/MAT/LAW87 (BARLAT2000)

ブロックフォーマットキーワード この弾塑性則は、アルミニウム合金を中心とした異方性材料向けに開発されています。

降伏応力は、ユーザー定義関数(塑性ひずみと応力の関係)またはSwiftモデルとVoceモデルの組み合わせから解析的に定義できます。このモデルは、Barlat YLD2000基準に基づいています。 1

フォーマット

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW87/mat_ID/unit_IDまたはMAT/BARLAT2000/mat_ID/unit_ID
mat_title
ρ i                
E ν  Iflag VP c p
Ifit =0の場合、以下の3つの行を挿入
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
α 1 α 2 α 3 α 4 Ifit  
α 5 α 6 α 7 α 8  
空白行
Ifit =1の場合、以下の3つの行を挿入
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
σ 00 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaaicdacaaIWaaapaqabaaaaa@3A10@ σ 45 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaaicdacaaIWaaapaqabaaaaa@3A10@ σ 90 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaaicdacaaIWaaapaqabaaaaa@3A10@ σ b MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaadkgaa8aabeaaaaa@3983@ Ifit  
r 00 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaaIWaGaaGimaaWdaeqaaaaa@3944@ r 45 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaaIWaGaaGimaaWdaeqaaaaa@3944@ r 90 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaaIWaGaaGimaaWdaeqaaaaa@3944@ r b MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaWGIbaapaqabaaaaa@38B7@  
空白
材料の降伏および硬化について入力
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
  a α sv MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aaS baaSqaaiaadohacaWG2baabeaaaaa@39B5@ n Fcut Fsmooth Nrate
A ε 0 Q B K0
Nrate > 0の場合にのみ読み出し(行毎に各関数):
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
fct_IDi   Fscalei ε ˙ i    

定義

フィールド 内容 SI 単位の例
mat_ID 材料識別子

(整数、最大10桁)

 
unit_ID 単位識別子

(整数、最大10桁)

 
mat_title 材料のタイトル

(文字、最大100文字)

 
ρ i 初期密度

(実数)

[ kg m 3 ]
E ヤング率

(実数)

[ Pa ]
ν ポアソン比

(実数)

 
Iflag 降伏応力定義フラグ
= 0(デフォルト)
Nrateで定義される関数番号と表形式入力。
= 1
Swift-Voce解析定式化で、Nrate = 0.

(整数)

 
VP ひずみ速度選択フラグ 4
= 0(デフォルト)
降伏応力に対するひずみ速度効果は全ひずみ速度に依存します。
= 1
降伏応力に対するひずみ速度効果は塑性ひずみ速度に依存します。
この場合、ひずみ速度のフィルタリングはないので、FsmoothFcutは使用されません。

(整数)

 
Ifit 材料パラメータフィッティングのフラグ
= 0(デフォルト)
α 1 から α 8 までにBarlatパラメータを入力します。
=1
Barlatパラメータは、 σ 00 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaaicdacaaIWaaapaqabaaaaa@3A10@ σ 45 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaaicdacaaIWaaapaqabaaaaa@3A10@ σ 90 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaaicdacaaIWaaapaqabaaaaa@3A10@ σ b MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaadkgaa8aabeaaaaa@3983@ r 00 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaaIWaGaaGimaaWdaeqaaaaa@3944@ r 45 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaaIWaGaaGimaaWdaeqaaaaa@3944@ r 90 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaaIWaGaaGimaaWdaeqaaaaa@3944@ r b MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaWGIbaapaqabaaaaa@38B7@ として入力される試験データから計算されます。
 
α i i=1~8のBarlat材料パラメータ。 1

(実数)

 
σ 00 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaaicdacaaIWaaapaqabaaaaa@3A10@ 00方向(回転方向)の降伏強度 [ Pa ]
σ 45 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaaicdacaaIWaaapaqabaaaaa@3A10@ 45方向の降伏強度 [ Pa ]
σ 90 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaaicdacaaIWaaapaqabaaaaa@3A10@ 90方向の降伏強度 [ Pa ]
σ b MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaadkgaa8aabeaaaaa@3983@ 2軸載荷の降伏強度 [ Pa ]
r 00 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaaIWaGaaGimaaWdaeqaaaaa@3944@ 00方向(回転方向)のLankford r-値  
r 45 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaaIWaGaaGimaaWdaeqaaaaa@3944@ 45方向のLankford r-値  
r 90 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaaIWaGaaGimaaWdaeqaaaaa@3944@ 90方向のLankford r-値  
r b MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaWGIbaapaqabaaaaa@38B7@ 2軸載荷のLankford r-値  
a 降伏関数の指数部。 1

