刚性球体打击spg沙土和eps泡沫保护的桥墩

1，项目描述

本项目为落石冲击堆满沙土和EPS泡沫防护的桥墩，其中沙土采用spg算法。桥墩为钢筋混凝土结构，内含纵筋和箍筋钢筋，EPS泡沫采用24号材料的试验曲线模拟。

2，几何模型

首先利用workbench的dm模块建立沙土、EPS泡沫、桥墩及钢筋的几何模型，其中钢筋为1D线体。模型如下图所示。

3，材料

落石为刚体，采用rigid本构

*MAT_RIGID_TITLE

luoshi

$#     mid        ro         e        pr         n    couple         m     alias

         4    2730.02.00000E10       0.3       0.0       0.0       0.0          

$#     cmo      con1      con2    

       0.0         0         0

$#lco or a1        a2        a3        v1        v2        v3  

       0.0       0.0       0.0       0.0       0.0       0.0

沙土采用可压缩泡沫崩MAT_CRUSHABLE_FOAM，沙漏采用5号，系数0.03.

*MAT_CRUSHABLE_FOAM_TITLE

shatu

$#     mid        ro         e        pr      lcid       tsc      damp    

         7    1628.04.000000E7       0.3         2       0.0       0.0

*HOURGLASS_TITLE

shatu

$#    hgid       ihq        qm       ibq        q1        q2    qb/vdc        qw

         7         5      0.03         0       1.5      0.06      0.03      0.03

EPS泡沫采用24号多线性弹塑性本构，借助试验曲线；

*MAT_PIECEWISE_LINEAR_PLASTICITY_TITLE

eps

$#     mid        ro         e        pr      sigy      etan      fail      tdel

         9      20.0   6000000      0.12  100000.0  600000.01.00000E21       0.0

$#       c         p      lcss      lcsr        vp  

       0.0       0.0         3         0       0.0

$#    eps1      eps2      eps3      eps4      eps5      eps6      eps7      eps8

       0.0       0.0       0.0       0.0       0.0       0.0       0.0       0.0

$#     es1       es2       es3       es4       es5       es6       es7       es8

       0.0       0.0       0.0       0.0       0.0       0.0       0.0       0.0

桥墩采用混凝土材料，使用jhc本构，采用4号0.03沙漏。并定义额外的失效参数。

*MAT_JOHNSON_HOLMQUIST_CONCRETE_TITLE

hunningtuban

$#     mid        ro         g         a         b         c         n        fc

         1    2650.01.68000E10      0.79       1.6     0.007      0.618.400000E7

$#       t      eps0     efmin     sfmax        pc        uc        pl        ul

   6000000       1.0      0.01       7.02.800000E7     0.0011.400000E9       0.1

$#      d1        d2        k1        k2        k3        fs  

      0.04       1.08.50000E10-1.7100E112.08000E11     0.004

*HOURGLASS_TITLE

hunningtuban

$#    hgid       ihq        qm       ibq        q1        q2    qb/vdc        qw

         1         4      0.03         0       1.5      0.06      0.03      0.03

*MAT_ADD_EROSION_TITLE

hunningtuban-shixiao

$#     mid      excl    mxpres     mneps    effeps    voleps    numfip       ncs

         1       0.0       0.0       0.0       0.0       0.0       1.0       1.0

$#  mnpres     sigp1     sigvm     mxeps     epssh     sigth   impulse    failtm

       0.0       0.0       0.0      0.06       0.0       0.0       0.0       0.0

$#    idam         -         -         -         -         -         -    lcregd

         0         0         0         0         0         0         0         0

$#   lcfld      nsff   epsthin    engcrt    radcrt   lceps12   lceps13   lcepsmx

         0        10       0.0       0.0       0.0         0         0         0

$#  dteflt    unused     mxtmp     dtmin     

       0.0                 0.0       0.0

钢筋采用弹塑性本构，定义0.2的有限塑性应变失效参数。

*MAT_PLASTIC_KINEMATIC_TITLE

pingmian-gangjin

$#     mid        ro         e        pr      sigy      etan      beta    

         2    7850.02.00000E11       0.35.000000E82.000000E9       0.0

$#     src       srp        fs        vp  

       0.0       0.0       0.2       0.0

4，单元及有限元网格

沙土采用SPG算法，其他均采用lagrange算法。

*SECTION_SOLID_SPG

7,47

$DX,DY,DZ,,KERNEL,,SMSTEP

1.8,1.8,1.8,,2,,2

$IDAM,FS失效，

1,0.004

workbench下划分lagrange网格，网格数5万以上。

5，接触建立

泡沫与桥墩之间采用绑定接触，沙土与泡沫之间为摩擦接触，球与沙土为自动接触。

*CONTACT_AUTOMATIC_SURFACE_TO_SURFACE_ID

$#     cid                                                                 title

         1luoshi-shatu

$#    ssid      msid     sstyp     mstyp    sboxid    mboxid       spr       mpr

