本研究提出一全新之連體損傷力學 (continuum damage mechanics) 理論，描述材料之線性彈性勁度劣化 (degradation of linearly elastic stiffness)。此理論的推導起源於一思想實驗所得之兩個臆測：1) 位於損傷發生的應力點之損傷面 (damage surface) 曲率與該損傷之多軸效應 (multiaxial effect) 有關聯性，2) 損傷面上兩鄰近應力點 (stress point) 所各自發生之損傷非彈性應變增量 (damage inelastic strain increment) 方向之差異亦與多軸效應有關。理論的推導中提出兩個假說。假說一由塑性力學中援引正交法則 (normality rule) 至連體損傷力學。此假說直觀地顯示損傷面曲率與在損傷面上損傷非彈性應變增量的方向變化之關聯性，亦證明損傷必造成能量消散。假說二闡述兩鄰近損傷增量之表達式的相似關係。此假說考慮各自發生於損傷面上無限微小鄰域 (infinitesimal neighborhood) 內兩應力點的損傷增量，如：σ 與 σ^*；其一以 σ^* 量測發生於 σ 之損傷非彈性應變增量，另一則直接以 σ^* 量測發生於 σ^* 之損傷非彈性應變增量。最終，由兩假說可推導出一簡明扼要之等式可用於計算勁度劣化增量 (incremental stiffness reduction)。該等式能重現上述損傷面曲率與多軸效應之間的關聯性。

This thesis presents a new continuum damage mechanics theory of degradation of linearly elastic stiffness. The theoretical development originates from two conjectures suggested by a thought experiment: 1) The curvature of the damage surface at a damage stress point is associated with the multiaxial effect of damage at the stress point. 2) The change in the direction of the damage inelastic strain increment from a damage stress point to a neighboring point is also associated with the multiaxial effect. Two postulates are proposed in the theoretical development. The first postulate is an extension of the normality rule of incremental plasticity theory to continuum damage mechanics. This postulate straightforwardly leads to the association of the curvature of the damage surface with the change in the direction of the damage inelastic strain increment. The first postulate also implies that the damage energy dissipation increment is always positive. The second postulate addresses similarity of damage inelastic strain increments attributed to two damage events that conceptually occur at respective damage stress points, e.g., σ and σ^*, which are within an infinitesimal neighborhood. The damage inelastic strain increment attributed to the incremental damage at σ is measured by applying σ^*. The other damage inelastic strain increment is directly presented by σ^* as soon as the damage event occurs at σ^*. A concise equation for computing incremental stiffness reduction can be derived from the two postulates. The equation can reproduce the association of the curvature of the damage surface with the multiaxial effect.

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