デフォルト = 2(整数)

 
α s v MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aaS baaSqaaiaadohacaWG2baabeaaaaa@39B5@ Swift Voce重み係数 2
= 1
Swift硬化則
= 0
Voce硬化則

デフォルト = 0.0(実数)

 
Q Voce硬化係数

(実数)

[ Pa ]
K0 Voce硬化パラメータ

(実数)

[ Pa ]
B Voce塑性ひずみ係数

デフォルト = 0.0(実数)

 
A Swift硬化係数

(実数)

[ Pa ]
n Swift硬化指数

デフォルト = 1.0(実数)

 
ε 0 Swift硬化パラメータ

デフォルト = 0.00(実数)

 
Fsmooth ひずみ速度スムージングオプションフラグ 3
= 0(デフォルト)
ひずみ速度を平滑化しません。
= 1
ひずみ速度スムージングはアクティブ。

(整数)

 
Fcut ひずみ速度フィルタリングのカットオフ周波数、 Appendix: フィルタリング

デフォルト = 1030(実数)

[Hz]
c Cowper Seymonds参照ひずみ速度

(実数)

[ 1 s ]
p Cowper Seymondsひずみ速度指数 4

(実数)

 
Nrate 降伏関数の数 2

Nrate > 0Iflag = 0の場合にのみ使用されます。

(整数)

 
fct_IDi 降伏応力対塑性ひずみの識別子

(整数)

 
Fscalei fct_IDiの縦軸のスケールファクター

デフォルト = 1.0(実数)

[ Pa ]
ε ˙ i fct_IDiに対応すするひずみ速度i

VP =0の場合、fct_IDiの全ひずみ速度

VP =1の場合、fct_IDiの塑性ひずみ速度

デフォルト = 1.0(実数) 5

[ 1 s ]

例 1 (Barlatパラメータ入力Ifit=0)

この例では、Barlatパラメータ入力(Ifit=0)および表形式降伏応力-ひずみ曲線入力(Iflag=0)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                  kg                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW87/1/1
Steel 
#              RHO_I
              7.8E-6                   0
#                  E                  Nu     IFlag        VP             coeff_c               exp_p              
                 210                 0.3         0         1             4.15401                3.57             
#                 A1                  A2                  A3                  A4 IFlag_fit
                 1.0                 1.0                 1.0                 1.0         0
#                 A5                  A6                  A7                  A8
                 1.0                 1.0                 1.0                 1.0
#Blank line

#              exp_a               ALPHA                NEXP                Fcut   Fsmooth     NRATE
                   2                   0                   0                             1         1
#             ASWIFT                EPSO               QVOCE                BETA                  KO
                   0                   0                   0                   0                   0
#  func_id                        YSCALE         strain rate
         4                           1.5                   1
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/4
Mat_Curev Quasi-static
#                  X                   Y
                   0                  .3
               0.007                  .5
                0.05                  .7
                 0.1                 .75
                 0.3                  .9
                   1                 1.2				 
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

例 2 (実験データ入力Ifit=1)

ここで、Ifit=1は、降伏強度の材料実験データおよび00、45、90方向のLankford r-値および2軸載荷を入力するために使用されます。関連するBarlatパラメータは自動的にフィッティングされ、使用されます。Iflag=1で使用されるSwift-Voceパラメータ。
#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                   g                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW87/1/1
ALU
#              RHO_I
              2.7E-3                   0
#                  E                  Nu     IFlag        VP             coeff_c               exp_p 
               70000                 0.3         1
#              sig00               sig45               sig90                sigb     I_fit
          133.179899          133.102756          132.330693          162.330301         1
#                r00                 r45                 r90                  rb
         0.703242569         0.486264221         0.865336191         0.546807587
#empty line 

