settings,this paper studied the impact dynamics of granular flow on rigid barriers with a number of Material Point Method(MPM)numerical tests.The impact behavior of granular flow on a rigid barrier was characterized by the initial dynamic impact stage,dynamic surge impact stage,compression impact stage and static stage of granular flow,where the impact force of granular flow was comprised of the dynamic and static forces of granular flow.The impact behavior of granular flow on a rigid barrier was characterized by the states of the fast or slow impact behavior of granular flow.The angle of slope and aspect ratio of granular soil greatly affected the impact behavior of granular flow on a column rigid barrier,where a power model was proposed to quantify the residual(Fnr)-over-maximum(Fnmax)normal impact force ratio of granular flow Fnr⁄Fnmax incorporating the effects of the angle of slope and aspect ratio of granular soil.With the increase of the column rigid barrier up to the semi-infinite column rigid barrier,the impact dynamics of granular flow gradually increased up to a maximum by progressively transforming the overflow into the dynamic surge impact of the incoming flow on the rigid barrier to capture more granular soil of granular flow against the rigid barrier.Presence of water in granular flow,i.e.,a mixture of solid and liquid in granular flow,yielded a dynamic coupling contribution of the solid and liquid,being accompanied by the whole dynamic process of granular flow,on the impact behavior of granular flow on a rigid barrier,where the liquid-phase material of granular flow,i.e.,the water,was predominant to contribute on the normal impact force of granular flow in comparison with the solid-phase material of granular flow.In addition,other factors,e.g.,the shape of rigid barrier(i.e.,the column barrier,arch barrier and circle barrier),and the gravity(i.e.,in the gravitational environment of the Moon,Earth and Mars),greatly affected the impact behavior of granular flow on a rigid barrier as well.

A hybrid contact approach for modeling soil-structure interaction using the material point method

The grid-based multi-velocity field technique has become increasingly popular for simulating the Material Point Method(MPM)in contact problems.However,this traditional technique has some shortcomings,such as(1)early contact and contact penetration can occur when the contact conditions are unsuitable,and(2)the method is not available for contact problems involving rigid-nonrigid materials,which can cause numerical instability.This study presents a new hybrid contact approach for the MPM to address these limitations to simulate the soil and structure interactions.The approach combines the advantages of point-point and point-segment contacts to implement contact detection,satisfying the impenetrability condition and smoothing the corner contact problem.The proposed approach is first validated through a disk test on an inclined slope.Then,several typical cases,such as granular collapse,bearing capacity,and deformation of a flexible retaining wall,are simulated to demonstrate the robustness of the proposed approach compared with FEM or analytical solutions.Finally,the proposed method is used to simulate the impact of sand flow on a deformable structure.The results show that the proposed contact approach can well describe the phenomenon of soil-structure interaction problems.

An Efficient Reliability-Based Optimization Method Utilizing High-Dimensional Model Representation and Weight-Point Estimation Method

The objective of reliability-based design optimization(RBDO)is to minimize the optimization objective while satisfying the corresponding reliability requirements.However,the nested loop characteristic reduces the efficiency of RBDO algorithm,which hinders their application to high-dimensional engineering problems.To address these issues,this paper proposes an efficient decoupled RBDO method combining high dimensional model representation(HDMR)and the weight-point estimation method(WPEM).First,we decouple the RBDO model using HDMR and WPEM.Second,Lagrange interpolation is used to approximate a univariate function.Finally,based on the results of the first two steps,the original nested loop reliability optimization model is completely transformed into a deterministic design optimization model that can be solved by a series of mature constrained optimization methods without any additional calculations.Two numerical examples of a planar 10-bar structure and an aviation hydraulic piping system with 28 design variables are analyzed to illustrate the performance and practicability of the proposed method.

AHermitian C^(2) Differential Reproducing Kernel Interpolation Meshless Method for the 3D Microstructure-Dependent Static Flexural Analysis of Simply Supported and Functionally Graded Microplates

This work develops a Hermitian C^(2) differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredependent static flexural behavior of a functionally graded(FG)microplate subjected to mechanical loads and placed under full simple supports.In the formulation,we select the transverse stress and displacement components and their first-and second-order derivatives as primary variables.Then,we set up the differential reproducing conditions(DRCs)to obtain the shape functions of the Hermitian C^(2) differential reproducing kernel(DRK)interpolant’s derivatives without using direct differentiation.The interpolant’s shape function is combined with a primitive function that possesses Kronecker delta properties and an enrichment function that constituents DRCs.As a result,the primary variables and their first-and second-order derivatives satisfy the nodal interpolation properties.Subsequently,incorporating ourHermitianC^(2)DRKinterpolant intothe strong formof the3DCCST,we develop a DRKIM method to analyze the FG microplate’s 3D microstructure-dependent static flexural behavior.The Hermitian C^(2) DRKIM method is confirmed to be accurate and fast in its convergence rate by comparing the solutions it produces with the relevant 3D solutions available in the literature.Finally,the impact of essential factors on the transverse stresses,in-plane stresses,displacements,and couple stresses that are induced in the loaded microplate is examined.These factors include the length-to-thickness ratio,the material length-scale parameter,and the inhomogeneity index,which appear to be significant.

