も構（かま）わず is an expression that combines も, the う-Verb 構（かま）う ‘to mind’, or ‘to care’, and the literary auxiliary verb ず, which connects to verbs in the same way, and has the same meaning as ない. Common translations for this pattern include ‘without worrying about (A), (B)’, and ‘without minding (A), (B)’. This structure is seen with verbs, い-Adjectives, and な-Adjectives followed by の, but may also follow nouns without the addition of の. Occasionally, にも may be used instead of も for further emphasis.

• 娘（むすめ）はレポートの提出（ていしゅつ）日（び）が迫（せま）っているのも構（かま）わず、友達（ともだち）と遊（あを）んでばかりいる。
  Without worrying about the due date of her paper, all she is doing is hanging out with friends.
• 彼（かれ）は遠（とお）いにも構（かま）わず、広島（ひろしま）まで休憩（きゅうけい）なしで運転（うんてん）し続（つづ）けた。
  Without worrying about the long distance, he kept driving to Hiroshima without taking a break.
• 彼女（かのじょ）は危険（きけん）なのも構（かま）わず、池（いけ）で溺（おぼ）れていた猫（ねこ）を救出（きゅうしゅつ）した。
  Without worrying about the danger, she rescued a cat that was drowning in the lake.
• 鈴木（すずき）先輩（せんぱい）は時間（じかん）も構（かま）わず、電話（でんわ）を掛（か）けてくるから困（こま）っている。
  I am annoyed because Suzuki-senpai calls me without worrying about the time.

も構（かま）わず is used most frequently to express that (A) is something that is either being ignored or that the speaker is not worried about. The (B) part of the statement will regularly highlight something that is being without any consideration for (A). This comes from the standard ‘to brace’, or ‘to give pause’ meaning of 構（かま）う.

• 医者（いしゃ）にストップをかけられていたにも構（かま）わず試合（しあい）に出（だし）て、大怪我（おおけが）をしてしまいました。
  I participated in the tournament without giving a pause about the doctor’s order to stop, and got seriously injured.