増分弾塑性構成則に用いる応力速度の選択  [in Japanese] CHOICE OF STRESS RATES IN INCREMENTAL ELASTOPLASTIC CONSTITUTIVE MODELS  [in Japanese]

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Abstract

亜弾性表現にはCauchy応力のJaumann速度が標準的に用いられるが,ここでは一般的な材料の亜弾性モデルとして,スピンのみならず変形速度も含めた客観的な応力速度を用いることを検討する.各応力速度の持つ特性は,解析的に結果が比較できる弾性問題と変形の局所化解析を通して比較検討した.その結果,1軸応力状態における局所化発生が荷重変位曲線のピークよりもかなりあとになる結論は少ししか改善されなかったが,実験で観察されるような引張圧縮で異なるせん断帯方向を予測できた.また平面ひずみ状態では,Cauchy応力のJaumann速度を用いた局所化予測よりも実験結果に近い局所化発生応力が,Truesdell応力速度を用いることによって得られることを明らかにした.

The Jaumann stress rate of the Cauchy stress is usually used to represent hypoelasticity. Since this stress rate takes into account only the effect of finite rotation; i.e. spin during motion, we here examined the effects of deformation rate terms which can be included in the definitions of the stress rates. First we have shown that the Truesdell stress rate can be defined as a rate of the 2nd Piola-Kirchhoff stress with the current state as reference; i.e. an updated Lagrangian measure. In order to compare the characteristics of the stress rates, localization of deformation was predicted by using the Truesdell stress rate and the convected stress rate, and the results were compared with those by the Jaumann stress rate of the Cauchy stress. All rates predicted the localization at the softening state which is far after the peak of the load-deformation diagram in 3D axisymmetric stress state. However, in plane strain state, the predicted stresses of incipience of the localization by the Truesdell stress rate become close to the experimental critical stresses, Also, the orientations of the localized deformation obtained by the Truesdell stress rate showed consistency with those by the infinitesimal deformation theory, when the stress levels of the localization were in practical order.

Journal

  • Journal of Japan Society of Civil Engineers, Ser. A2 (Applied Mechanics (AM))

    Journal of Japan Society of Civil Engineers, Ser. A2 (Applied Mechanics (AM)) 70(2), I_365-I_374, 2014

    Japan Society of Civil Engineers

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