Clinical Observation on Brachial Plexus Block with “One Injection Two Points” Method Guiding by Ultrasound

OBJECTIVE: To compare the clinical effect of brachial plexus block with "One Injection Two Points" guided under ultrasound and the conventional method guiding by ultrasound. METHODS: 70 patients were randomized evenly into 2 groups, with 35 patients in each group, while the Experiment Group(Group B) received One Injection Two Points" method, the Control Group(Group A) received the conventional method.The nerve block every 5 s, the success rate of anesthesia, the dosage of local anesthetics, second remedial anesthesia, adverse reactions, etc.were recorded. RESULTS: Group B was superior to group A in the success rate of anesthesia; There were 6 patients in group A who required constant pump injection of Remifentanil to remedy, while no patients in Group B needed remedy treatment. There were no serious adverse reactions in both groups.CONCLUSIONS: The clinical effect of brachial plexus block with "One Injection Two Points" method guided under ultrasoundguiding by ultrasound was superior to that of the conventional method.

A novel PID controller tuning method based on optimization technique

An approach for parameter estimation of proportional-integral-derivative(PID) control system using a new nonlinear programming(NLP) algorithm was proposed.SQP/IIPM algorithm is a sequential quadratic programming(SQP) based algorithm that derives its search directions by solving quadratic programming(QP) subproblems via an infeasible interior point method(IIPM) and evaluates step length adaptively via a simple line search and/or a quadratic search algorithm depending on the termination of the IIPM solver.The task of tuning PI/PID parameters for the first-and second-order systems was modeled as constrained NLP problem. SQP/IIPM algorithm was applied to determining the optimum parameters for the PI/PID control systems.To assess the performance of the proposed method,a Matlab simulation of PID controller tuning was conducted to compare the proposed SQP/IIPM algorithm with the gain and phase margin(GPM) method and Ziegler-Nichols(ZN) method.The results reveal that,for both step and impulse response tests,the PI/PID controller using SQP/IIPM optimization algorithm consistently reduce rise time,settling-time and remarkably lower overshoot compared to GPM and ZN methods,and the proposed method improves the robustness and effectiveness of numerical optimization of PID control systems.

Coupled GIMP and CPDI material point method in modelling blast-induced three-dimensional rock fracture

Three-dimensional rock fracture induced by blasting is a highly complex problem and has received considerable attention in geotechnical engineering.The material point method is firstly applied to treat this challenging task.Some inherent weaknesses can be overcome by coupling the generalized interpolation material point(GIMP)and the convected particle domain interpolation technique(CPDI).For the media in the borehole,unchanged GIMP-type particles are used to guarantee a homogenous blast pressure.CPDITetrahedron type particles are employed to avoid the fake numerical fracture near the borehole for the rock material.A blasting experiment using three-dimensional single-borehole rock was simulated to examine the applicability of the coupled model under realistic loading and boundary conditions.A good agreement was achieved between the simulation and experimental results.Moreover,the mechanism of three-dimensional rock fracture was analyzed.It was concluded that rock particle size and material parameters play an important role in rock damage.The reflected tensile waves cause severe damage in the lower part of the model.Rayleigh waves occur on the top face of the rock model to induce a hoop failure band.

FIXED POINTS AND STABILITY FOR QUARTIC MAPPINGS IN β-NORMED LEFT BANACH MODULES ON BANACH ALGEBRAS

The goal of the present paper is to investigate some new HUR-stability results by applying the alternative fixed point of generalized quartic functional equationin β-Banach modules on Banach algebras. The concept of Ulam-Hyers-Rassias stability （briefly, HUR-stability） originated from Th. M. Rassias stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 （1978）, 297-300.

An ideal point method adopting grey relational entropy to estimate life cycle cost with effectiveness of torpedo

To making the decision of the developing blue prints,ideal point method was selected to estimate the life cycle cost with effectiveness of torpedo.At the same time,the concept of grey relational entropy of the grey system theory was adopted to compute the distance between each blue print and the ideal point(or negative ideal point).The blue print,nearest to the ideal point and farthest to the negative ideal point,is the best one.As an example,four blue prints of torpedo were estimated.The result indicates the practical value of this method.

A Combined Homotopy Infeasible Interior-Point Method for Convex Nonlinear Programming

In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method （CHIIP） for convex nonlinear programming problems. For any convex nonlinear programming, without strict convexity for the logarithmic barrier function, we get different solutions of the convex programming in different cases by CHIIP method.