#              exp_a               ALPHA                NEXP                Fcut   Fsmooth     NRATE
                   8                0.55                0.21                             1         0
#             ASWIFT                EPSO               QVOCE                BETA                  KO
                415.             0.00220               174.7               11.19               132.4
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

コメント

  1. 降伏関数は、次のように表されます:(1)
    f = σ ¯ σ y
    (2)
    σ ¯ =   1 2 1 a ( φ ( X ) + φ ( X ) )   1 a
    (3)
    φ ( X ) = | X 1 X 2 | a  
    (4)
      φ ( X ) = | 2 X 2 + X 1 | a + | 2 X 1 + X 2 | a
    X ' X " はそれぞれテンソル X ' X " の主値です。これらのテンソルは、偏差応力の線形変換です。これにより、次の式が導かれます:(5)
    φ ( X ) =   [ ( X x x X y y ) 2 + 4 ( X x y ) 2 ] a 2  
    (6)
      φ ( X ) = [ 3 2 ( X x x X y y ) + 1 2 ( X x x X y y ) 2 + 4 ( X x y ) 2 ] a + [ 3 2 ( X x x X y y ) 1 2 ( X x x X y y ) 2 + 4 ( X x y ) 2 ] a MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOabaeqabaaeaaaaaa aaa8qacaGGGcGafqOXdOMbayaadaqadaWdaeaapeGabmiwayaagaaa caGLOaGaayzkaaGaeyypa0ZaamWaa8aabaWdbmaalaaapaqaa8qaca aIZaaapaqaa8qacaaIYaaaamaabmaapaqaa8qaceWGybGbayaapaWa aSbaaSqaa8qacaWG4bGaamiEaaWdaeqaaOWdbiabgkHiTiqadIfaga Gba8aadaWgaaWcbaWdbiaadMhacaWG5baapaqabaaak8qacaGLOaGa ayzkaaGaey4kaSYaaSaaa8aabaWdbiaaigdaa8aabaWdbiaaikdaaa WaaOaaa8aabaWdbmaabmaapaqaa8qaceWGybGbayaapaWaaSbaaSqa a8qacaWG4bGaamiEaaWdaeqaaOWdbiabgkHiTiqadIfagaGba8aada WgaaWcbaWdbiaadMhacaWG5baapaqabaaak8qacaGLOaGaayzkaaWd amaaCaaaleqabaWdbiaaikdaaaGccqGHRaWkcaaI0aWaaeWaa8aaba WdbiqadIfagaGba8aadaWgaaWcbaGaamiEaiaadMhaaeqaaaGcpeGa ayjkaiaawMcaamaaCaaaleqabaGaaGOmaaaaaeqaaaGccaGLBbGaay zxaaWdamaaCaaaleqabaWdbiaadggaaaGccqGHRaWkaeaadaWadaWd aeaapeWaaSaaa8aabaWdbiaaiodaa8aabaWdbiaaikdaaaWaaeWaa8 aabaWdbiqadIfagaGba8aadaWgaaWcbaWdbiaadIhacaWG4baapaqa baGcpeGaeyOeI0IabmiwayaagaWdamaaBaaaleaapeGaamyEaiaadM haa8aabeaaaOWdbiaawIcacaGLPaaacqGHsisldaWcaaWdaeaapeGa aGymaaWdaeaapeGaaGOmaaaadaGcaaWdaeaapeWaaeWaa8aabaWdbi qadIfagaGba8aadaWgaaWcbaWdbiaadIhacaWG4baapaqabaGcpeGa eyOeI0IabmiwayaagaWdamaaBaaaleaapeGaamyEaiaadMhaa8aabe aaaOWdbiaawIcacaGLPaaapaWaaWbaaSqabeaapeGaaGOmaaaakiab gUcaRiaaisdadaqadaWdaeaapeGabmiwayaagaWaaSbaaSqaaiaadI hacaWG5baabeaaaOGaayjkaiaawMcaamaaCaaaleqabaGaaGOmaaaa aeqaaaGccaGLBbGaayzxaaWdamaaCaaaleqabaWdbiaadggaaaaaaa a@835B@

    テンソル X ' X " は、応力テンソルの線形変換です:

    X = L σ     a n d     X = L σ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabCiwa8aagaqba8qacqGH9aqpceWHmbWdayaafaWdbiaaho8acaGG GcGaaiiOaiaadggacaWGUbGaamizaiaacckacaGGGcGabCiwa8aaga Gba8qacqGH9aqpceWHmbGbayaacaWHdpaaaa@4603@ (7)
    L = 1 3 [ 2 α 1 α 1 0 α 2 2 α 2 0 0 0 3 α 7 ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabCita8aagaqba8qacqGH9aqpdaWcaaWdaeaapeGaaGymaaWdaeaa peGaaG4maaaadaWadaWdaeaafaqabeWadaaabaWdbiaaikdacqaHXo qypaWaaSbaaSqaa8qacaaIXaaapaqabaaakeaapeGaeyOeI0IaeqyS de2damaaBaaaleaapeGaaGymaaWdaeqaaaGcbaWdbiaaicdaa8aaba WdbiabgkHiTiabeg7aH9aadaWgaaWcbaWdbiaaikdaa8aabeaaaOqa a8qacaaIYaGaeqySde2damaaBaaaleaapeGaaGOmaaWdaeqaaaGcba Wdbiaaicdaa8aabaWdbiaaicdaa8aabaWdbiaaicdaa8aabaWdbiaa iodacqaHXoqypaWaaSbaaSqaa8qacaaI3aaapaqabaaaaaGcpeGaay 5waiaaw2faaaaa@5181@
    (8)
    L = 1 9 [ 2 α 3 + 2 α 4 + 8 α 5 2 α 6 α 3 4 α 4 4 α 5 + 4 α 6 0 4 α 3 4 α 4 4 α 5 + α 6 2 α 3 + 8 α 4 + 2 α 5 2 α 6 0 0 0 9 α 8 ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabCita8aagaGba8qacqGH9aqpdaWcaaWdaeaapeGaaGymaaWdaeaa peGaaGyoaaaadaWadaWdaeaafaqabeWadaaabaWdbiabgkHiTiaaik dacqaHXoqypaWaaSbaaSqaa8qacaaIZaaapaqabaGcpeGaey4kaSIa aGOmaiabeg7aH9aadaWgaaWcbaWdbiaaisdaa8aabeaak8qacqGHRa WkcaaI4aGaeqySde2damaaBaaaleaapeGaaGynaaWdaeqaaOWdbiab gkHiTiaaikdacqaHXoqypaWaaSbaaSqaa8qacaaI2aaapaqabaaake aapeGaeqySde2damaaBaaaleaapeGaaG4maaWdaeqaaOWdbiabgkHi TiaaisdacqaHXoqypaWaaSbaaSqaa8qacaaI0aaapaqabaGcpeGaey OeI0IaaGinaiabeg7aH9aadaWgaaWcbaWdbiaaiwdaa8aabeaak8qa cqGHRaWkcaaI0aGaeqySde2damaaBaaaleaapeGaaGOnaaWdaeqaaa GcbaWdbiaaicdaa8aabaWdbiaaisdacqaHXoqypaWaaSbaaSqaa8qa caaIZaaapaqabaGcpeGaeyOeI0IaaGinaiabeg7aH9aadaWgaaWcba Wdbiaaisdaa8aabeaak8qacqGHsislcaaI0aGaeqySde2damaaBaaa leaapeGaaGynaaWdaeqaaOWdbiabgUcaRiabeg7aH9aadaWgaaWcba WdbiaaiAdaa8aabeaaaOqaa8qacqGHsislcaaIYaGaeqySde2damaa BaaaleaapeGaaG4maaWdaeqaaOWdbiabgUcaRiaaiIdacqaHXoqypa WaaSbaaSqaa8qacaaI0aaapaqabaGcpeGaey4kaSIaaGOmaiabeg7a H9aadaWgaaWcbaWdbiaaiwdaa8aabeaak8qacqGHsislcaaIYaGaeq ySde2damaaBaaaleaapeGaaGOnaaWdaeqaaaGcbaWdbiaaicdaa8aa baWdbiaaicdaa8aabaWdbiaaicdaa8aabaWdbiaaiMdacqaHXoqypa WaaSbaaSqaa8qacaaI4aaapaqabaaaaaGcpeGaay5waiaaw2faaaaa @872F@
  2. 降伏応力は、表形式入力または解析的なSwift-Voceモデルを使用して定義できます。
    • 表形式の場合は、関数の数Nrateを定義することでひずみ速度依存の合計を追加できます。
    • 解析的なSwift-Voceモデルは次のように表されます:(9)
      σ y = α sv [ A ( ε ¯ p + ε 0 ) n ]+( 1 α sv )[ K 0 +Q( 1exp( B ε ¯ p ) ) ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadMhaaeqaaOGaeyypa0JaeqySde2aaSbaaSqaaiaadoha caWG2baabeaakmaadmaabaGaamyqamaabmaabaGafqyTduMbaebada WgaaWcbaGaamiCaaqabaGccqGHRaWkcqaH1oqzdaWgaaWcbaGaaGim aaqabaaakiaawIcacaGLPaaadaahaaWcbeqaaiaad6gaaaaakiaawU facaGLDbaacqGHRaWkdaqadaqaaiaaigdacqGHsislcqaHXoqydaWg aaWcbaGaam4CaiaadAhaaeqaaaGccaGLOaGaayzkaaWaamWaaeaaca WGlbWaaSbaaSqaaiaaicdaaeqaaOGaey4kaSIaamyuamaabmaabaGa aGymaiabgkHiTiGacwgacaGG4bGaaiiCamaabmaabaGaeyOeI0Iaam Oqaiqbew7aLzaaraWaaSbaaSqaaiaadchaaeqaaaGccaGLOaGaayzk aaaacaGLOaGaayzkaaaacaGLBbGaayzxaaaaaa@6301@