         7         4         3         3         0         0         0         0

$#      fs        fd        dc        vc       vdc    penchk        bt        dt

       0.4       0.4       0.0       0.0       0.0         0       0.01.00000E20

$#     sfs       sfm       sst       mst      sfst      sfmt       fsf       vsf

       1.0       1.0       0.0       0.0       1.0       1.0       1.0       1.0

$#    soft    sofscl    lcidab    maxpar     sbopt     depth     bsort    frcfrq

         1       0.1         0     1.025       2.0         2         0         1

*CONTACT_AUTOMATIC_SURFACE_TO_SURFACE_ID

$#     cid                                                                 title

         4ban-duntai

$#    ssid      msid     sstyp     mstyp    sboxid    mboxid       spr       mpr

         5         1         3         3         0         0         0         0

$#      fs        fd        dc        vc       vdc    penchk        bt        dt

       0.4       0.4       0.0       0.0       0.0         0       0.01.00000E20

$#     sfs       sfm       sst       mst      sfst      sfmt       fsf       vsf

       1.0       1.0       0.0       0.0       1.0       1.0       1.0       1.0

*CONTACT_TIED_SURFACE_TO_SURFACE_ID

$#     cid                                                                 title

         9tie eps-huxingban

$#    ssid      msid     sstyp     mstyp    sboxid    mboxid       spr       mpr

         2         1         0         0         0         0         0         0

$#      fs        fd        dc        vc       vdc    penchk        bt        dt

       0.4       0.4       0.0       0.0       0.0         0       0.01.00000E20

$#     sfs       sfm       sst       mst      sfst      sfmt       fsf       vsf

       1.0       1.0       0.0       0.0       1.0       1.0       1.0       1.0

$#    soft    sofscl    lcidab    maxpar     sbopt     depth     bsort    frcfrq

         1       0.1         0     1.025       2.0         2         0         1

6，边界及载荷

施加z方向重力；

*LOAD_BODY_Z

$#    lcid        sf    lciddr        xc        yc        zc       cid   

         1       1.0         0       0.0       0.0       0.0         0

*DEFINE_CURVE_TITLE

zhongli

$#    lcid      sidr       sfa       sfo      offa      offo    dattyp     lcint

         1         0       1.0       1.0       0.0       0.0         0         0

$#                a1                  o1  

                 0.0                 9.8

                10.0                 9.8

落石Z方向速度伪18.8m/s。

*INITIAL_VELOCITY_GENERATION

$#nsid/pid      styp     omega        vx        vy        vz     ivatn      icid

         4         2       0.0       0.0       0.0 -18.80632         0         0

$#      xc        yc        zc        nx        ny        nz     phase    irigid

       0.0       0.0       0.0       0.0       0.0       0.0         0         0

7，求解设置

计算时间0.2s。为防止容易负体积，时间步因采用0.5

*CON*T*ROL_TERMINATION

$#  endtim    endcyc     dtmin    endeng    endmas     nosol     

       0.2         0      0.05       0.01.000000E8         0

*CON*TROL_TIMESTEP

$#  dtinit    tssfac      isdo    tslimt     dt2ms      lctm     erode     ms1st

       0.0       0.5         0       0.0       0.0         0         1         0

$#  dt2msf   dt2mslc     imscl    unused    unused     rmscl     

       0.0         0         0                           0.0

施加全局阻尼0.05

*DAMPING_GLOBAL

$#    lcid    valdmp       stx       sty       stz       srx       sry       srz

         0      0.05       0.0       0.0       0.0       0.0       0.0       0.0

$

8，求解

6核cpu求解时间1.5小时。

9，结果分析

通过计算，沙土由于采用可压碎泡沫本构MAT_CRUSHABLE_FOAM，非常容易出现负体积，因此采用了SPG算法，经过计算可见沙土的成坑性能非常好，也与试验进行了对比，接触反力与试验测得值非常接近。

落石打击沙土、桥墩等的变形应力如下图所示：

落石与沙土之间的接触力如下：

沙土沙漏能几乎为0；精度非常高。

 

sph对比spg优劣势：

Ø Sph效率高但是精度低；spg反之；

Ø Sph难以与fem耦合，spg容易与fem耦合；

Ø Sph用于高速问题，spg低速高速问题都适用；

Ø Sph支持2D-3D，spg只支持3D；

Ø Fem失效后动量能量不守恒，spg在失效后仍然守恒。