I’m sorry for the late response, here it is a sample .obj model that has the described behavior.
OBJ:
[patch]
3ds Max Wavefront OBJ Exporter v0.97b - ©2007 guruware
mtllib ShadowTestModels.mtl
#
# object Box001
#
v -43.703072 0.000000 -53.466736
v -43.703072 0.000000 46.057602
v 39.985809 0.000000 -53.466736
v 39.985809 0.000000 46.057602
v 39.985809 -3.840992 46.057602
v -43.703072 -3.840992 46.057602
v 39.985809 -3.840992 -53.466736
v -43.703072 -3.840992 -53.466736
# 8 vertices
vn 0.000000 1.000000 -0.000000
vn 0.000000 -1.000000 -0.000000
vn 0.000000 0.000000 1.000000
vn 1.000000 0.000000 -0.000000
vn 0.000000 0.000000 -1.000000
vn -1.000000 0.000000 -0.000000
# 6 vertex normals
vt 0.000000 1.000000 0.000000
vt 0.000000 0.000000 0.000000
vt 1.000000 1.000000 0.000000
vt 1.000000 0.000000 0.000000
# 4 texture coords
g Box001
usemtl 01___Default
s 2
f 1/1/1 2/2/1 3/3/1
f 4/4/1 3/3/1 2/2/1
s 4
f 5/2/2 6/4/2 7/1/2
f 8/3/2 7/1/2 6/4/2
s 8
f 4/4/3 2/2/3 5/3/3
f 6/1/3 5/3/3 2/2/3
s 16
f 3/4/4 4/2/4 7/3/4
f 5/1/4 7/3/4 4/2/4
s 32
f 1/4/5 3/2/5 8/3/5
f 7/1/5 8/3/5 3/2/5
s 64
f 2/4/6 1/2/6 6/3/6
f 8/1/6 6/3/6 1/2/6
# 12 faces
#
# object Pyramid001
#
v 16.790106 22.596392 -31.991638
v 6.335835 0.005000 -17.833244
v 27.244377 0.005000 -17.833244
v 27.244377 0.005000 -46.150032
v 6.335835 0.005000 -46.150032
v 16.790106 0.005000 -31.991638
# 6 vertices
vn 0.000000 0.531044 0.847344
vn 0.907539 0.419968 -0.000000
vn 0.000000 0.531044 -0.847344
vn -0.907539 0.419968 -0.000000
vn 0.000000 -1.000000 -0.000000
# 5 vertex normals
vt 0.500000 1.000000 0.000000
vt 0.000000 0.000000 0.000000
vt 1.000000 0.000000 0.000000
vt 0.130810 0.000000 0.000000
vt 1.130810 0.000000 0.000000
vt 0.000000 1.000000 0.000000
vt 0.500000 0.500000 0.000000
vt 1.000000 1.000000 0.000000
# 8 texture coords
g Pyramid001
usemtl 07___Default
s 4
f 9/5/7 10/6/7 11/7/7
s 2
f 9/5/8 11/8/8 12/9/8
s 16
f 9/5/9 12/6/9 13/7/9
s 32
f 9/5/10 13/8/10 10/9/10
s 8
f 10/10/11 14/11/11 11/12/11
f 11/12/11 14/11/11 12/7/11
f 12/7/11 14/11/11 13/6/11
f 13/6/11 14/11/11 10/10/11
# 8 faces
#
# object Box002
#
v -17.053314 0.000000 41.072510
v -17.053314 0.000000 1.378830
v -14.225887 0.000000 1.378830
v -14.225887 0.000000 41.072510
v -17.053314 14.472441 41.072510
v -14.225887 14.472441 41.072510
v -14.225887 14.472441 1.378830
v -17.053314 14.472441 1.378830
# 8 vertices
vn 0.000000 -1.000000 -0.000000
vn 0.000000 1.000000 -0.000000
vn 0.000000 0.000000 1.000000
vn 1.000000 0.000000 -0.000000
vn 0.000000 0.000000 -1.000000
vn -1.000000 0.000000 -0.000000
# 6 vertex normals
vt 1.000000 0.000000 0.000000
vt 1.000000 1.000000 0.000000
vt 0.000000 1.000000 0.000000
vt 0.000000 0.000000 0.000000
# 4 texture coords
g Box002
usemtl 02___Default
s 2
f 15/13/12 16/14/12 17/15/12
f 17/15/12 18/16/12 15/13/12
s 4
f 19/16/13 20/13/13 21/14/13
f 21/14/13 22/15/13 19/16/13
s 8
f 15/16/14 18/13/14 20/14/14
f 20/14/14 19/15/14 15/16/14
s 16
f 18/16/15 17/13/15 21/14/15
f 21/14/15 20/15/15 18/16/15
s 32
f 17/16/16 16/13/16 22/14/16
f 22/14/16 21/15/16 17/16/16
s 64
f 16/16/17 15/13/17 19/14/17
f 19/14/17 22/15/17 16/16/17
# 12 faces
[/patch]
MATERIAL:
[patch]
# 3ds Max Wavefront OBJ Exporter v0.97b - (c)2007 guruware
newmtl 01___Default
Ns 9.999999
Ni 1.500000
d 1.000000
Tr 0.000000
Tf 1.000000 1.000000 1.000000
illum 2
Ka 1.000000 1.000000 1.000000
Kd 1.000000 1.000000 1.000000
Ks 0.000000 0.000000 0.000000
Ke 0.000000 0.000000 0.000000
newmtl 07___Default
Ns 9.999999
Ni 1.500000
d 1.000000
Tr 0.000000
Tf 1.000000 1.000000 1.000000
illum 2
Ka 0.588235 0.596078 0.776471
Kd 0.588235 0.596078 0.776471
Ks 0.000000 0.000000 0.000000
Ke 0.000000 0.000000 0.000000
newmtl 02___Default
Ns 9.999999
Ni 1.500000
d 1.000000
Tr 0.000000
Tf 1.000000 1.000000 1.000000
illum 2
Ka 0.541176 0.541176 0.541176
Kd 0.541176 0.541176 0.541176
Ks 0.000000 0.000000 0.000000
Ke 0.000000 0.000000 0.000000
[/patch]