      ここで ε ¯ p は相当塑性ひずみです。

  3. 表形式入力を選択した場合は、ひずみ速度をスムーズにするひずみ速度フィルタリングを使用できます。

    アニメーション出力(/ANIM/SHELL/USRII/JJ)のリスト:

    USR 1= 塑性ひずみ

    USR 2= 有効応力

    USR 3= 塑性ひずみの増分

  4. Iflag= 1の(解析的Swift-Voce定式化が使用されている)場合、ひずみ速度効果は下記のCowper Symonds式を用いて考慮されます:(10)
    σ y = σ y ( 1 + ( ε ˙ c ) 1 p )

    VP= 0の場合: ε ˙ は全ひずみ速度

    VP = 1の場合: ε ˙ は塑性ひずみ速度

  5. Iflag= 0(表形式定式化)の場合:

    VP= 0の場合: ε ˙ i は全ひずみ速度

    VP = 1の場合: ε ˙ i は塑性ひずみ速度

  6. Ifit =1の場合、係数 α i Radioss Starterに自動的にフィッティングされます。引張降伏強度 σ 00 , σ 45 , σ 90 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaaicdacaaIWaaapaqabaGccaGG SaWdbiabeo8aZ9aadaWgaaWcbaWdbiaaisdacaaI1aaapaqabaGcca GGSaWdbiabeo8aZ9aadaWgaaWcbaWdbiaaiMdacaaIWaaapaqabaaa aa@42D8@ およびLankford比率 r 00 , r 45 , r 90 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaaIWaGaaGimaaWdaeqaaOGaaiil a8qacaWGYbWdamaaBaaaleaapeGaaGinaiaaiwdaa8aabeaakiaacY capeGaamOCa8aadaWgaaWcbaWdbiaaiMdacaaIWaaapaqabaaaaa@4074@ は、0.2%に等しい塑性ひずみに対応する塑性仕事の量における回転、対角および横方向に沿った単軸引張試験から決定される必要があります。 σ b MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaadkgaa8aabeaaaaa@3983@ r b MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaWGIbaapaqabaaaaa@38B7@ は、同じ量の塑性ひずみについて、2軸試験から決定されなくてはなりません。
1 Barlat F., Brem J.C., Yoon J.W, Chung K., Dick R.E., Lege D.J., Pourboghrat F., Choi, E. Chu S.-II, (2003), Plane stress yield function for aluminum alloy sheets part 1: Theory, International Journal of Plasticity, Volume 19, Issue 8, August, Pages 1215-1244.