A Flux Based Approximation to Simulate Coupled Hydromechanical Problems for Mines with Heterogeneous Rock Types Using the Material Point Method

Advances in numerical simulation techniques play an important role in helpingmining engineers understand those parts of the rock mass that cannot be readily observed.The Material Point Method(MPM)is an example of such a tool that is gaining popularity for studying geotechnical problems.In recent years,the original formulation of MPM has been extended to not only account for simulating the mechanical behaviour of rock under different loading conditions,but also to describe the coupled interaction of pore water and solid phases in materials.These methods assume that the permeability of mediums is homogeneous,and we show that these MPM techniques fail to accurately capture the correct behaviour of the fluid phase if the permeability of the material is heterogeneous.In this work,we propose a novel implementation of the coupled MPM to address this problem.We employ an approach commonly used in coupled Finite Volume Methods,known as the Two Point Flux Approximation(TPFA).Our new method is benchmarked against two well-known analytical expressions(a one-dimensional geostatic consolidation and the so-called Mandel-Cryer effect).Its performance is compared to existing coupled MPM approaches for homogeneous materials.In order to gauge the possible effectiveness of our technique in the field,we apply ourmethod to a case study relating to a mine known to experience severe problems with pore water.

Modeling footing resting on anisotropic sand using material point method

Sand typically exhibits anisotropic internal structure which may significantly influence its mechanical behavior. The material point method (MPM) can eliminate mesh distortion and thus is suitable for investigating geotechnical problems with large deformation. In this study, an advanced anisotropic critical state theory (ACST)-based soil model is implemented in MPM to study the response of strip footing resting on anisotropic sand. The capability of the model is verified by simulating several element tests and strip footing tests with different soil densities and fabric bedding plane orientations. For the footing problem with a vertical load, as the fabric bedding plane orientation increases, the bearing capacity decreases and its corresponding settlement increases. The failure pattern becomes asymmetrical when the bedding plane orientation or the loading direction is inclined. A comparison between the simulation results predicted by the anisotropic and isotropic models is made, which demonstrates that neglecting the fabric anisotropy may lead to the overestimation of the bearing capacity.

Modeling pipe-soil interaction under vertical downward relative offset using B-spline material point method

To analyze the pipeline response under permanent ground deformation,the evolution of resistance acting on the pipe during the vertical downward offset is an essential ingredient.However,the efficient simulation of pipe penetration into soil is challenging for the conventional finite element(FE)method due to the large deformation of the surrounding soils.In this study,the B-spline material point method(MPM)is employed to investigate the pipe-soil interaction during the downward movement of rigid pipes buried in medium and dense sand.To describe the density-and stress-dependent behaviors of sand,the J2-deformation type model with state-dependent dilatancy is adopted.The effectiveness of the model is demonstrated by element tests and biaxial compression tests.Afterwards,the pipe penetration process is simulated,and the numerical outcomes are compared with the physical model tests.The effects of pipe size and burial depth are investigated with an emphasis on the mobilization of the soil resistance and the failure mechanisms.The simulation results indicate that the bearing capacity formulas given in the guidelines can provide essentially reasonable estimates for the ultimate force acting on buried pipes,and the recommended value of yield displacement may be underestimated to a certain extent.

Dynamic economic dispatch combining network flow and interior point method

Under the environment of electric power market, economic dispatch (ED) problem should consider network constraints, unit ramp rates, besides the basic constraints. For this problem, it is important to establish the effective model and algorithm. This paper examines the decoupled conditions that affect the solution optimality to this problem. It proposes an effective model and solution method. Based on the look-ahead technique, it finds the number of time intervals to guarantee the solution optimality. Next, an efficient technique for finding the optimal solution via the interior point methods is described. Test cases, which include dispatching six units over 5 time intervals on the IEEE 30 test system with line flows and ramp constraints are presented. Results indicate that the computational effort as measured by iteration counts or execution time varies only modestly with the problem size.

A multiscale material point method for impact simulation

To better simulate multi-phase interactions involving failure evolution, the material point method （MPM） has evolved for almost twenty years. Recently, a particle-based multiscale simulation procedure is being developed, within the framework of the MPM, to describe the detonation process of energetic nano-composites from molecular to continuum level so that a multiscale equation of state could be formulated. In this letter, a multiscale MPM is proposed via both hierarchical and concurrent schemes to simulate the impact response between two microrods with different nanostructures. Preliminary results are presented to illustrate that a transition region is not required between different spatial scales with the proposed approach.

Simulation of Seawater Intrusion in Coastal Confined Aquifer Using a Point Collocation Method Based Meshfree Model

Seawater intrusion caused by groundwater over-exploitation from coastal aquifers poses a severe problem in many regions. Formulation of proper pumping strategy using a simulation model can assure sustainable supply of fresh water from the coastal aquifers. The focus of the present study is on the development of a numerical model based on Meshfree (MFree) method to study the seawater intrusion problem. For the simulation of seawater intrusion problem, widely used models are based on Finite Difference (FDM) and Finite Element (FEM) Methods, which demand well defined grids/meshes and considerable pre-processing efforts. Here, MFree Point Collocation Method (PCM) based on the Radial Basis Function (RBF) is proposed for the simulation. Diffusive interface approach with density-dependent dispersion and solution of flow and solute transport is adopted. These equations are solved using PCM with appropriate boundary conditions. The developed model has been verified with Henry’s problem, and found to be satisfactory. Further the model has been applied to another established problem and an attempt is made to examine the influence of important system parameters including pumping and recharge on the seawater intrusion. The PCM based MFree model is found computationally efficient as preprocessing is avoided when compared to other numerical methods.